Mech 4 Sem Course Info Feb June 07

PESITDESIGN OF MACHINE ELEMENTS - I Subject Code: AU46 Faculty: RSS No. of Hours: 52 B.E Mechanical 4th Semester Course Information Class # Chapter Title / Reference Literature Chapter : 1 Introduction T1: page 13 – 35 T2: page 44 – 74 R1: page 3 – 29 R2: page 13-15, 70 – 72 Chapter : 2 Design for static strength T1: page 182 – 212 T2: page 103 – 107 R1: page 13 – 53 R2: page 67 – 92 Topics to be covered Materials and their properties, Design considerations, codes, standards, stress- strain diagram, Definitions – stress, strain, shear stress, biaxial and triaxial loads, Stress tensor, Principal stress Static loads – Types of loads and problems, Theories of failure and problems. Members under combined loads, Stress concentration – explanation and examples, Reduction of stress concentration, Determination of stress concentration factor, combined stress concentration factor, Problems Introduction, S-N diagram, low cycle fatigue, high cycle fatigue, Endurance limit. Modifying factors – size effect, surface effect, stress concentration effects; Fluctuating stresses, Fatigue strength under fluctuating stresses, Goodman and Soderberg relationship; stresses due to combined loading, cumulative fatigue damaged. Derivation of instantaneous stress due to axial, bending and torsion loading, effect of inertia. % of Portions covered Reference Cumulativ chapter e 1-6 10% 10 % 7 – 14 15% 25% 15– 20 Chapter : 3 Design for fatigue strength T1: page 227 – 275 T2: page 114 – 125 R2: page 117 – 156 10% 35% 21 – 25 26 – 31 Chapter : 4 Impact Loading T1: page T2: page T3: page R1: page R2: page Chapter : 5 Design of Shafts T1: page 565 – 576 T2: page 465 – 473 R1: page 465 – 481 R2: page 234 – 246 Chapter : 6 Fasteners T1: page 301 – 317 T2: page 493 – 498 R1: page 269 – 340 R2: page 247 – 255 5% 40% 32 – 40 Torsion of shafts, design for strength and rigidity, with steady loading, ASME and BIS codes for design of transmission shafting, shafts under fluctuating and combined loads design of rigid flange coupling and bushed pin type flexible coupling. Key types, Stresses in Keys, Pins and Retainers. Threaded Fasteners – Stresses, Effects of initial tension, effect of compression, effect of fatigue loading, impact loading, shear loading and eccentric loading. 20% 60% 15% 75% 41 – 48 49 – 52 Chapter : 7 Power Screws T1: page 291 – 300 T2: page 266 – 273 R1: page 441 – 450 R2: page 163 – 185 Chapter : 8 Mechanical joints: T1: page 336 – 352 T2: page 171 – 227 R1: page 213 – 256 R2: page 213 – 229 Mechanics of power screw, stresses in power screws, Efficiency and self locking. 15% 90% Cotter and knuckle joints, Riveted Joints – Types, rivet materials, Failures of Riveted joints, Efficiency, Boiler Joints, Tank and Structural Joints, riveted brackets. Welded joints – Types, strength of butt and fillet welds, Eccentrically loaded welds. 10% 100% Text Books: T1: Mechanical Engg. Design by Joseph. E Shigley & Charles R MirchKe. Tata 6th Ed 2003. Mc Graw Hill Edition 2001 T2: Design of Machine Elements by C.S.Sharma and Kamlesh Purohit, PHI 2003. Reference Books: R1: Machine Design by Maleev & Hartman, CBS Publishers & Distribution, New Delhi R2: Design of Machine Elements – V.B.Bhandari,. Tata McGraw Hill Pub. New Delhi R3: Theory and Problems of Machine Design by Hall Holowenko, (Schaum series) R4: Machine Design by Robert L Norton, Pearson Education Asia, 2001 R5: Design of Machine Elements by M.F.Spotts, PHI 2003. R6: Machine Design by Paul H- Black, D.E.Adams McGraw Hill, 2001 Design Data Hand Books: Design Data Hand Book – K.Lingaiah, McGraw Hill, 2nd Ed, 2003 1. Design Data Hand Book – K.Mahadevan & Balaveera Reddy, CBS Publication 2. Machine Design Data Hand Book by H.G.Patil, Shri Shashi Prakashan, Belgaum If the shaft is subjected to an axial load of 10KN. * List the factors which govern the selection of a material for a machine component (3) 5. A round steel bar having σy = 800 MPa is subjected to the loads producing the calculated stresses of P/A = 70MPa. A wall bracket as shown in figure 5 is subjected to a pull of 5KN at 60o to the vertical. (5) 2. (8) 3.1. Discuss the factors influencing selection of an appropriate material for a machine element. find its dimensions. (i) Determine the safety factor with respect to initial yielding according to maximum shear stress theory and maximum distortion energy theory (ii) Draw the sketch showing the location of maximum normal stress and maximum shear stress planes. Write full note on stress concentration factor. A C–Clamp carries a load P=20000N. (05) 10. A load of 10KN is applied at the center of the crank pin. The cross-section (Figure 6) of the clamp at x-x is rectangular having width equal to twice thickness. My/J = 300 MPa and 4V/3A = 170MPa. Determine the dimensions ‘b’ and ‘t’. find the maximum stress induced. A flat bar shown in figure 3 is subjected to an axial load of F equal to 50KN. (8) . A for the crank shown in figure. (7) 4. TR/Jp = 200 MPa. (8) 5. (3) Chapter – 1 Introduction Chapter – 2 Design for Static Strength 1. Also determine the stress at section zz. The cross section of the bracket is rectangular having b = 3t.QUESTION BANK 1. Determine the maximum normal stress and maximum shear stress at section A. A stepped shaft has maximum diameter 45 mm and minimum diameter 30 mm. (6) 11. State the standards used in machine design. Discuss the factors influencing selection of appropriate value for the factor of safety (8) 4. Assuming that the clamp is made of steel casting with an allowable stress of 120 MPa. Determine the cross section of the cantilever beam of square cross – section if the allowable stress in the material of the beam is limited to 80MPa. (12) 7. (11) 9. if the tensile stress in the material of the bracket is limited 30 MPa. The fillet radius is 6 mm. Assuming that the stress in the bar is limited to 200N/mm2. (12) 6. (5) 3. A weight of 1 KN is dropped from a height of 50 mm at the free end of a cantilever beam of effective length 300 mm. maximum shear stress and von Mises theory of failures. Neglect the effect of transverse shear. Determine the thickness of flat bar. *Define Standardization. (09) 8. taking stress concentration into account. Explain the term ‘factor of safety’. Explain the maximum normal stress. Determine the critical stress in the machine component shown in the figure 2. Explain the influence of stress concentration in the design of machine elements. (10) 2. Selecting a suitable material and assuming an appropriate value for the factor of safety. determine the diameter of the rod as per the following theories of failure: (i) Maximum shear stress theory for failure. It is necessary to replace this member by one having a 15 mm hole as shown. For the following stresses calculate the factor of safety using the following theories of failure: (i) Maximum normal stress theory. Determine the thickness t and radius r at the fillet of the second member. (ii) Compute the maximum torsional stress and the maximum principal stress in the crank at a section 80mm from the pin-end. (i) Maximum shear stress theory (ii) Octa hedral shearing stress theory (12) 19.0 mm is to sustain an axial compressive load of 20 kN and a twisting moment of 150 Nm. The rod is made of carbon steel C40. Determine normal stresses at the extreme fibers on the cross section AA of a Cclamp loaded as shown in figure 12. A round rod of diameter 30.8 and D/d is 1. (10) 15. Take a value of 2. σ2 = -70MPa (c) σ1 = 70MPa.2 as shown in figure 8. Stress on the fillet if the stress concentration factor for the filleted flat bar in tension is 1. Determine the factor of safety if it is made of steel having yield strength of 320N/mm2. supports an axial load P. (8) 20. *A machine part is statically loaded and has yield strength of 350 MPa. so that the maximum stress will not exceed that of the first member.12. A rod of circular cross section is to sustain a torsional moment of 300 KNm and a bending moment of 200 KNm. (iii) Locate the stress element on the top surface of the shaft at A and find the principal stresses and the maximum shear stress at the same point. (iii) Total energy theory for failure. Find the value of the max. Label the directions of the co ordinates axis on these diagrams. σ2 = 0MPa (b) σ1 = 70MPa. (12) 21. A tension member shown in figure 7.50 for the factor of safety. Determine factors of safety as per following theories of failure . bending moments and turning moments that act on the crank and on the shaft. Determine the diameters of a round rod to sustain a combined torsional load of 1500 Nm and a bending moment of 100 Nm by the following theories of failure. (ii) Von Mises or distortion energy theory for failure. Explain the following theories of failure (i) Maximum principle stress theory for failure (ii) Maximum shear stress theory for failure (iii) Octahedral shear stress theory for failure (9) 22. Explain six theories of failure. (10) 14. (15) 17. (15) 16. Obtain the magnitude of normal and shear stresses at the extreme fibers on the cross section AA of a clamp loaded as shown in figure 11 (12) 18. Material selected for the rod has a value of 300 MPa and 180 MPa for the normal stress and shear stress at yield respectively. (ii) Maximum shear stress theory (iii) Von mires theory (a) σ1 = -70MPa. σ2 = 70MPa 13. Figure 9 shows a crank shaft loaded by a force Fy = 1500N (i) Draw separate free body forces. Calculate the stresses at each of three holes. (8) (i) (ii) (iii) 3Ø 10 Ø 5Ø . * A rectangular plate 15mm thick made of brittle material is shown in fig below.Maximum principal strain theory for failure Maximum Elastic energy theory for failure Distortion energy theory for failure (12) 23. The free end of the beam is subjected to a transverse load that fluctuates between 8 KN down to 5KN up. Determine the diameter of the shaft required selecting suitable material.65 (14) 9. The size factor may be taken as UNITY and the surface has a mirror polish. (14) 3. (12) 6.1d. A steel member of circular cross section is subjected to a torsional stress that varies from 0 to 35 MPa and at the same time it is subjected to an axial stress that varies from 14 MPa to 28 MPa.5KNm together with a bending moment that fluctuates between +1KNm . The material has an endurance limit = 260 MPa and a yield strength = 480 MPa.80 and the notch sensitivity is 0. Determine maximum stress induced in the following cases taking stress concentration in case (i) A rectangular plate under an axial load of 10KN. The material selected for the shaft has a shear stress value of 100 MPa at endurance limit and a shear stress value of 120 MPa of the yield limit. Take factor of safety 2. determine the width of rectangular cross section.90. A stepped shaft with its diameter reduced from ‘1.85 and 1. size factor = 0. Selecting carbon steel C 30 as material for the beam and selecting a value of 2. The maximum bending moment occurs at the same instant as that of maximum torque.Chapter – 3 Design for fatigue strength 1. (14) 2.2d is reduced to a diameter d with a fillet radius of 0.50 for the factor of safety.8. Surface factor and size factor are respectively 0.0 respectively. Determine the diameters of the shaft and the radius of fillet to transmit a power of 60 KW at a rated of 1000 RPM limiting the maximum shear stress induced to 65MPa. (figure 14) (3) (ii) The circular shaft with a step under transverse load of 10KN as shown (figure 15) (3) (iii) The shaft under a twisting moment of 50Nm. 0. Explain the significance of Goodman’s line and soderberg line in design of members subjected to reversal of stresses. Determine diameter of shaft based on the factor of safety of 2.95. A shaft can transmit power of 20 KW at 1000 RPM. The actual torque transmitted by shaft is ± 60% of the mean torque calculated. (figure16) (3) 4.95 and 0.2 d’ to ‘d’ has a fillet radius of 0. A shaft of circular cross section is subjected to a turning moment that fluctuates between 800 KNm and 600 KNm and also a bending moment that fluctuates between + 500 KNm and – 300KNm. size factor and load factor can be taken as 0. and surface factor = 0. Shaft is also subjected to a variable bending moment of 500 N-m to 1000 N-m. Stress concentration factor is given to be 1. This stepped rod is to sustain a twisting moment that fluctuates between +2. 8. (8) 5. A round rod of diameter 1.5KNm and +1. Determine the diameter of the solid circular shaft taking a value of 2.90. The rectangular cross section of the beam has a depth of 200 mm.85. Shear stress concentration factor is 1. A cantilever beam of rectangular cross section has a span of 800 mm. (ii) the design factor of safety based upon yield in shear. Surface factor.1d. (7) 7. The shaft is machined. The shaft is made of steel with ultimate tensile strength of 400 MPa.50 for the factor of safety. Neglecting stress concentration and column effect determine (i) the maximum equivalent shear stress. A stepped shaft shown in figure 13 is subjected to the transverse load. Motor transmits 10 KW at 1440 RPM.and –1. A weight of 1400 N is dropped on to a collar at the lower end of a vertical steel shaft of 3m long and 25 mm. The rod is made of carbon steel C40. Determine a suitable value for d. The pulley A is mounted at 300 mm to the right of left bearing and receives 30KW at 200RPM from a pulley vertically below it. whose depth is 1. At the same time there is an alternative stress due to axial loading that varies from 14 MPa (compression) to 28 MPa (tension).1 x 105 MPa. A cantilever beam of span 800. Assume the same material. determine the width of the rectangular cross section.5 times of the width.0 mm has a rectangular cross section of depth 200. The driver transmits 50KW at 350 RPM. key and bolts are 40 MPa. Allowable stress in shear for shaft. The free end of the beam is subjected to a transverse load of 1KN. Allowable bearing pressure for rubber bush is 0. and surface correction factor = 0. for both the members. Find the maximum stress due to impact in the bolt and in the beam shown in figure 10. diameter. Take E= 70MPa. The material has an ultimate strength of 412 MPa. a) Draw the moment diagram b) Calculate the diameter of the solid shaft required c) Calculate the torsional deflection in degrees (20) 2. size correction factor = 0. Check for stresses. A horizontal piece of commercial shafting is supported by two bearing 1.0m. namely steel. Chapter – 5 Design of Shafts 1.85. Take E = 2. Three identical pulleys of 500 mm diameter and weighing 500 N each are mounted on a line shaft supported on two bearings 4000 mm apart. with the slack side on top. The tension ratio of the belt is 3:1. A 600 mm diameter pulley is keyed to the shaft 600mm to the right of left bearing and drives a pulley with a horizontal belt directly behind it. Derive an expression for shock/impact factor. The pulley B is mounted 1000 mm to the right of left bearing and . A 5 Kg block is dropped from a height of 200 mm on to a beam shown in figure 4. yield strength of 309 MPa.5.3 MPa.0KNm. calculate the height of drop if the maximum instantaneous stress produced is not to exceed 120 MPa.9. Determine the dimensions of the rectangular section. A keyed gear 20o involute and 200 mm in diameter is located 400 mm to the left of right bearing and is driven by a gear directly behind it. dropped onto it from a height of 40. (8) 6. Design a bush type flexible coupling to connect motor and centrifugal pump shafts. The material has an allowable yield stress of 50 MPa.*A cantilever beam of circular cross-section is subjected to an alternating stress at a point on the outer fiber in the plane of the support that varies from 21 MPa (compression) to 28 MPa (tension). Assume that actual stress concentration factor =1. selecting a suitable material and assuming an appropriate value for the factor of safety. (5) 5. (14) 10. Determine i) ii) iii) the equivalent normal stress due to axial loading the equivalent normal stress due to bending and the total equivalent normal stress due to axial loading and bending (12) Chapter – 4 Impact Loading 1.0 mm. (5) 4. (14) 3. Kb= Kt = 1. (12) 3. Explain the influence of stress raiser on impact strength (06) 2.5 m apart. The inside dia. (14) 5.35N/mm2. Compare the weight. The remaining power is taken out through another pulley C which is mounted at 3000 mm to the right of left bearing and drives a planning machine the drive being 30o to the front of the vertical. (06) 6.2KN. what would be the dimensions of a hollow shaft made of the same material as the solid shaft. It is supported in bearings at C and D. 14. (10) 11. The angle of lap for all pulleys may be taken as 180o and the coefficient of friction is 0.5 KW at 720 RPM. determine the inner and outer diameters of the shaft. bolt and key material = 33MPa. A 250mm diameter solid shaft is used to drive the propeller of a marine vessel. bolt and key material = 50 MPa. A shaft is required to transmit 1 MW power at 240RPM.7 and material of the shaft to be cold rolled steel. The shaft is also subjected to an end thrust 1. Determine the stress induced in shaft and the angular deflection between bearing. The shaft of uniform diameter as shown in figure 17 carries belt pulleys at A and B with vertical belts. Design a cast Iron flange coupling (protected type) to connect two shafts and transmits a torque a 5000 Nm.2 m hollow shaft is subjected to bending moment 900N-m and turning moment 600 N-m. Write a brief note on materials and heat treatments used for the shaft. (10) 12. Shear stress for cast iron = 15MPa. Do not neglect the weight of the shaft. The maximum tensile or compressive stress in not exceed 50 MPa. 7. Assume bearing pressure on the bushes as 0. The working stress in shear for the shaft material is 80N/mm2. The shaft must not twist more that 1o on a length of 15 diameters. adopting a working shear stress of 45 MPa. A shaft is mounted between bearings located 9. (5) 8. Crushing stress for bolt and key material = 60 MPa. 10. of the hollow shaft being half the external diameter. Pulley A weighs 200 N and pulley B 400 N. If the shaft carries a central load of 900N and is simply supported between bearing 3 meter apart. 13. The shaft weighs 66000N has an outside diameter of 450 mm and inside diameter of 300 mm. Permissible shear stress for shaft. A line shaft is to transmit 600 KW at 500RPM. (10) 9. the following permissible stresses may be used permissible shear stress for shaft. State the advantages of hollow shafts over solid shafts in transmission of power (5) . Permissible shear stress for CI = 16MPa. Design a cast iron protective flange coupling to connect two shafts in order to transmit 7. determine the diameter of the shaft. allowable shear stress in the material of the pins as 45 N/mm2 and allowable bending stress in the material of the pin is 80 N/mm2. and that on the slack side of belt B is 900N.3. strength and stiffness of a hollow shaft of the same external diameter as that of solid shaft. the shaft transmits 10 KW at 400 rpm. 15. Estimate suitable diameter for the shaft. The allowable shear stress for the material of the shaft is 42N/mm2 (42MPa). Taking di/do = 0. The tension on the tight side of belt A is 2000 N. find the diameter of the shaft and the shear stress induced.5 m apart the transmits 10000 KW at 90 rev/min.(20) 4.delivers 6KW to a pulley through a belt drive inclined backward at 45o to the vertical. If the modulus of rigidity for the material of the shaft is 80 KN/mm2. The following permissible stresses may be used. Determine the diameter of the shaft. Both the shafts have the same material and length. It is necessary to reduce the weight of the shaft by 70%. A 1. Consider heavy shock condition. Design a bushed pin type flexible coupling to transmit 90 KW at 1440 RPM for connecting two shafts of diameter 60 mm. A power of 50 kW is received at 500 RPM through a gear drive located at the left extreme end of the shaft. A 60 cm pulley A receives 15 KW at 500 RPM from below at angle of 45o as shown in the figure 18. Assuming working stress in shear 40 MN/m2 and in tension at 80 MN/m2 and in tension as 80 MN/m2 for the shaft material.0 mm long receives power of 25 KW through a belt drive located at its right extreme end.0 mm. Whereas A is at a distance of 300mm from the left extreme end of the shaft. take the maximum torque to be 20% more than the full-load torque. The teeth are of involute profile with a pressure angle of 20o. Selecting a suitable material and assuming an appropriate value for the factor of safety. The gear which receives from this gear is located exactly behind. The belt moves towards the observer below the horizontal. A power transmission shaft is supported on two bearings 2000. The pressure angle is 20o. Determine the diameter of the solid circular shaft selecting carbon steel C40 as material & assuming a value of 2. Design the shaft of uniform diameter. (20) 17. the remaining power is given out through a gear drive located at a distance of 400 mm from the right support. The ratio of belt tensions is 3. The shaft operates at 750 RPM. The power is transmitted out of the shaft through a gear drive located on the shaft at a distance of 500. 21. The weight and pitch diameter of the gear mounted on the shaft are respectively 600N and 300. The driven gear is located exactly above. determine the diameter of the solid circular shaft.0 mm apart. Both the gears have 20o involute teeth. The belt on the pulley moves below towards the observer making an angle of 30o with the vertical. Selecting appropriate material and assuming a suitable value for the factor of safety determine the diameter of a solid shaft for the purpose.0mm. The power is taken out through a gear drive located at distance of 400mm form the left support. Design a rigid flanged coupling to transmit a power of 40 kW at a rated speed of 100RPM (10) .0. The weight & diameter of the pulley are respectively 800N and 400. (20) 18. A gear C with 450 mm pitch circle diameter delivers 30% of the power horizontally to the right gear D with pitch circle diameter of 300 mm delivers the remaining power downward to the left at an angle of 30o below the horizontal.0 mm to the left of the right bearing. Design a protected type CI flange coupling for a steel shaft transmitting 15 KW at 1200 RPM.50 for the factor of safety. Design a protected type of CI flange coupling to connect two shafts of the same diameters and transmit 150 KW at 100 RPM. While A is at the left extreme end. The belt is directed towards the observer below the horizontal and inclined at 45o to it. The gear mounted on the shaft has a pitch diameter of 250mm and weighs 500 N. A power of 30KW is given out through a belt drive located at a distance of 600mm from the left support. The pulley mounted on the shaft has a diameter of 400 mm and weighs 1000N. The ratio of tensions in the belt is 2. (14) 20. The shaft receives a power of 40KW through a belt drive situated. Assume 25% over load. The other gear which receives power form this gear is placed just above this gear.16. (20) 19. Draw to scale the coupling designed giving all important dimensions. 22. The driver gear is located exactly behind. The shaft is supported at two points A and B. inclined at 60o to it. A power transmission shaft 1800 mm long is supported at two points A and B. The driver gear has a pitch diameter of 200 mm and weighs 500N. Select suitable materials and factors of safety. B is at a distance of 300mm from the right extreme end.0 mm to the right of the left bearing. A power transmission shaft 1200. B is at the right extreme end. The ratio of the belt tensions is 3. The gear mounted on the shaft here has a pitch diameter of 300mm and weighs 700N. The pulley on the shaft has a diameter of 500mm and weighs 800N. at a distance of 600. (12) 2. 7. If the tensile stress in the bolt is not to exceed 63 MPa. The static pressure in the cylinder is 6N/mm2.75. Determine load capacity of the riveted joint loaded as shown in figure 19. (6) 3. (12) . A 100mm shaft rotating at 100 RPM transmit 300 hp power is taken off through a gear whose hub is 200 mm long. and that for the pinned shaft is 1. Assume only torsional load and the same material for all parts. The stress concentration for the key way in the shaft is 1. The initial tightening load on the bolt is 5 KN. Find the size of the bolt. Select the size of the metric bolts for a factor of safety of 3. (08) 4.Chapter – 6 Fasteners 1. Determine the bolt size.3. (12) 5. For the system shown in figure 22 find the maximum stress in the weld. The key is made of steel having an ultimate shearing stress of 350N/ mm2. Select a rectangular parallel key for transmitting a power of 50 KW at a rated speed of 500 RPM to mount a hub of length 60mm on a solid circular shaft of diameter 50 mm. A flanged bearing is fastened to a frame by means of four bolts spaced equally on 400mm bolt circle as shown in figure 20. (20) 8. Using a factor of safety of 5. determine the width of key required. Determine the power capacity ratio of the two system: one a 24 mm diameter shaft with a 48 x 6 x 6 mm key and another a 24 mm diameter shaft with a 6 mm dia pin. Determine the size of the bolt taking allowable stress for the bolt material to be 80 MPa. A bolt in a steel structure is subjected to a tensile load of 9 KN. Figure 21 shows the cylindrical head of a pressure vessel using 10 bolts and a confined gasket. if the shear stress of the material of the rivet is 100 N/ mm2. (6) 6. The diameter of the flange is 500 mm and a load of 200 KN acts at a distance of 250 mm from the frame. determine : (i) Power required to drive (ii) height of the bronze nut required if allowable bearing pressure is 17MPa. What are power screws? State their applications. Root Dia. for a travel of 200mm (iv) Screw rod (v) Nut (vi) The hand lever 8. (4) 7. along the spindle of a square thread (single start). A weight of 500KW is raised at a speed of 6m/min by two screw rods with square threads of 50 x 8 cut on them. 8mm pitch screw jack at a maximum speed of 600m/min. If the coefficient of friction between the threads is 0. The coefficient of collar friction is 0.1. Determine: . The screw has trapezoidal metric thread. (14) 3. The axial thrust is absorbed by a collar of 100mm outside diameter and 70 mm inside diameter.Chapter – 7 Power screws 1. against a load of 20KN. A machine weighing 20KN is to be raised by a single start square threaded 50mm diameter.2. The following data applies to a C clamp shown in Figure 23. Using an allowable compressive stress of 80N/mm2 and bearing pressure on the threads 17. determine the power required to lift the machine. of screw – 12mm.15. (iii) Bearing pressure on threads. It utilizes a square threaded screw having outside diameter of 75mm and pitch of 6 mm determine the force required to operate the handwheel of 300 mm diameter if the coefficient of friction for threads is 0.5 mm. what is the maximum shear stress induced in the screw of the turn buckle if the rope is to be tightened to a tension of 8 KN. The thrust collar of the screw has inside diameter of 30mm and out side diameter of 60mm. The coefficient of friction between the screws and nuts is 0. A shaft straightner is designed to exert a load of 25 KN.75mm. select an appropriate material and assume a suitable value for the factor of safety.12. (8) 6. A split nut used with a lead screw is propelled at a speed of 5 m/min. Also determine efficiency of straightner.25 Friction circle radius of collar – 6mm Maximum thrust on the screw – 4 KN Determine: (i) Length of handling if the operator exerts a force of 80N at the end of the handle (ii) Maximum shear stress induced in the body of the screw and where does it exist. having nominal diameter of 30 mm and a pitch of 6 mm. – 9. The threads are single right and left hand square in section. Select thread proportions for the screw rod of a screw press to sustain an axial compressive load of 40 KN for an unsupported length of 350. A turn buckle is used to tighten a wire rope. Pitch – 1. A 15KN screw jack with a maximum extension of 150 mm has double square threads.0mm.12 Coefficient of collar friction – 0. Assuming suitable coefficient of friction.853 Coefficient of thread friction – 0. Design the following parts of 20 KN screw jack selecting suitable materials and assuming appropriate values for the factors of safety. The outside diameter of the screw is 38mm and the pitch is 8. (10) 4. 9.5 MPa Find: (ii) Size of screw (iii) Height of nut (10) 5. Outer dia. (10) 10. (10) 2. The two screw rods are driven through bevel gear drives by a motor. τ shear stress = 50MPa crushing stress σc = 120MPa. 8. (08) Chapter – 8 Mechanical Joints 1. τ = 60MPa. (10) 3. Design a sleeve type of cotter joint to connect two tie rods subjected to an axial pull of 60KN. Diameter of the boiler is 1 m. Find the diameters of the rod and the pin.(i) The torque required to raise the load (4) (ii) The speed of rotation of the screw rod assuming the threads are of double start (2) (iii) The maximum stresses induced on the cross section of the screw rod (4) (iv) The efficiency of screw drive (3) (v) The length of nuts for the purpose of supporting the load (vi) check for overhaul (2) 11. The allowable stress of C – 30 material used for rods and cotters are σt = 65 N/mm2. if the allowable working stresses are 112 MPa in tension. Calculate the size of the weld. (10) 7. 84 MPa in shear and 200MPa in crushing. Cast steel material used for the sleeve has the allowable stresses σt = 70 N/mm2 and τ = 45 N/mm2 5.5m in diameter when working pressure is 1 MPa. Use the following data: . The pitch in the outer rows of the rivets is to be double that in the inner rows and the width of the cover plates is unequal. σc = 120 MPa. Two lengths of mild steel flat tie bars 200 mm x 10mm are to be connected by a double riveted double cover butt joint using 24 mm diameter rivets. if the allowable shear is not exceed 80MPa. taking the permissible stress in the weld to be 84 N/mm2. Sketch and explain the types of riveted joint failure. (10) 2. A bracket as shown in figure 26 carries a load of 40000N. The allowable stresses are σt = 70MPa. (20) 6. Calculate the size of weld. A steel bracket is welded to a structure and loaded as shown in figure 25. The longitudinal joint is a triple riveted butt joint with an efficiency of about 85% and the circumferential joint is a double riveted lap joint with an efficiency of about 70%. A knuckle joint is required for a rod which has to withstand a tensile load of 100 KN.875 times that of single shear. Design the longitudinal joint for a boiler for a steam pressure of 2 MPa. The material of which the turn buckle is to be made has a design normal stress of 165 N/mm2 and design shear stress of 100N/mm2. (8) 9. σc = 75 N/mm2 and τ = 35 N/mm2. (12) 4. An eccentrically loaded bracket welded to its support is loaded as shown in figure 24. safe working stress both in tension and shear are 80 MPa and 60 MPa respectively. Assume that the resistance of the rivets in double shear is 1. Design and draw a fully dimensioned neat sketch in two view of a double riveted butt joint with double cover plates for the longitudinal seam of a boiler 1. Select a double riveted butt joint with a required efficiency of 75%. Determine the size of the weld required. 10. σt = 80 MPa. Design the joint. Take the following allowable stresses. Suggest the suitable dimensions for the entire joint. Design the longitudinal and circumferential joints for a boiler whose diameter in 2 meters and is subjected to a pressure of 1 MPa.Design a turnbuckle to take an axial load of 100KN. 1 x 105 MPa and Poisson’s ratio = 0. The material selected for the joint has the following design stresses. A joint efficiency of 75% can be assumed at this stage. is twice the pitch of rivets in the inner rows which are in double shear. (14) 18. σt = 120 MPa. Allowable shear stress for rivets: 45 MN/m2. Normal stress at yield = 300 MPa Shear stress at yield = 150 MPa Allowable bearing pressure = 40 MPa (12) 17. Find the difference in the diameters to be allowed for shrinkage when a compound cylinder 200 mm external diameter. Design a knuckle joint to transmit an axial load of 120 KN. have a pitch which is twice the pitch of rivets in the inner rows.Allowable stress in tension for steel plate = 80MPa Allowable stress in shear for rivets = 60 MPa Allowable stress in crushing for rivets = 120 MPa. Also determine the various strengths & efficiencies of the joint. What is the maximum value of P if the normal stress on the throat section is not to exceed 98 MN/m2? (10) 14. Design a longitudinal butt joint with equal widths of cover plates for a pressure vessel of diameter 1200. (10) 15. The allowable stress for the material of the joint are as follows: σt = 120 MPa and τ = 80 MPa (10) 16. σc = 160 MPa and pb = 60 MPa (10) 19. Design a cotter joint to sustain an axial load of 80 KN. For practical reasons the pitch of rivets is to be restricted a value not less than 3 d and not more than 3. Material selected for the joint has the following mechanical properties. Design a triple riveted butt joint to join two plates of thickness 10 mm. Draw to scale two views of the designed joint giving all dimensions. A triple-rivetted butt-joint with equal cover plates is used to connect two plates 16 mm thick. (12) 11. A bracket supporting a load is welded to a stanchion by four fillet welds of 6mm size as shown in the figure 28. Design a triple riveted butt joint with unequal widths of cover plates to join two plates of thickness 10mm. Take E = 2. The extreme row of rivets. Design the joint if the allowable crushing stress for rivet and plates is 60 MN/m2. Find the joint efficiency.0 mm subjected to an internal pressure of 0. The pitch of rivets in the extreme rows. Material selected for the main plate and rivets has the following safe values: Design normal stress for material of the main plate = 120 MPa Design shear stress of the material of the rivet = 80 MPa Design Crushing stress of the material of the rivet = 160 MPa Sketch the joint and determine the various efficiencies. The design stresses of the materials of the main plate and the rivets are as follows: . (10) 13. 100 mm internal diameter and 150 mm diameter at the junction of the two tubes has a radial pressure of 31 MPa at the junction. which are in single shear. The allowable stresses are as follows: Tensile stress of the material of the plates = 80 MPa Shear stress of the material of the rivets = 60 MPa Crushing stress of the material of the rivets = 120MPa Sketch the joint.5 d where d is the diameter of the rivets.90 MPa.25. Design a socket and spigot type of cotter joint to sustain an axial load of 100kN. (10) 12. which are in single shear. 12. 22. 20. 27. 19. 31. 8. 32. poles Calculation of Residues and problems Residue theorem and examples.3% Chapter 2 Special Functions T1. 14. 30. differentiability and problems Analytical functions and problems Cauchy-Riemann equations in Cartesian form Cauchy-Riemann equations in Polar form Problems Consequences on C-R equations Problems Conformal transformations: z2. 33. 25.29 (10) ENGINEERING MATHEMATICS – IV – MAT41 Subject Code : MAT 41 Peri ods 1 2. of Periods : 65 Chapter title Chapter 1 Complex Analysis T1. 13. (10) 20. pg#194 14 21. 10.Pg#651 Topics to be covered COMPLEX VARIABLES Introduction Definition of Limit. ez and z + a2 / z Bilinear transformations Problems Complex integration: Line integral Problems Cauchy’s theorem – corollaries Cauchy’s integral formula Problems Taylor’s series and examples Laurent’s series and examples Singularities. 28. No. 11. 16. 7. 4. Pg#500 R1. Rodrigue’s formula Recurrence relations Problems Referenc e Chapter Cumulat ive 21 32.5% 35 53. Suggest a suitable weld size for a welded joint loaded as shown in figure. 23. 17. 24. 21. 3. continuity. 18. 9. SPECIAL FUNCTIONS Series Solution of Bessel’s Differential equation Problems Recurrence relations Generating function Problems Orthogonality Property and examples Bessel’s integral formula and examples Series Solution of Legendre’s differential equation Problems Generating functions . 34.3% 21 32. 623 R1. 6. 26. 15.8% .Pg#592. 29.for plate material in tension σt = 12MPa for rivet material in compression σc = 160 MPa for rivet material in shear τ = 80 MPa Draw neat sketches of the joint in two views. 5. 39.177. 64 65 11 16. 63. Chapter 3 Statistics and Probability T1. 50.5% 47 72. 41.9% 65 100% Literature Book Type Text Book Reference Books Code T1 R1 R2 Title & Author Higher Engineering Mathematics.85. 48. 52.Pg#822 . 60. B.1% 55. JOINT PROBABILITY DISTRIBUTION AND MARKOV CHAINS Concept of Joint Probability and Joint distribution Discrete and independent random variables Expectation and variance Problems Introduction to Markov Chains Probability vectors and problems Stochastic Matrices and problems Fixed points and regular Stochastic Matrices Higher transition probabilities Stationary distribution of regular Markov chains Absorbing states 12 18.1 19. 57. conditional probability Problems Baye’s rule and problems Discrete and continuous random variables PDF and CDF Binomial distribution and problems Poison distribution. Pg#733. 43. 59.59. Grewal Advanced Engineering Mathematics. 51.78 0 R1. 45. Pg#1049 R2.S. 38.Pg#224 282 Orthogonality Property and problems STATISTICS AND PROBABILITY Curve fitting by the method of Least squares Problems Correlation and problems Regression Probability. Erwin Kreyszig Schaum’s Outlines :Probability Edition 38th 8th 2nd Publisher Khanna Wiley McGrawHill Year 2004 2001 2000 . Sampling distribution. 40. Exponential distribution and problems Normal distribution and problems SAMPLING DISTRIBUTION Sampling. 62. Standard error Type-I and Type-II errors and problems Testing of hypothesis for means large samples Testing of hypothesis for means small samples Level of Significance and problems Confidence limits for means Large and Small samples Student’s t-distribution.245 Chapter 4 Sampling distributio n T1.8% 54 83.3% 07 10. 42. 61. 53. 37.35.Pg#110 4 Chapter 5 Joint Probability Distributio n& Markov Chains R2. 44. 54. 56. 47. 49. 36. 58. R1. 46. . 6. prove that 2 2 ⎧⎛ ∂φ ⎞ 2 ⎛ ∂φ ⎞ 2 ⎫ ⎪ ⎪ ⎛ ∂φ ⎞ ⎛ ∂φ ⎞ ⎜ ⎟ = ⎨⎜ ⎟ + ⎜ ⎟ ⎬ | f ′(z ) |2 ⎜ ⎟ +⎜ ⎟ ∂x ⎠ ⎝ ∂y ⎠ ∂u ⎠ ⎝ ∂v ⎠ ⎪ ⎝ ⎪⎝ ⎭ ⎩ 2 2 (e) If f (z ) = u + iv is analytic. 13. If f (z ) = u + iv is analytic and ψ is any differential function of x and y prove that 2 ⎧⎛ ∂ψ ⎞ 2 ⎛ ∂ψ ⎞ 2 ⎫ ⎞ ⎪ ⎪ 2 ⎟ = ⎨⎜ ⎟ ⎬ | f ′(z ) | ⎟ +⎜ ⎟ ⎪⎝ ∂u ⎠ ⎝ ∂v ⎠ ⎪ ⎠ ⎭ ⎩ 8. The necessary sufficient condition for the function f(z)= u + iv to be analytic is ∂u ∂v ∂v ∂u = =− . ∂x ∂y ∂x ∂y 4. show that ∂ 2u ∂ 2u + =0 ∂x 2 ∂y 2 ∂v ∂ 2v + = 0 i. given (a) u =2x(1-y) (b) u = ex (x cosy – y siny) (c) x sinx cushy – ycosx sinhy (d) v=exsiny sinxsiny (e) v= cos2x + cosh2y x (f) u + v = 2 x + y2 . Show that the function f ( z ) = z is continuous at every point but not differentiable at any point. If f(z) = u + iv is analytic then the families of curves u= c1 and v= c2 here c1& c2 are constant are orthogonal. Show that an analytic function with constant real part is constant.e . Show that an analytic function with constant modulus is constant. 2 2 ∂x ∂y 2 11. 12. Prove that ∂2F ∂2F ∂2F Here F=F(x. If f (z) is analytic on an open set S and f ′(z ) = 0 for all z ∈ S show that f (z) is constant.QUESTION BANK COMPLEX ANALYSIS (20 marks) Analytic Functions: 1. 7. If f (z ) = u + iv is an analytic function.. Find the analytic function f(z)=u + iv. Show that an analytic function constant modulus is constant. If f(z) = u +iv is analytic u and v satisfy Laplace’s equation. 5. y) z= x+ iy. z = x − iy + 2 =4 2 ∂z∂z ∂x ∂y 10. 3. 2. u & v are harmonic functions. prove the following ⎛ ∂ψ ⎞ ⎛ ∂ψ ⎟ +⎜ ⎜ ⎜ ⎝ ∂x ⎠ ⎝ ∂y 2 ⎛ ∂2 ∂2 ⎞ (a) ⎜ 2 + 2 ⎟ | f (z ) |2 = 4 | f ′(z ) |2 ⎜ ∂x ∂y ⎟ ⎠ ⎝ ⎞ ⎞ ⎛ ∂ ⎛ ∂ (b) ⎜ | f (z ) | ⎟ + ⎜ | f (z ) | ⎟ =| f ′(z ) |2 ⎜ ∂y ⎟ ∂x ⎠ ⎝ ⎝ ⎠ 2 2 ⎞ ⎛ ∂ ∂ (c) ⎜ 2 + 2 ⎟ log | f (z ) |= 0 ⎜ ∂x ∂y ⎟ ⎝ ⎠ (d) If f (z ) = u + iv is analytic and φ is any differentiable function of x and y. Show that the function f (z ) =| z |2 is continuous at every point but is not differentiable at any point other than origin. show that ∇ 2 | f (z ) |2 =| f ′(z ) |2 9. . θ ) + iv(r . =− ∂r r ∂θ ∂r r ∂θ 14. B. θ ) prove that 15. -1 ± i 5. (b) 1<|z|<2 (c) |z|>2 (1 + z )(z + 2) 2 1 for (a)|Z|<1 12. where C is a simple closed contour enclosing the origin.. z2 ez 3 ∫z dz where C is the circle |z|=1 ∫ c z2 +1 dz .PESIT (g) u − v = cos x + sin x − e −y 2 cos x − e y − e − y ∂u 1 ∂v ∂v 1 ∂u = . If c1.. θ ) is analytic function.E. f (z ) = u (r .c3….r ≠ 0 r2 Complex Integration 1. + ∫ f (z )dz c c1 c2 cn 4. show that u and v satisfy the function (a) (b) (c) ∂ 2ϕ 1 ∂ϕ 1 ∂ 2ϕ + + =0 ∂r 2 r ∂r r 2 ∂θ 2 ∂ 2u 1 ∂u 1 ∂ 2u + + =0 ∂r 2 r ∂r r 2 ∂θ 2 ∂ 2 v 1 ∂v 1 ∂ 2 v + + =0 ∂r 2 r ∂r r 2 ∂θ 2 16. θ ) + iv(r . Obtain Laurent’s expansion for f (z ) = 1|<2. Prove that ∫ f (z )dz = ∫ (udx − vdy ) + i ∫ (udy + vdx ) c c c ∫ f (z )dz = 0 c 3. If f(z) is analytic within and on a simple closed curve c in the complex plane and a is f (z ) 1 any point c then prove that f (a ) = dz 2πi z − a ∫ c 6. Evaluate 9. Obtain the Taylor’s and Laurent’s series for the function f(z)= 11.. Evaluate 8.. Verify the Cauchy’s theorem for the function f (z ) = 3 z 2 + iz − 4 with c as the square having vertices at 1 ± i .c2. Mechanical z2 in the region (a) 1<|z|<3 (z − 1)(z − 3) (b) |z- 4th Semester Course Information . where C is a circle of unit radius with center at z2 −1 (i) z= 1 10.cn are ‘n’ non overlapping simple closed curves within C and f(z) is analytic on these curves in the region bounded by them then prove that ∫ f (z )dz = ∫ f (z )dz + ∫ f (z )dz + . Prove that 2. Evaluate (ii) z=-1 ∫ c c z +1 dz. given cos 2θ (a) u = r 2 cos 2θ − 4 sin θ (b) u = . If f(z) is analytic within and on a simple closed curve C and a is any point within C then n! f (z ) f n (a ) = dz 2πi (z − a )n +1 ∫ c 7. If z = reiθ and f (z ) = u (r . Find the analytic function f (z ) = u + iv. . 4..x + 2x + 2x + x in terms of Legendre’s polynomials.Rn are residues of f(z) at a1. 17. 4th Semester Course Information B. w2 = i. Find the series solution of Bessel's differential equation. dx d −n x J n (x) = x-n J n+1 (x) . Find the bilinear transformation that transforms the points z1 = 1. 3. BESSELS FUNCTIONS: (10 marks) 1. Find the series solution of Legendre's differential function.. LEGENDRE POLYNOMIALS: (10 marks) 1. 6. Show that y = c1 Jn(kx ) + c2 J-n (kx) is the solution of x2 y2 + xy1 + (k2 x2 . R2 . Show that the transformation w = z2 transforms the circle | z-a | = c to a cardioid or a limacon. 8.E.……an 14. State and prove orthogonal property of Bessel's functions.a3. Show that cos (x sinθ) = J0(x) +2ΣJ2n(x)cos 2nθ 12.a3…. Prove that J n(x) = [ πx {(Cosx)/x +sinx} ] 14. Find the fixed points of the transformation. Show that e −ax J 0 (bx)dx = 0 ∫ 1 a + b2 2 16. ∞ π ∫ 15. If C is a simple closed curve and f(z) is analytic within and on simple closed curve c except at finite points a1.. 2. Show that (a)Pn (1) = 1 (b)Pn (-x) = (-1) n Pn (x) . Hence deduce that Pn (-1) = (-1)n 2 3 4 Express 3 . Find the images of (i) x-y = 1 (ii) x2 – y2 = 1 under the transformation w = z2. 9.J2 n-1 (x)] dx 11. 4. Show that (a) J ½ (x) = πx πx Show that 2n J n(x) = x [J n-1 (x) + J n + 1 (x) ] Show that J n'(x) = x [J n-1 (x) . z3 = -1 onto the points w1 = 2..J n + 1 (x) ] d n Show that x J n (x) = xn J n-1 (x) . R3 .an inside c then prove that PESIT ∫ f (z )dz = 2πi(R + R 1 c c 2 + R3 + .13.. 2 2 Sinx (b) J -½ (x) = Cosx. 5.. 18. = x[ J2 n (x) . 3. Show that dx 2 {(Sinx )/x . ∫ z(z − 1)(z − 2) dz 3z − 4 where C: |z|=3/2 ∫ c 2z + z dz... where n is a positive integer. 7. By using Rodrigue’s formula verify that Pn (x) satisfies Legendre’s differential equation. where (i) C: |z|=2 (ii) C: |z-1|=1 z2 −1 2 16. Show that --3/2 (x) = 2 d x J n ( x) J n−1 ( x).a2. Prove that J − n (x ) = (− 1)n J n (x ). w3 = -2. Mechanical .a2. Show that sin (x sinθ) = 2ΣJ2n-1(x)sin (2n-1)θ 1 cos(nθ − x sinθ )dθ 13.cosx } Show that (a) J 3/2 (x) = πx [ [ ] ] (b) J 10.n2)y =0. z2 = i.Rn ) here R1 .. Evaluate 15. Verify that y = xn Jn(x) is the solution of x y2 +(1-2n)y1 + xy =0. 2. 7. Fit the straight line of the form y= a + bx to the given data 5 10 15 17 2.1 6.26 5.0 3. x: 10 12 14 16 18 20 y: 20 25 30 35 40 45 6. Prove that P ' n ( x ) = xP ' n −1 ( x ) + nPn −1 ( x ) STATISTICS: (10 marks) 1. Fit a curve of the form y=axb for the data x: 1 2 3 4 5 6 y: 4.Pn + 1 (x). Σy2 = 460& Σ xy = 508. Fit a parabola y = ax 2 + bx + c to x: 20 40 60 12 x: y: 0 15 22 80 20 24 25 30 the following data. 4th Semester Course Information B. 100 120 y: 5. Σ x = 125.1 14. Show that Pn (x) = ⎣ π ⎢ 0 1 ⎡ x ± x 2 − 1 cosθ ⎤dθ ⎥ ⎦ π ∫ Show that [ (2n+ 1) x Pn (x)] = (n+1) Pn+1 (x) + n Pn-1 (x) Show that Pn (x) = xP'n (x) .E. 9.Pn (x). Express x 3 + 3x 2 − 4 x + 5 in terms of Lagendre’s Polynomials.3 46. 12. Find the lines of regression for the following data: x: 1 2 3 4 5 6 7 8 9 10 y. 10 12 16 28 25 36 41 49 40 50 9.r2 σ x σ y and explain the significance when r = 0.5 & r = 0.8 7.5 9.Pn − 1 (x) dx = (2n − 1)(2n + 1)(2n + 3) 2 −1 1 1 2n (n + 1) 10. 2. Mechanical .P' n (x) dx = (2n − 1) 1 n 2 n! dx 13.2x P'n (x) + P'n-1 (x) Show that −1 1 ∫ x . 14) & (8. 6.8 find the value of x corresponding to y= 75 & y corresponding to x = 70. If θ is the angle between two regression lines show that 1. Show that ∫ x .8 33. 7. Show that 11. Later it was discovered it had copied down the pairs (8. 12) & (6. 8) as (6. Show that there is a perfect correlation between x & y .Pn − 1 (x) dx = (4n 2n 2n 2 − 1) −1 ∫ x . A computer while calculating the correlation coefficient bet x & y from 25 pairs of observations got the following constants n = 25.P'n-1 (x) Show that Pn (x) = P'n+1 (x) . mean of y is 67. 6) respectively. σx = 3.9 22.98 4. Prove that Pn (x ) = dn n (x − 1) 2 n 14. σx = 7. Sub A : 77 54 27 52 14 35 90 25 56 60 Sub B: 35 58 60 40 50 40 35 56 34 42 5. 5.5 The following table gives the marks obtained by a student in two subjects in ten tests. Find the coefficient of correlation. 8. Obtain the correct value of the correlation coefficient. Σ x2 = 650. If the mean of x is 65. Σ y = 100.PESIT 5.Pn (x). tan θ = r σ x2 + σ y2 8.21 6. 10. regression equations are y = x + 5.1 19.5 6. Exponential distribution. 2. find the variance of x.. The probability of a man hitting a target is 1/3. 12. Estimate y for x = 8. 12. 3 red & 1 green and 3 white. Mechanical 4th Semester Course Information PESIT (b) . 7. (a) If he fires 5 times what is the probability of hitting a target at least twice. The probabilities of solving the problem individually are ½. variance of y is 16. 4.1 8.E. Find the probability that (a) they are all of different suits (b) no 2 cards are of equal value. A class consists of 6 girls & 10 boys If a committee of 3 is chosen at random find the probability that (a) exactly 2 boys are selected (b) at least 1 boy is selected (c) exactly 2 girls are selected. Define a sample space and probability of an event. 4 14. P(B) = 1/3. & 1. 11.3 x: 1 2 3 4 5 y: 14 13 9 5 2 13.94. for the following data: x: 1 2 3 4 5 6 7 y: 87 97 113 129 202 195 193. B & C are 2. 50% & 10% of the total production of a factory respectively.5 respectively. 1/3. The chance that a patient will die after correct diagnosis is 40% and the chance of death after wrong diagnosis is 70%. uniform distribution. 13. Estimate y for x = 2. When are two events said to be (a) mutually exclusive (b) mutually independent. Fit an exponential curve of the form y = abx. 15. (b) How many times must he fire so that the probability of hitting a target B. P(A∩B) = 1/4.8 5.9 14. Find the probability that (a) the problem is solved (b) the problem is solved exactly by one of them. An experiment succeeds twice as often as it fails.5. 2 marbles are drawn from a bag chosen at random and they are found to be 1 white & 1 red. 16. A certain problem in mathematics is given to 4 students for solving. 1 red & 2 green marbles respectively. Fit a second degree parabola of the form y = ax2 + bx + c for the data: x: 1 2 3 4 5 y: 1. Four cards are drawn from a pack of 52 cards without replacement. 8. State & prove Baye's theorem. Find the probability that the balls came from the second bag. An item is chosen at random & is found to be defective. 2 white.8 . 16x = 9y . The two regression lines are x = 4y + 5 & 16y = x + 64 find the mean values of x. find (a) P(A/B) (b) P(B/A) (c) P(A∪B) (d) P(Ac) 3. Find the probability that a leap year selected at random will contain 53 Fridays.3 4. 9. Find the chance that in the next 6 trials there will be at least 4 successes. Define (a) a random variable (b) Discrete and continuous random variable 11. Fit a straight line to the data: (a) x: 0 1 2 3 4 y: 1 1.8 3. 2red & 3 green. 10. The chance that a doctor will diagnose a disease correctly is 60%. ¼. Exponential and Normal. PROBABILITY: (10 marks) 1. Poisson. B & C manufacture 40%. The percentage of defective items produced by A. 6. y & r. There are 3 bags which contains 1 white. If A & B are events P(A) = ½. 3 machines A. Obtain the mean and variance for the following distributions: Binomial. Find the probability that it was a product of C. If a patient dies what is the chance that his disease was not diagnosed correctly. Define probability mass function and probability distribution function for a discrete random variable. 14. Define Geometrical distribution. 4. 5. In a partially destroyed laboratory record of correlation data only the following results are legible. & 1/5 respectively. The duration of time that an overhead tank will serve without refilling is found to follow an exponential distribution with mean 10 days.2 0. If it plays 4 games. B.20 0. 21.5 Find the joint probability distribution of X & Y. (iv) V(c) = 0 (v) V (aX + b) =a2 V(X). find the probability that it wins (i) 2 games (ii) at least one game. elsewhere ⎩0 average profit per automobile and also E(X2). Given that 2% of the fuses manufactured by a firm are defective. find the probability that a box containing 200 fuses has (a) at least 1 defective fuse (b) at most 3 defective fuses. Determine the probability that out of 2000 individuals (a) exactly 3 (b) more than 2 individuals will suffer a bad reaction.Assuming that the marks are normally distributed find the no.D of a normal distribution of marks in an examination where 44% of candidates obtained below 55 & 6% above 80 and rest between 55 & 80. Show that (i) E(c) = c (ii) E (aX + b) = a E(X) + b (iii)V(X) = E(X2) . If 70% of such items are shipped in perfect condition and arrive on time. If such a lot contains 6 batteries with slight defects.17 0.m. 19. 22. & 10 p.008 30.5. A quality control engineer inspects a random sample of 3 batteries from each lot of 24 car batteries that is ready to be shipped.D 16.E(X)2 . 33.at least once is more than 90%. Find the probability that (i) it needs filling within 8 days & (ii) it will serve for more than 10 days. If 8 employees are chosen by lot to serve on a committee. 18.24 0.8 P(Y) 0.14 0. Find E(x) & V(x) for the following probability distribution: x: 3 4 5 6 7 8 9 p: 0. 26.4 0. What is the probability that the 8th child born is the first one to have a defective heart? 23. If a person reaches a bus stop on this route at a random time during this period. 31. A cricket team has probability 2/3 of winning whenever it plays. 25. The distribution of 2 independent random variables X & Y are given below: X 0 1 Y 1 2 3 P(X) 0. 0 < x < 1 random variable X having the density function f(x) = ⎨ Find the .4 & S. 17.5. If it is shipped from the factory in perfect condition and arrives on time but it is reduced by $2 if it does not arrive on time & $12 regardless of whether it arrives on time if it is not shipped from the factory in perfect condition.m. 32. Mechanical 4th Semester Course Information PESIT .1 0. A distributor makes a profit of $20 on an item. A group of 20 airplanes are sent on an operational flight. 29. of students obtaining marks (i) bet 30 & 60 (ii) bet 70 & 80. what is the probability that he will have to wait for at least 20 minutes? 24.(iii) below 20 (iv)above 80. find the probability that 5 of them will be union members. buses ply every 30 minutes between 6 a. If a dealers profit in units of $1000 on a new automobile can be looked upon as a ⎧2(1 − x). Find the mean & S. 27.E. What is the probability that it will be destroyed in the 6th shot only and not before. Among 300 employees of a company 240 are union members while the others are not. 28.05 0. 10% are shipped in perfect condition but do not arrive on time and 20% are not shipped in perfect condition what is the distributors expected profit per item. what are the probabilities that an inspectors sample will contain (i) none of the batteries with defects (ii) only one of the batteries with defects (iii) at least 2 of the batteries with defects. On a certain city transport route. If the probability of the birth of a child with a defective heart in a certain city is 0. The probability that an individual suffers a bad reaction from a certain injection is 0.12 0. The chance that an aero plane fails to return from the flight is 5 %.01. The mean marks of 1000 students is 34. Find the probability that (a) one plane does not return (b) at the most 5 planes do not return.001. If the probability that a target is destroyed on any one shot is 0. 20. PESIT 34.The following table gives the joint probability distribution of 2 random variables X &Y X/Y -1 0 1 -1 0 0 0.2 1 0 0.1 0.1 0.2 0.2 0.1 0.1 Find the conditional probability of X given Y = 0. 35. The joint distribution of two random variables X and Y is given by the following table. X /Y -4 2 1 1/8 1/4 5 ¼ 1/8 Determine (i) the marginal distributions of independent random variables? 7 1/8 1/8 X and Y. (ii) E (X) and E(Y) (iii) are X and Y Sampling Distribution: (20 marks) 1. A Sample of 5 measurements of the diameter of a sphere was recorded as 6.33, 6.37, 6.36, 6.32, 6.37mm. Find unbiased and efficient estimates of (i) the population mean (ii) the population variance. 2. For the frequency distribution given below find the unbiased and efficient estimates for the mean and variance Xi fi 60 02 61 00 62 15 63 29 64 25 65 12 66 10 67 04 68 03 3. The sample mean of a population was recorded as 184.67 with a probable error of 0.236. Find the 99.74% confidence limits for the true (population) mean. 4. The S.D of life time of 200 electric bulbs was computed to be 80 hours. Find (i) 95%& (ii) 99% confidence limits for the S.D of all such bulbs. 5. How large a sample should one take in order to be (i) 99% & (ii) 99.74 % confident that a population S.D will not differ from a sample S.D by more than 2%. 6. A die is thrown 9000 times and a draw of 3 or 4 observed 3240 times. Show that a die cannot be regarded as an unbiased one. Also find the limits between which the probability of throw of 3 or 4 lies at 99.74% level of confidence 7. A mean of a sample of size 900 is 3.4.Can the sample be reasonably as a true random sample for a large population with means 3.25 and S.D 1.61 8. Ten screws are chosen at random from a population and their lengths are found as (in mms) 63,63,66,67,68,69,70,70,71,71. On the basis of this information can we say that the mean length in the population is 66mm at 95%confidence level? 9. Find 99% confidence limits for the correlation coefficient, which is computed to be 0.60 from a sample of size 28 TESTING OF HYPOTHESIS: 1. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a mean of 500 hours and a S.D of 40 hours. Test the hypothesis Ho: μ ≠ 800 of a random sample of 30 bulbs has an average life of 788 hours. Use 5 % level of significance. 2. Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of the random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3 & Use 0.01 level of significance and assume that the distribution of contents is normal. B.E. Mechanical 4th Semester Course Information PESIT 3. A random sample of size n1 = 2.5 taken from a normal population with a S.D σ1 = 5.2 has a mean x1 = 81. A second random sample of size n2 = 36 taken from a different normal population with a S.D σ2 = 3.4 has mean x2 = 76 . Test the 4. hypothesis that μ1 = μ2 against the alternative μ1 > μ2 at 5% level of significance. A large automobile manufacturing company is trying to decide whether to purchase brand A or B tyres for its new models. To help arrive at a decision, an experiment is conducted using 12 of each brand. The tyres are run until they wear out. The results are Brand A : x1 = 37,900kms, s1 = 5100kms Brand B : x 2 = 39,800kms, s 2 = 5900kms . Test the hypothesis at the 0.05 level of significance that there is no difference in the 2 brands of tyres. Assume the population to be approximately normally distributed. a) Tests of Hypothesis b) Type I and Type II errors find 5. Explain the following mean and variance of the Chi square distributions. JOINT PROBABILITY AND MARKOVCHAINS (20 marks) x ⎤ ⎡1 − x P= ⎢ ⎥ ⎣ y 1 − y⎦ ⎡1 / 2 1 / 4 1 / 4⎤ 2. Find the unique fixed probability vector of the regular stochastic matrix ⎢1 / 2 0 1 / 2⎥ ⎥ ⎢ ⎢ 0 1 0 ⎥ ⎦ ⎣ o ⎤ ⎡ 1 is the transition matrix with initial probability distribution p (0 ) = (1 / 3,2 / 3) . 3. If P= ⎢ 1 / 2 1 / 2⎥ ⎣ ⎦ 1. Show that the vector (y, x) is a fixed point of the stochastic matrix Define and compute.(a) p (3)21 (b) p (3) (c) p (3)2 4. A salesman’s territory consists of three cities A, B &C. He never sells in the same city on consecutive days. If he sells in a city A, the next day he sells in city B. However if he sells in either B or C then the next day he is twice as likely to sell it in city A or in other city. Show that in the long run he sells 40% of the time in the city A, 45% of the time in city B and 15% of the time in the city C 5. A software engineer goes to his workplace everyday by motorbike or by car. He never goes by bike on 2 consecutive days but if he goes by car on a day then he is equally likely to go by car or by bike the next day. Find the transition probability matrix for the chain mode of transport he uses. If car is used on the first day of a week find the probability that after 4 day s (i) bike is used (ii) car is used. 6. A gambler’s luck follows a pattern. If he wins a game, the probability of winning the next game is 0.6. However if he loses a game, the probability of losing the next game is 0.7. There is an even chance that he wins the first game. If so, (a) Find the transition matrix M of the Markov process. (b) Find the probability that he wins the second game. (c) Find the probability that he wins the third game. (d) Find out how often, in the long run, he wins. Define stochastic ⎡0 3 4 ⎢ 1 matrix ⎢ 1 2 ⎢ 2 1 ⎢0 ⎣ matrix. Find the unique fixed probability vector for the regular stochastic 1 ⎤ 4⎥ 0⎥ ⎥ 0⎥ ⎦ B.E. Mechanical 4th Semester Course Information PESIT APPLIED THERMODYNAMICS – ME 43 (2 hours / week for both IV ‘A’ and IV ‘B’ sections) Faculty :Dr.T.R.Seetharam Lecture Coverage syllabus 1–2 Topics To be Covered % of Review of Basic Thermodynamics – Applications of I & II law for closed and open systems, Important property relations for ideal gases, properties of pure substances ; Use of tables & charts Gas Power Cycles: Introduction; Air – standard cycles for IC engines – analysis of Carnot,Otto,Diesel & Dual- combustion cycles ; Gas Turbine Cycles – Simple Brayton cycle, modified Brayton cycle for improvement in work output & thermal Efficiency, deviations of practical cycles from ideal cycle Vapour Power cycles- Carnot vapour power cycle and its limitations; Simple Rankine cycle; effects of pressure & temperature on performance of Rankine cycles; modifications of simple Rankine cycle to increase net work output & thermal efficiency – Reheat cycle, Regenerative cycle, types of feed water heaters used in regenerative cycles; Reheat-Regenerative cycle; practical vapour power cycles . Refrigeration – Definition of Refrigeration, refrigerated space, refrigerant Refrigeration cycle, refrigeration effect; units of refrigeration effect – Ton of refrigeration; COP ; Carnot refrigerator – analysis and its limitations; Air refrigeration plant – Bell-Coleman / Reversed Brayton cycle; practical air refrigeration cycles Nil 08 3–6 7- 11 08 12 – 17 12 18 - 20 06 21 - 23 Vapour compression refrigeration cycle – analysis, effects of sub-cooling and superheating on the performance ; desirable properties of refrigerants for vapour compression cycle; steam jet refrigeration 06 24 - 25 Psychometrics – Thermodynamics of air-water vapour mixture – definitions Of moist air, dry air, specific humidity, relative humidity, dries – bulb and wet – bulb and dew point temperatures; adiabatic saturation temperature, saturated unsaturated air, enthalpy of moist air, construction and use of psychometric chart 04 26 - 28 Thermodynamic analysis of psychometric processes like heating, cooling Heating & humidification, cooling and de-humidification, adiabatic mixing Air streams, summer and winter air conditioning 08 B.E. Mechanical 4th Semester Course Information The volumetric ratio of isentropic compression is 6 and the volumetric ratio of isothermal expansion is 1.4 bar. The minimum pressure in the cycle is 1 bar. In an air standard Carnot cycle heat is transferred to the working fluid at 1110 k and heat is rejected at 273 K. Determine (i) the thermal efficiency and (ii) the m e p.5.8.6.2. The volume of air at the beginning of isothermal expansion is 0.1. (ii) air standard efficiency. substance. 1. Problems on Otto Cycle 1. Determine (i) percent clearance. (vi) maximum work output and (vii) thermal efficiency corresponding to maximum work output. works between the limits are 60 bar and 1 bar. (iii) net work output mean effective pressure. Mechanical . From the p-v diagram of an engine working on Otto cycle. Also calculate the ratio of maximum pressure to the minimum pressure in the cycle.5. 1. After 5/8th of the compression stroke is completed. the efficiency of the cycle is doubled. B. The pressure (i) pressure and temperature at salient points of the rejected per unit mass of air. (v) compression ratio corresponding to maximum work output. (ii) cycle efficiency.5 bar. (ii) Thermal efficxiency of the cycle.(ii) air standard efficiency. In an air standard Otto cycle the maximum and minimum temperatures are 1400 C and 15 C respectively. The maximum pressure and temperature in a Carnot cycle is limited to 20 bar and 400 C. (iv) power developed by the engine if there are 200 cycles per minute. Determine the temperature of the source and the sink. 1. Determine (i) the compression ratio. The heat supplied is 800 kJ / kg. (iii) net work output per unit mass of air. Assume that the minimum temperature in the cycle to be 27 C. Find cycle. In an engine working on Otto cycle. Calculate the compression ratio and the thermal efficiency.ME 43: Applied Thermodynamics Tutorial 1: Problems on Gas Power Cycles A. (iii) MEP. At the end of the compression process the pressure is 10 bar. (iv) mep. (ii) heat supplied and heat and thermal efficiency.1 m3. 1.7. the clearance volume is 50 cm3. and (iii) 1. 1. Problems on Carnot Cycle PESIT 1.E. A Carnot power cycle using air as the working emperature limits of 900 K and 300 K. (iii) net work output per unit mass of air and (iv) mep. a temperature of 27 C and a pressure of 1 bar at the beginning of the compression process. Find (i) the minimum temperature in the cycle. 4th Semester Course Information B. The heat transfer to the working fluid is 105 kJ / kg.5 m3 . The maximum temperature in the cycle is limited to 1000 C. the pressure was found to be 3.4. while the stroke volume is 350 cm3.3. If the temperature at the commencement of the compression process is 27 C and the maximum temperature in the cycle is 1000 C determine (i) the compression ratio. When the temperature of the sink is reduced by 70 C. (iii) power output form the cycle if the number of cycles per minute is 200. it is found that the pressure inside the cylinder after 1/8th of the compression stroke is completed is 1. A Carnot engine converts 1/6 of the heat input into work. Heat added is 200 kJ /kg. An engine working on Otto cycle has a volume of 0. The compression curve is polytropic with index n = 1. 1.35. and (ii) MEP 2. 2. If the temperature of air at entry to the engine is 27 C. (ii) the net work output per unit mass of air.7 kPa. respectively. The compression ratio is 7.3 respectively. (ii)MEP. Initial pressure and temperature of air are 1 bar and 27 C. Assume that the compression process is according to the law pv1. Find (i) pressure and temperatures at salient point of the cycle. If the cut-off ratio is 1.2.1. find B.38 and 1.2. Determine (i) heat supplied per kg of air. The bore and stroke of the engine are 16 cm and 20 cm respectively.10. find the thermal efficiency and the relative efficiency based on the air standard Otto cycle. The compression curve in an Otto cycle may be approximated by the equation pV1. (iv)MEP. Determine (i) thermal efficiency and (ii) MEP 2. In a diesel cycle. (iv) relative efficiency 2.E. Find the compression ratio if the compression and expansion indices are 1. in terms of the compression ratio.8.65 bar.5.32 = constant and the expansion process is according to the law pv1. The heat added at constant pressure is twice that at constant volume. In an air standard diesel cycle. Problems on Dual Combustion cycles 2.7.30 = constant. D. (iii) maximum temperature in the cycle.6939 kJ/(kg – K). At the beginning of the compression process the pressure and temperatures are 1 bar and 300 K respectively. determine the cycle efficiency and the relative efficiency based on the air standard cycle. (iii) thermal efficiency. (iii) thermal efficiency. the pressures at two points on the compression curve are 1.6. air is compressed isentropically from 26 C and 105 kPa to 3. PESIT 2. The compression and expansion ratio of an oil engine working on a dual cycle is 9 and 5 respectively.4 bar. Determine (i) air standard efficiency. maximum cycle temperature ratio and the ratio of specific heats. Problems on Diesel Cycles 2. Mechanical 4th Semester Course Information . Tutorial 2 : Gas Power Cycles (continued) C. and (iv) specific air consumption in kg/kWh. The entropy change during heat rejection is − 0. The cyclider bore is 250 mm and the stroke is 400 mm. If 60 % of the energy addition occurs at constant volume while 40 % occurs at constant pressure. At the beginning of the cycle the pressure and temperature of air are 0. The maximum temperature in the cycle is 1000 K. The pressure in the cycle after 1/3rd of the compression stroke is completed is 1. The expansion curve is isentropic. Find (i) the pressure and temperature at salient points of the cycle.7 bar and 13.98 bar and 300 K respectively. Assume the specific heats of air to be constant and γ = 1. corresponding to positions where 3/10th and 9/10th of the stroke have been executed.4. and (iv) temperature at the start of the heat rejection. Heat addition takes place up to 10 % of the stroke. An oil engine works on a diesel cycle with compression ratio of 20.3. The maximum and the compression pressures in a dual cycle are 64 bar and 32 bar respectively. Derive an expression for the air standard efficiency of a cycle similar to Otto cycle except that the compression process is isothermal.9.1. The initial pressure and temperature are 1 bar and 30 C.5. The compression ratio of an air standard diesel cycle is 14 and the cut-off ratio is 2.35 = constant.4. (ii) thermal efficiency. An air standard diesel cycle has a compression ratio of 18 and the heat transfer to the working fluid is 1800 kJ/kg. Determine (i) pressure and temperature at salient points of the cycle. 3. two thirds of the total energy added occurs at constant volume. The overall pressure ratio of the cycle is 4.1.000 kJ/kg. The energy addition during combustion is 550 kJ /kg. and the maximum pressure in the cycle is 53 bar. (ii) compressor and turbine work per unit mass of air.148 kJ/kg – K and γ = 1. A diesel engine works between the temperatures of 1250 C and 25 C.4 and cp = 1. and (ii) thermal efficiency.005 kJ/kg – K and γ = 1. 2. (iii) thermal efficiency of the plant. (ii) the suction pressure.Also assume that for air cp = 1. The isentropic discharge temperature for the air flowing out of a compressor is 195 0C while the actual temperature is 240 0C. If the air-fuel ratio in the combustion chamber is 75:1 and net power output is 650 kW. The air at the start of the compression is at 101 kPa and 20 0C.2 kg/min of fuel supplied and the calorific value of the fuel used is 42. The maximum temperature in the cycle is 800 0C. and has the same total energy addition as for diesel cycle except that this energy is equally divided between the constant volume and constant pressure processes. what would be the improvement in the B. Mechanical 4th Semester Course Information .E. 2. Assume standard conditions of air at the start of the compression process. (iii) net work output and work ratio. At the end of the constant volume process.Assuming that cp and γ remains same throughout the cycle and equal to those values for air determine (i) Net work output per unit mass of air. The cylinder diameter is 25 cm and the stroke is 30 cm. Hence show using T-s diagram that the diesel cycle is more efficient than the dual cycle under the same maximum and minimum temperatures as well as the same amount of heat addition.(i) the compression ratio. (iv) specific fuel combustion in kg / kWh. (ii) Air-fuel ratio. and (iv) thermal efficiency. (iv) thermal efficiency and specific air consumption in kg/(kWh). compute (i) the net work output from the cycle. Determine the thermal efficiency of a gas turbine cycle having two stages of compression and two stages of expansion. The conditions of air at compressor inlet are 1 bar and 17 0C. If heat is added at constant pressure during 3 percent of the stroke.The compressor inlet conditions are 1 bar and 15 0C. There is a pressure drop of 2 % of the inlet pressure in the combustion chamber. 2. Compare the efficiencies of the two cycles.0 kg / s. 3. (ii) the thermal efficiency.000 kJ/kg. The pressure ratio is 10 and the maximum allowable temperature is 1350 K.333 for products of combustion. If an ideal regenerator is incorporated in the cycle to heat the air coming out of the second stage compressor. The compressor efficiency is 85 %. Assume that the plant consumes 5. (iii) work output from the cycle if the expansion index is 1. the turbine efficiency is 90 % and the combustion efficiency is 95 %.8. compute (i) the isentropic efficiencies of the compressor and turbine and (ii) the overall cycle efficiency.2. If the compression ratio is 15. In a dual cycle.3. An air standard Brayton cycle has air enter the compressor at 27 C and 100 kPa.34.. and (iv) the mean effective pressure Tutorial 3: Gas Power Cycles (Gas Turbine Cycles) PESIT 3.9.4. the pressure is 5600 kPa. Air enters both the stages of compression at 15 0C and enters both the stages of turbine at 900 0C.The pressure ratio of an open gas turbine cycle is 6. 3. (iii) the amount of heat added. A dual combustion cycle operates between the same temperature limits. and (v) power output form the plant for a mass flow rate of air of 1. compute(i)the temperatures at the salient points of the cycle.10. The compression ratio for an engine working on dual cycle is 7. The calorific value of the fuel used is 42. The low and high pressure limits are 1. Calculate the power output from the plant and the cycle efficiency.98 0.1 bar.15 bar.87 0. The exhaust pressure of the second turbine is 1.E. Assuming that the intermediate pressure between the two stages of compression is same as that at the exit of the first stage expansion and equal to the geometric mean of the high and low pressures of the unit.80 is incorporated in the cycle. calculate (i) the air fuel ratio if the calorific value of the fuel used is 38650 kJ/kg.0 1100 K 0. 1250 k.5. Assume the compressor efficiency is 0. the gas temperature at the entry to both the turbines is the same. (ii)power output for an air flow rate of 1 kg/s. Pressure ratios in all the compressor stages are equal and expansion ratios in all the turbine stages are equal. The pressure drop through the intercooler is negligible.If ‘t’ represents the maximum cycle temperature ratio in the cycle show that t = (r a) (m+n)/mn where r = ratio of maximum pressure to minimum pressure in the plant and a = (γ – 1) / γ. The air from the first stage turbine is reheated back to 1250 K and then expanded in the second stage. The intercoolig between the compressor stages is perfect and the working fluid is reheated to Tmax in between the stages of expansion.6. A Brayton cycle works between 1 bar. 4th Semester Course Information B. The maximum and minimum temperatures in the cycle are 25 C and 1000 C.99 0. 300 K and 5 bar.8. 3.85 0. Determine the specific work output.7.89 for both the stages.In a gas turbine unit with two-stage compression and two-stage expansion. What would be the power output and cycle efficiency if an ideal regenerator is incorporated in the cycle? 3.04 bar PESIT 3. The work output from the first stage turbine is used to drive the two compressors. The pressure drop through the regenerator and first combustion chamber is 0. specific fuel consumption and cycle efficiency for a gas turbine power plant using a regenerator having the following specifications. There are two stages of compression with perfect intercooling and two stages of expansion. The maximum temperature permitted in the plant is Tmax. Assume that a regenerator with an effectiveness of o. What would be the net work output and cycle efficiency if the compressor and expansion stages have efficiencies of 80 % each and the regenerator effectiveness is 75 % 3.05 bar. An ideal gas turbine power plant operates with ‘m’ number of stages of compression and ‘n’ number of stages of exp[ansion. Compressor pressure ratio Turbine inlet temperature Isentropic efficiency of compressor Isentropic efficiency of turbine Mechanical transmission efficiency Combustion efficiency Heat exchanger effectiveness Pressure losses :(i) Combustion chamber pressure (ii) Heat exchanger air side loss pressure (iii) Heat exchanger gas side loss 4.80 2 % of compressor delivery 3 % of compressor delivery 0. The intercooler in between the two stages of compression has an effectiveness of 83 %. while the pressure drop through the second combustion chamber is 0. Mechanical .thermal efficiency of the cycle.02 bar and 7 bar.84 for both trhe stages and turbine efficiency is 0. After expansion to 5.000 kJ/kg. P1. pressure ratio across the intercooler = 0.(d) the net work output from the plant.30 T1 = 20 C.T4.9. PESIT 1 2 C1 3 C2 4 5 6 T1 CC1 T2 9 7 Inter cooler 10 Regenerator 8 CC2 Fig.97.98.The states of the flowing gas at various points along the circuit are numbered. pressure drop across intake = p1 / p∞ = p∞ / p10 = 0. (e) the overall cycle thermal efficiency.3.96. pressure ratio across the combustion chamber = p6 / p5 = 0. (c) the air fuel ratios at the two combustion chambers.30. the compressor inlet and exit conditions are 5 bar and 32. Calculate (a) the cycle thermal efficiency. and (c) the heat transfer at the reactor and the net air flow rate if the net power output from the plant is 650 kW. Pressure ratio for each compressor = 3. enthalpy of combustion of fuel = − 42. The following are the data referring to these states.80) again at 20 C.85.88. pressure ratio across the regenerator = p5 / p4 = 0.5 bar respectively. regenerator effectiveness = 0. before being ready to enter the compressor ( efficiency = 0.95. 3. P 4. the air is heated in a nuclear reactor to 945 K. In a closed cycle gas turbine plant. turbine efficiencies = 0. Mechanical 4th Semester Course Information . After passing through a regenerator with an effectiveness of 0.bar.98. The pressure drop in the regenerator and the reactor reduces the air pressure at the turbine inlet to 31.10. Calculate (a) T2. Tutorial 4 : Vapour Power Cycles B. Intercooler effectiveness = 0. (b) the total work required to drive the compressors and hence the output of turbine T1. The schematic diagram of a gas turbine power plant is shown in Fig.5.T3.25 bar in the turbine with an efficiency of 0. T6 = 1110 K. (b) the turbine and compressor power.T5. the air passes through the regenerator and a cooler. combustion efficiency = 0.5.95.84. T8 = 1050 K.4 : Figure for problem P1.88.E.83.T7 and T9. Compressor efficiencies = 0. and (f) the specific power output from the plant in kW/(kg – s) of air flow through the compressor. Pressure drop for gases leaving the turbine and flowing back through the regenerator = p10 / p9 = 0.97. The condensed steam from the low pressure heater is fed to the intake of the feed pump through a drain cooler. (iv) the thermal efficiency.86. 4. 360 0C to a condenser pressure of 0. Steam conditions at the boiler exit are 10 bar and 300 C. (iii) the net work out put. The reheated steam expands in an intermediate stage and again emerges as dry saturated steam at a lower pressure. (ii) the turbine work. 4. find the overall thermal efficiency of the plant and the specific steam consumption.5.0 kg/s. (iv) condition of steam entering the condenser.0 bar.08 bar.3.87. 4. A fraction of the steam is now extracted for feed water heating. Assumiing the high and low pressure turbines to have efficiencies of 0. Assuming the work output is the same for the high and intermediate stages. 4. while the remaining steam expands in a LP turbine to a final pressure of 35 mm of mercury.2 bar.90.7 bar respectively.0 kg/s. and the efficiencies of the high and low pressure stages are equal. the HP turbine receives steam at 20 bar and 300 0C. 0. to be reheated a second time to 280 C. and 0. the steam is reheated to 300 0C and then it expands in an intermediate stage to 1 bar. and (iv) net power output from the cycle for a mass flow rate of 1. Steam at 50 bar and 350 C expands to 12 bar in a high pressure stage and is dry saturated at the stage exit.85 respectively. In a reheat cycle. find: (i) efficiency of the high pressure stage. During expansion steam is bled at two stages where the pressures are 5 bar and 0. The heaters are of closed type.4. (iii) specific steam consumption in kg/kWh.05 bar..2.04 bar. (v) quality of steam entering the condenser and (vi) steam rate in kg/kWh. there is an energy loss of 42 kJ/kg and a drop in pressure of 0. Assuming the feed water in each heater to be heated to the saturation temperature corresponding to the bled steam pressure for that heater and that the temperature of the condensate from the heaters at the exit of the drain cooler is 30. intermediate and low pressure stages are respectively 0. Finally. What would be the corresponding values when the condenser pressure is decreased to 0. If the efficiencies of high.6.2 0C.82 and the steam condition at any point in the turbine may be assumed to be on a straight line joining the initial and final states. A simple Rankine cycle dry saturated steam at 20 bar enters the turbine and the condenser pressure is 1 bar. The isentropic efficiency is 0. the efficiency of the turbine being 0. Find the stream conditions at the turbine inlet. (ii) pressure of steam at exit of the intermediate stage. After expansion to 7 bar. Steam expands in a turbine from 30 bar. the condensed steam from the high pressure heater is being led to the steam space of the low pressure heater through a steam trap. Determine the improvement in thermal efficiency which will result if one stage of regenerative feed heating is added to a simple Rankine cycle which has the boiler exit condition of 14 bar and 300 C and a condenser pressure of 0. the exit pressure of steam at the end of the first turbine is 5 bar.E. and (v) thermal efficiency of the cycle 4. Determine (i) the pump work. In the pipe line between the boiler exit and turbine inlet.1. B.09 bar at the turbine exit. the steam expands in a low pressure turbine to 0.87 and 0.88. 4. In a reheat – regenerative steam power plant cycle. (iii) total power output from the three stages for a mass flow rate of 1. The steam expands in the turbine to a pressure of 0. drawn on an h – s chart.4. This is now reheated to 280 C without any pressure drop. The steam is reheated to 300 C before it is expanded in the second turbine to 0. Mechanical 4th Semester Course Information PESIT . determine the overall cycle efficiency of the plant. the actual enthalpy drop across the turbine and the final condition at discharge from the turbine. (ii) the overall thermal efficiency of the cycle. Steam for feed heating is to be extracted at 2.05 bar. the boiler exit conditions are 25 bar and 300 C. determine (i) the thermal energy input in the reheater.7.1 bar other things being the same. Pressure of air at compressor exit = 404 kPa.1. (ii) Power required to produce 1 ton of refrigeration.65.2. (iii) the mass of steam bled out for each feed water heater per unit mass of steam generated in the boiler. Isentropic efficiency of turbine = 85 %.5 0C to 89. Draw a schematic for the system and indicate all the salient points on the Mollier diagram. The low pressure feed water heater receives steam at 0.PESIT 4. The work supplied is 10 kW. determine (i) refrigeration effect per unit mass of air.9 bar and heats the feed water from 33. (b) refrigeration effect in tons and (c) COP if the cycle is used as a heat pump. A reversed Carnot cycle is used for heating and cooling. determine (i) the pump work to turbine work. An ideal air refrigeration cycle has the following specifications: Pressure of air at compressor inlet = 101 kPa. An ideal Rankine cycle with regenerative heating operates between the pressure limits of 10 MPa and 40 kPa. the air flow rate is 1700 kg / h and the relative COP of the actual plant is 0. 320 0C and 0. Temperature of air at turbine inlet = 27 C.5 for cooling determine (a) the ratio of maximum temperature to minimum temperature in the cycle . Temperature of air at compressor inlet = −6 C. After compression to 5.5 0C to 140 0C.4:.For the high pressure heater.E. 5. If the total steam generation is 18. find the power output of the plant in kW. the compressor takes in air at 1 bar and 10 C. On the basis of optimum design. Pressure of air at turbine inlet = 404 kPa. Isentropic efficiency of compressor = 85 %. Temperature of steam at turbine inlet is 500 0C. Determine (i) The COP of the cycle. The condensed steam is cascaded back into the condenser through a steam trap.5 0C. and (iii) air circulation rate per ton of refrigeration. (ii) the ratio of heat rejection to heat addition. Tutorial 5 : Refrigeration Cycles A. There are two open feed water heaters.8. Assume the turbine efficiency to be 0. In a two-stage regenerative feed heating system. Relative pressure drop in each heat exchanger = 3 % B. Also determine the overall cycle efficiency of the plant and specific steam consumption.5 bar. Its condensate is pumped by a drain pump into the boiler feed line. Find the mass flow rates of steam to each feed water heater per kg of steam generated in the boiler.82 and the condition of steam at any point in the turbine to be on a straight line on the h – s diagram connecting the steam states at inlet and exit.3 In an air refrigerating machine. Determine the power required for the actual plant for the same refrigeration effect 5. 5. steam is extracted at 4 bar and heats the water from 89. Assuming ideal conditions. Problems on Air Refrigeration cycles 5.(ii)heat rejected by air per unit mass in the intercooler. If the COP is 3. the steam conditions at the turbine inlet and exit are 20 bar. Temperature of air at turbine inlet = 27 C.000 kg/h. and (ii) COP of the cycle.An air refrigeration system is to be designed according to the following specifications: Pressure of air at compressor inlet = 101 kPa. 4.08 bar. Temperature of air at compressor inlet = − 6 C. the air is cooled to 30 C before expanding it back to 1 bar. Mechanical 4th Semester Course Information . In an actual plant using the above cycle.9. and (iv) cycle thermal efficiency. Mechanical 4th Semester Course Information PESIT .5 bar. Neglecting the clearance volume of the compressor and expander find the COP and the amount of air circulation per minute if 2000 kg of ice at 0 C is to be formed per day from water at 25 C.9:.8 bar according to the law pv1. The compressed air is cooled to a temperature which is 10 C above the ambient temperature of 30 C before being expanded isentropically in an expander. 5. If the refrigerant is RB.6:-In an ideal air refrigeration cycle.5:-An air refrigerator unit uses a reciprocating compressor and a reciprocating expander. Determine (a) the power required to drive the unit if the mechanical efficiencies of the expander and the compressor are both equal to 85 %.Repeat part (i) and (ii) of the above problem if the refrigerant after condensation is found to be subcooled by 6 0C. (ii) Power required in kW.14. The index of compression is 1. 5.8:-In a vapour compression refrigeration system using ammonia. (ii) the mass flow rate of ammonia. assuming the clearance volume to be zero.An air refrigeration unit takes in air from a cold chamber at 5 C and compresses it from 1 bar to 6. the condensation and the evaporator temperatures are 330C and − 12 0C respectively. Assume that the compression in the compressor occurs polytropically with a compression index of 1. and (iii) air circulation rate 5.8 bar and (d) the actual COP of the plant. After expansion. If the liquid emerging from the condenser is sub-cooled by 4 0C compute (i) the isentropic efficiency of the compressor. (ii) the ideal power required to produce 1 ton of ice at 00C per day from water at 27 0C and (iii) the actual power required if the actual COP of the unit is 50 % of that of the Carnot COP working between the same evaporator and condensation temperature.4 MPa. 5 kg / min of air at 30 C (ambient temperature is 25 C) and 4. 5.25. the evaporator temperature is − 15 0C and the condensation temperature is 30 0C.The evaporator operates at − 30 0C and the condenser pressure is 1. Problems on Vapour Compression Refrigeration Cycles 5. An ideal vapour compression refrigerator uses a sub-cooling cum superheating heat exchanger where the refrigerant vapour coming from the evaporator in dry saturated state is superheated by 10 0C by absorbing heat from the saturated liquid refrigerant coming from the condenser. (c) energy rejected by air to the ambient during the cooling process at 4.Capacity of the plant = 1 ton Determine (a) COP of the cycle.9:-In a refrigerator using ammonia as the refrigerant. It is then expanded in a turbine and after expansion the air flows through the regenerative heat exchanger where it exchanges heat with the air coming from the intercooler. the air enters a cold chamber where its temperature rises to 0 C and the it is compressed back to 4. The expansion is according to the law pv1.(a) Draw the schematic layout of the plant.(b) obtain an expression for the COP of the cycle in terms of the pressure ratio of the compressor and the temperature ratio of the compressor inlet temperature to the turbine inlet temperature.E.35= constant. air after compression in the compressor is first cooled in an intercooler and then passed through a regenerative heat exchanger. compute (i) the COP of the unit. If there is no sub-cooling of the refrigerant after condensation. Then the cold air is passed through the cold chamber before it enters the compressor.8 bar expand behind a piston to 1 bar.10. The vapour entering the condenser is 60 0C and the compressor piston sweeps a volume of 400 lit/minute. The vapour before entering the compressor is just dry and saturated. There is a cooling requirement of 50 tons.28 = constant. (b) capacity of the refrigerator in tons. (iii) the refrigeration effect in tons and (iv) the COP 5.7 :. What will be the tonnage of the unit? B. 5. Moist air at 40 0C.6. The pressure and temperature in a room are 101.5. (e) Specific volume of air per kg of dry air.3.325 kPa. Determine: (a) The amount of water added to the air. the air is at 45 0C and 30%RH.9. Tutorial 6 : Air Conditioning 6. Assume the total pressure of air to be 101. When the DBT is 35 0C.12. (d) Degree of saturation.2.E.4.7. determine (i) the mass flow rate of the refrigerant. PESIT B. 6. If the relative humidity is 40% determine: (a) Saturation pressure of water vapour at the dry bulb temperature.101. WBT is 23 0C and the barometer reads 750mm of Hg. Find: (a) Partial pressure of water vapour. (d) Density. © Specific humidity. At the beginning of the process.8. Air is to be conditioned from a DBT of 40 0C and a RH of 50% to a final DBT of 200C and a final RH of 40% by a dehumidification process followed by a reheat process. Determine: (a) The final relative humidity. and a relative humidity of 60% initially is cooled at a constant mixture pressure to 20 0C. Moist air is at a temperature of 21 0C under a total pressure of 736mm of Hg. 6. (ii) the COP. 6. The dew point temperature is 15 0C. Relative humidity and Enthalpy if the air were adiabatically saturated. The use of steam tables only is permitted. Relative humidity and Enthalpy of the sample. (b) Relative humidity. 6. Calculate: (a) Relative humidity. Calculate: (a) Humidity ratio. The final temperature is 30 0C . 6. Warm air is to be cooled by an adiabatic humidification process. 6. (b) The dew point temperature. Mechanical 4th Semester Course Information . Solve the problem using steam tables only and compare the answers with those obtained using psychrometric chart. Find the heat transfer rate required to warm 40 m3/min of air at 32 0C and 90 % RH to 50 0C. Air at 15 0C and 80%RH is conditioned to 25 0C and 50%RH.325 kPa and 25 0C. The barometer reads 760mm of Hg. 6.1. A sample of air has DBT of 35 0C and 25 0C respectively. © Specific humidity. Determine the amount of water added per kg of dry air.325 kPa. © Dew point temperature. Assuming the make up water is added at 15 0C determine the heat supplied during the process. (b) The final relative humidity. (iv) the power required to drive the compressor. (b) Humidity Ratio. (b) Change in specific humidity. 6. (iii) the degree of subcooling. (d) Enthalpy of air per kg of dry air. (e) Enthalpy of atmospheric air. (b) Humidity ratio. 36 R1 : Page : 1-31 % of portions covered Topic to be Covered Introduction to fluid mechanics.Mass density. specific volume. 20˚ C and 30% RH. properites of fluids .325 kPa. (c) Refrigeration in tons for an air flow rate of 0.47 m3/s and heating required in kW. Determine RH. For the mixed stream calculate: (a) Specific Humidity. (c ) The heating coil capacity and (d) The COP of the refrigeration from unit. provided with a refrigeration circuit. flows at a rate of 15 m3/min and mixes adiabatically with another stream of air at 35˚ C and 80% RH at 20 m3/min. 6.Assume that the entire process is carried out at a constant pressure of 101. (b) The temperature of air leaving the dehumidifier. (c) Relative Humidity. The effective surface temperature of the coil is 4. Surface tension. (d) Specific Volume.A Stream of air at atmospheric pressure. The return air is 300 kg / min.10. (a) Constant Dry Bulb Temperature (b) Constant Relative Humidity (c) Adiabatic evaporative process.E.4 0C. 39. capillarity Reference Cumulativ Chapter e 1-2 3 12% 12% B. specific gravity. While the make up air is 20 kg / min taken from atmosphere.11.0 properties of fluids T1: Page : 3-17 T2 : Page : 13.12. Mechanical 4th Semester Course Information .5 0C WBT. (b)Temperature. 6. The surface area of the coil is designed so as to give 12. Krishna / Ramachandra L. FLUID MECHANICS – ME 45 Faculty : V. (b) The amount of the humidification per hour. Determine the dry and wet bulb temperatures of air leaving the coil and the coil bypass factor.6 m3/min of a mixture of recirculated room air and outdoor air enters a cooling coil at 31 0C DBT and 18. The appended figure shows the air condition in a central air conditioning plant. Determine: (a) The amount of water to be removed from air. specific weight. 6. Assuming that the humidifying water is at 12˚ C. It is meant to supply conditioned air at 20˚ C Dry bulb temperature and 66% RH.13. the Temperature of the conditioned air and heat transfer per rate for the following humidifying process.005 kg of water vapor / kg of dry air as it enters an insulated room with a flow rate of 60 m3 / min. Class # Chapter title/ Reference Literature Chapter : 1. PESIT 6.5 kW of refrigeration with the given entering state of air. Atmospheric air at 12˚ C and 25 % RH is to be conditioned to a humidity ratio of 0. Find: (a) The heat transfer at the cooling coil. Derivation from R8:Page # : 132. Similitude. Compressibility.Dimensions of physical quantites. Buckingham pi theorem. Numerical fluid statics Problems T1:Page # : 23-61 Hydrostatic forces and location of T2:Page # : 142-144 hydrostatic forces on submerged & Page # : 59-77 plane surfaces and curved surfaces. Classification of fluids & regimes of flow Pressure variation in a static fluid. Euler's equation of motion R1:Page # : 233-240 along stream line. Relationship between stream function and velocity potential function. General energy and Momentum T2:Page # : 250-276 equation. Euler's equation and Bernoulli's equation for real fluids. Streak line. Chapter # : 5.220 R5:Page # : 76-92 Bernoulli's Priniciple . Types of fluid flow.0 Dimensional analysis T1:Page # : 156-173 T2:Page # : 138. Important dimensionless numbers. 172 12% 60% 28-29 B. # : 502-549 R4:Page # : 464-478 R5:Page # : 230-258 R8:Page # : 245-281 Raleigh's method.0 U tube manometers. R8:Page # : 51-80 Stability of floating bodies. 301 R1:Page Dimensional homogenity. Determination of metacentric height by experimental and analytical methods. Numerical problems. Metacentre. Lines of flow path line.PESIT 4-5 6 7-8 9-10 R4 : Page : 9-36 Bulk Modulus. Mechanical 4th Semester Course Information . R4:Page # : 171-189 Page # : 212. Numerical Problems.E. Stream line. velocity potential function for 2D flow.0 Fluid kinematics T1:Page# : 320-334 T2:Page# : 204-218 R1:Page# : 139-182 R4:Page# : 104-141 R5:Page# : 31-57 R8:Page# : 36-44 22-23 Chapter # : 4. Flow net. R5 : Page : 1-29 Viscosity and Newton's law of R8 : Page : 1-25 viscosity. R4:Page # : 43-85 R5:Page # : 104-138 Buoyancy and floatation. Pascal's law of pressure. R1:Page # : 31-134 Numerical problems. Stream function for 2D flow.0 Fliud Dyanmics 8% 48% 24-25 26-27 Introduction-Forces acting on a fluid T1:Page # : 85-110 mass. Stream tube Continuity equation in cartesian coordinates. Numercial problems Fluids flow concepts. manometers: Simple and Differential Chapter : 2. Numerical problems 12% 40% 11-12 16% 28% 13-14 15-16 17-19 20-21 Chapter # : 3.fundamentals. compressible flow T1:Page # : 262-271 R1:Page # : 636-642 R4:Page # : 442-460 R5:Page # : 535-552 Numerical problems. R8:Page # : 511-570 8% 76% 36-38 39-40 41-42 8% 84% 43-44 8% 92% 45-46 47-48 8% 100% 49-50 Literature Book Type Text Book Code T1 Title and Author Fliud Mechanics by Streeter Edition 7th B.0 Flow past immersed Lift & Drag. skin friction & form drag. bodies T1:Page # : 210-222 T2:Page # : 9971000 R1:Page # :552-556 and Page Calculation of laminar boundary layers thickness.0 Friction loss in pipe flow . 8% 68% 34-35 Viscous flow.PESIT Chapter # : 6.0 Laminar and Viscous critical Reynolds number. numerical R1:Page # :347-366 problems Chapter # : 9. R5:Page # : 406 442 Chapter # : 10. Numerical problems. venturimeter.E.Poisuille's Flow equation T1:Page # : 410-417 T2:Page # : 443-449 R1:Page # :420-450 Laminar flow between parallel R4:Page # : 318-416 stationary plates. V-notch.0 Fluid flow measurements T1:Page # : 337357 T2:Page # : 602-623 R1:Page # : 241-260 R4:Page : 223. speed of sound wave. Introduction to Isentropic flow. Orifice meter. laminar flow through pipes .Hagen . Reynolds number. Pitot tube.246 R5:Page # :155 -171 30-33 Application of Bernoulli's equation. Numerical problems R5:Page # : 362-378 R8:Page # : 598-602 Chapter # : 8. Chapter # : 7. displacement & momentum # :591-624 R4:Page # : 347-377 thickness.minor loss Flow through pipes in pipe flow. Mechanical 4th Semester Course Information . T1:Page # : 182-199 T2:Page # : 391-417 Darcy's & Chezy's equation. Mach number.0 Sonic velocity. Energy line & Hydraulic gradient line. Boundary layer concept. Gasiosek and John.5 mm. Find the force and power required to maintain this velocity.Garde and Dr. 1.J. The oil film enclosed between the shaft and the bearing has a viscosity of 0. 6. Calculate the power lost in the bearing for a sleeve length of 90 mm.. * Define the following fluid properties giving their SI units. What is the power lost in friction. Janul and M. Bansal Fluid Mechanics by Agarwal Fluid Mechanics by Binder Engineering Fluid Mechanics by K. The shaft is of diameter 0. if the shaft revolves at 240 rpm? Find also the torque developed. (6) 4.1 m2 area is pulled at 400mm/s relative to another plate located at 0. (6) Explain the terms Compressibility and Bulk Modulus of Elasticity. 9. * State Newton’s law of viscosity.0 poise.A.K. the fluid separating the two being water with μ = 1 centi-Poise.E. Mechanical . (6) A flat plate 0. (6) The dynamic viscosity of an oil used for lubrication between a shaft and sleeve is 6.Mirajgaoker Introduction to fluid Mechanics and Machinery by Som and Biwas Fluid Mechanics by John F. A standard bearing 500 mm long and 151 mm in diameter encases a shaft of 150mm outer dia. 8. Hence define Absolute viscosity.A. R1 R2 R3 R4 A Text Book of fluid Mechanics and Hydralics by Dr.PESIT T2 Reference Book Fliud Mechanics and Hydraulics by Jagadishlal Dr. Give its SI unit? (4) 3.9 poise. Distinguish between Real and Ideal fluids.Swaffied Fluid Mechanics by White 2nd 4th 5th QUESTION BANK Chapter I: Properties of Fluids 5. * Define a fluid.R. 7. (3) 2.L.15 mm from it. (2) 4th Semester Course Information B. The thickness of the oil film is 1. and rotates at 190 rpm.4 m.J.Kumar R5 R6 R7 R8 Engineering Fluid Mechanics by Dr. Pressure (i) (ii) Specific mass (iii) Specific Weight Relative density (iv) (v) Kinematic Viscosity Surface tension (vi) (vii) Capillarity (2 marks each) What do you understand by the term capillarity? (2) Mention the fluids in which this fluid phenomenon is observed (2) Derive an expression for the capillary rise.Douglas.R. 20. Also determine the shear stress at these points if the absolute viscosity. (6) 12. The volume of the liquid decreases by 0. 18.58 Stokes and 2 respectively. (2+6) 23. * Determine the bulk modulus of elasticity of a liquid if the pressure of the liquid is increased form 70N/ cm2 to 130n/cm2.42 kg/m3. The tube is held vertically and is partially filled with liquid of surface tension 0. What will be the % age increase in the value of height if the dia of the glass tube is 2mm. find the kinematic viscosity of the oil. (b) Viscosity of liquids decreses on heating whereas that of gases increases. *Differentiate between (a) Density and relative Density (b) Absolute viscosity and Kinematics Viscosity (c) Absolute pressure and Gauge pressure (d) Simple manometer and differential manometer.071 N / m. (4) 24.2 N/m2 and the velocity gradient is 0.E. * Distinguish between Newtonian and Non-Newtonian Fluids.073 N/m). (2) 21. μ =8.* A bubble of air is released at a depth of 1m in tank of water. If the equation of velocity distribution of a fluid over a plate is given by v = 2y-y2 in which ‘v’ is the velocity n m/s at a distance ‘y’ measured in meters above the plate. what is the velocity gradient at the boundary and at 75 mm from it. * What are the characteristics of the fluid properties to which the following phenomena are attributed? (a) Rise of sap (liquid) in a tree. Mechanical 4th Semester Course Information .15%.0196 N / cm2. where σ = Surface tension. *Give technical reason for (a) Viscosity of liquids decreases on heating whereas viscosity of gases increases on heating (b) Water will wet clean glass but mercury will not. * Give technical reasons for the following : (a) certain insects are able to walk on the surface of water. * Explain how certain insects are able to walk on the surface of water. The surface tension of water drop let in contact with air at 200 . 15. 19.G. * At a certain point in castor oil film. calculate the gauge pressure inside the bubble( Surface tension for the air water interface is 0. greater than the outside pressure. Calculate the mass density of the liquid if the estimated difference in the level of two menisci is 12.216s-1.5mm.2mm.10. If the mass density is 959. Calculate the diameter of the droplet. (4) (4) 14. Take surface tension of water as 0. Prove that the relationship between surface tension and pressure inside a droplet in excess of inside pressure is given by P=4 σ/d. 21. Calculate the absolute viscosity of the fluid in i) Ns/m2 ii)poise. is 0. (c) Rising of a ship as it sails fresh water to sea water.05 N/m and zero contact angle. (d) A needle heavier than water can float if it is placed lengthwise on the surface of water. The Kinematic viscosity and S. PESIT (4) 22. by means of a graph. the shear stress in 0. (4) 11.* State Newton’s law of viscosity.075 N / m and α = 600.6 poise. ( 4) 13. Determine the height of water which will rise in the tube. A U-tube is made up of two capillaries of bore 1mm and 2mm respectively. of a certain liquid are 5. (6) 17. (6) 16. If the diameter of the bubble at the time of release is 0.* With the help of a neat plot ( stress vs. (b) Spherical shape of drop a drop of a liquid. The pressure inside the droplet of water is 0. A Capillary tube having an inside dia of 4mm is dipped in water at atmospheric temperature of 200 C. rate of strain) show the characteristics B. d = dia of droplet. (6) 14. Find the force exerted on the gate and the position of center of Pressure. (6) 22. If the difference of levels of water columns in the two limbs is equal to 0. (8) 3. (4) 15. (6) 7. (4) (2) 10. Find the reading shown by the differential Hg gauge.8 flows upwards though a vertical pipe.75 (ii) m of Hg of SG 13.12m.18 N/mm2. (4) 4. It is required to float in oil of specific gravity B. Give its applications. (6) 13. which has the form of an inverted ‘U’ tube. * Define the terms Total Pressure and Center of Pressure 11. A hollow cylinder of specific gravity 0. What is the absolute pressure of that fluid in terms of the following units. (a) Elastic solid (b) Ideal fluid (c) Newtonian fluid (d) Ideal plastic (e) dilatant Fluid (f) Pseudo plastic fluid. State and prove Pascal’s Law.behaviour for the following materials. 6. Indicate their relative positions on a chart. Prove BM = I / V . (6) (2) 17. Find the thrust on the surface and the depth of center of pressure. The space above the water in the two limbs of the manometer is filled with toluene of SG 0.6 ( 2+ 4) 2. Specific Gravity of Wood is 0. What is the corresponding difference of pressure in N/m2. A flat angular ring of 30m ext. Two pressure points in a water pipe are connected to a manometer. * Show that for a vertical Lamina immersed in a liquid. The pressure of a fluid is recorded as 60mm of Hg vacuum.6 . *Petrol of SG 0. (4) 21. * What are the conditions of equilibrium of a floating body . What is the atmospheric pr. * Derive an expression for the total pressure and center of pressure for an inclined surface immersed in a liquid.5m and an altitude of 2m lies in a vertical plane.6m and an inner diameter of 0. Distinguish between a simple and differential manometer. Show that the pressure at a point depends on the head of liquid above it in a static liquid 8. (6) 18. Atmospheric pressure measured at a place showed 700 mm of Hg. Vacuum Pressure and absolute Pressure. dia is immersed in water such that its top most edge is 1m below and the lower most edge is 2m below the free surface of water obtain the location of center of pressure of the ring and the total pressure. * (a) Distinguish between Pressure head and Pressure intensity (b) Convert a Pressure head of 15m of water to (i) m of oil of SG 0. Give examples.56.Explain with reference to the metacentric height . (6) Chapter II: Fluid Statics PESIT 1. between A and B is 0.E. A triangular gate which has a base of 1. A wooden cylinder of diameter “d” and length 2d floats in water with its axis vertical . (3) (3) 5.8.Is the equilibrium stable ? Locate the metacentre with reference to water surface. * Define Metacentre and metacentric height . intensity in N/m2 and in metres of H2o if the SG of Hg is 13. (8) 9. dia and 15 m int. If the difference of pr. (6) 20. Connections are led from A and B to a ‘U’ tube containing Hg. (6) 12. (i)N/m2 (ii) m of H2O. *Explain the method of determining the metacentric height of a floating body experimentally. A trapezoidal plate having its parallel sides equal to 2a and a at distance H apart is immersed vertically in a liquid with 2 a side uppermost and at a distance H below the surface of the liquid. * Explain with sketches the stability of a submerged body. The vertex of the gate is 1m below the surface of a tank which contains oil of SG 0. 19. * With usual notations.3m and has its ends open. (6) 23. B being 300 mm higher than A. A and B are two points in the pipe. the center of Pressure always lies below the centroid.55 has an outer diameter of 0.875. (6) 16. Mechanical 4th Semester Course Information . * Derive an expression for hydrostatic force on an inclined submerged plane surface and depth of centre of pressure. * Define the terms Gauge Pressure. 5m side and hinged in the middle as Shown. show that ‘l’ cannot exceed 0.6 and diameter D and length L is required to float in oil of specific gravity 0.5m . The gate is a square of 0.05 H2 ρw=1000kg/ m3 32. 26. *Determine the pressure difference Pa-Pb for the system shown below. Find the metacentric height and position of C.6 is required to float in an oil of specific gravity 0.8 ρw H1 ρ3=0. (8) 24.84 Calculate the maximum height of the cylinder so that it shall be stable when floating with its axis vertical . Explain the terms buoyancy and centre of buoyancy . 27. where ‘p’ is the pressure intensity at a depth ‘h’ from a liquid surface of specific weight ‘γ’. A ship 60m long and 12m broad has a displaced water of 19620kN. (6) 31. (3) (2) 25. A weight of 294. If the diameter of the cylinder is ‘d’ and length ‘l’.E. What is the significance of Metacentric height . (10) 30. For the element derive the hydrostatic equation in the form p=γ h.Find also the depth to which it will sink .6 Diameter D H1=0.3kN is moved across the deck through a distance of 6. indicating the pressure on the faces. the centre of buoyancy is 2. The moment of inertia of ship at water surface is 75% moment of inertia of the circumscribing rectangle.* Determine the minimum force F.2m H2=0. *A wooden cylinder having a specific gravity of 0. Find the L / D ratio for the cylinder to float with its longitudinal axis vertical. required to keep the gate closed.0. *Derive the criterion for stability of a floating body. in the Figure below.The ship is tilted through 5 . (6) 28.8. B. Mechanical 4th Semester Course Information . The centre of the gate is 1m below the water surface. (8) 29. (4) PESIT Diameter Diameter D ρ1=.75m below waterline. A wooden cylinder of specific gravity 0. *Draw a rectangle parallelopied element of a fluid at rest.817d for the cylinder to float with its longitudinal axis vertical.9. Take specific weight of sea-water as (6) 10104N/m3 .G of the ship . * Obtain an expression for the continuity equation for a three dimensional flow. What do you understand by the term continuity equation.5 H D Hing F Wate H=1m D=0.5*0.* calculate the horizontal and vertical forces.E. Mechanical 4th Semester Course Information . 3. 4. iv) Laminar and turbulent flow. (8) H=5m W=5m R=2m H W R Chapter III: Fluid Kinematics 1. * Define the terms : 1)Velocity potential 2) Stream function (4) 7. * Distinguish between i) Steady flow and unsteady flow ii) Uniform flow and non uniform flow iii) Compressible and incompressible flow. W is 5m. R is 2m. Explain in brief Lagrangian method and Eulerian method of studying fluid in motion. (8) (4) 2. * Define the following : (i) Path line (ii) Streak line (iii) Stream line (iv) Stream tube (8) 5. Determine whether the continuity equation is satisfied by the following velocity components for incompressible fluid: B.5m 33. the level of water in the tank. The radius of the cylinder. due to the gauge pressure of water On the cylinder portion of the tank shown below. H is 5m and the width of the tank. The tank is open at the top.PESIT Gate ( 0. (6) 6. Derive an expression for Q by using Buckingham's π theorem. (4) Chapter IV: Dimensional Analysis PESIT (3) 1. rotating at speed N.(10) 10. The drop in pressure due to an obstruction in a pipe depends on the pipe diameter. *Assuming that the rate of discharge Q of a hydraulic machine is dependent upon the mass density ‘ρ’ and viscosity μ. D is the diameter of the orifice . [i] Euler's Number [ii] Weber Number 7. (8) 9.2 y . diameter of rotor & discharge. (6) 9. (2) 5. Vo and D as repeating variable find all the revelant π groups. in a fluid of viscosity μ and density ρ in a turbulent flow.x3 /3. * Briefly explain [a] Geometric Similarity [b] Kinematic Similarity [c] Dynamic Similarity (3) 3. the diameter of the impeller D. v =y3 .d.ω. (2) 12.y3 .m) Where. μ / ς VH ® where H is head causing the flow.y and z are in metres and t in seconds. μ is the viscosity . ς is the mass density and g is the acceleration due to gravity. Vo is the initial velocity of the ball. Express η in terms of dimensionless parameters. Mechanical 4th Semester Course Information . w = -3 x2 z .z3 . angular velocity. (4) 8. μ / . ν/ND2] H being the head and ν the kinematic viscosity of the fluid. * The rate of discharge Q of a centrifugal pump is dependent upon density ρ of the fluid. * State Buckingham’s π theorem.* Given V= (xy+2zt)I+(2y2+xyt)J+(12xy)k where x. D is the diameter of the ball ‘d’ is the diameter of the dimples.theorem.1. Viscosity of fluid and the characteristic length of obstruction.z2 x . (2) (2) (b) 1D vs. (6) 6. What is similitude. (4) (b) What is the equation of the steam line passing through (1. Express the pressure drop in terms of dimensionless parameters. obtain an expression for the frictional torque T of a disc of diameter D. * What you mean by upper critical and Lower Critical Reynolds number.*The distance traveled by a golf ball in still air. 12.3 y2 z + z3/ 3.u = x3 .μ. * By Buckingham’s π theorem. For dynamic similarity find the ratio of the initial velocity of the model to that of the actual ball. Using Buckingham's π. (3) 4.D. Write a note on Model studies. is known to be a function of the following: L=ƒ (Vo. pump speed N (rpm).E. ρ is the density of air ω is the angular speed of the ball. average velocity. dynamic viscosity. Obtain an expression for the stream function. The efficiency η of a fan depends on density. (6) 8. (2) B. * Compare and contrast the following: (a) Path line vs. (4) 10. mass density. (a)using ρ.1). show using Buckingham’s π theorem that it can be represented by Q= ND3 φ [9H/N2D2. the pressure P & the viscosity of fluid μ. Define the following non-dimensional numbers. 11. The velocity components in a two dimensional flow field for an incompressible fluid are as follows : u = y3 / 3 + 2 x . determine ax the x component of the acceleration of the fluid particle at (1. show that the velocity through a circular orifice is given by V = √ 2 g H X Φ 〈 D / H . (8) (b) Experiments are to be conducted on a model ball that is twice as large as the actual golf ball. The fluid in both cases is air at STP. L . streak line. 3D flow. (8) 11.1) at t=1s. 2.x2 y and v = x y2 . μ is the viscosity of air and m is the mass of the ball.* The stream function for 2D incompressible flow is given by: ψ= xy3+x2y (a) Find φ if it exists. (8) 8. If the pressures at A and B are 200KN/m2 and 152KN/m2 respectively and the discharge is 150l/s.5m above the datum line. The differential U-tube manometer shows a gauge deflection of 25 cm. In order to determine experimentally the co-efficients of contraction.G 0. Take Cd= 0. (3) th B. the following data were collected. 14. (6) (8) 4. Name the different forces present in a fluid flow. * State and prove Bernoulli’s theorem making clearly the assumption’s made. (8) (2) 7. A pipe of diameter 0.6m. Cv and Cd. (6) 5. Clearly explain the meaning of the terms in it.39m from vena-contracta. Find the discharge of water through the meter. Mention the devices that work on the above principle. Mechanical 4 Semester Course Information . velocity and discharge for a 100mm dia sharp orifice in the side of a tank .00131m3/s under a head of 1. calculate the total energy at point A in m of oil. (6) 11.98.8 changes in diameter from 300mm at position A to 500mm diameter at position B which is 5m higher. vertical distance y.PESIT Chapter V: Fluid dynamics 1. Obtain an expression for the coefficient of velocity for a sharp edged orifice located in the side of a tank in terms of horizontal distance x. Q=0. * Explain with a neat sketch the working of pitot's tube with inverted U tube differential manometer. Take Cd of venturimeter as 0. State the assumptions made. (2) (4) 13.E. For the Euler’s equation of motion.07m. Obtain Cc. Derive an expression for the discharge through a venturimeter. A horizontal venturimeter with a inlet diameter 200mm and throat diameter 100mm is used to measure the flow of water. A jet of water issuing from a 25mm dia orifice in the side of a tank drops 0. What do you understand by Vena-Contracta. 5.25 diameter pipe carries an oil of SG 0. H= 3. (10) (2) 6. If the point A is 3. (2) 2. which forces are taken into consideration?. The pressure at inlet is 150KN/m2 and vacuum pressure at the throat is 400mm of Hg.9. Clearly state all the assumptions made.0385 m3/ s. Distinguish between venturimeter and orifice meter.42mm. 7. (8) 4. (4) 3. * Draw neat sketches of venturimeter and orifice meter labeling all the main parts. determine the loss of head and direction of flow. How are they related. Cv and Cd.98. traveled by the jet and head H over the orifice . If it discharges 0. (4) 12. 8.3m carries water at a velocity of 20m/s. determine Cc. while the datum head at A and B are 25m and 28m. (3) 9. Define the hydraulic co-efficients of an orifice.48m in a horizontal distance of 1. (3) 2. Find the loss of head between A and B. Derive an expression for the velocity for the same pitot's tube. (6) Chapter VI: Fluid flow measurements 1. The pressure at the points A and B are given as 350KN/m2 and 300 KN/m2 respectively.8 at the rate of 120 l/s and the pressure at a point A is 19. * Derive an expression for discharge over a V-notch. 9. A pipe line carrying oil of S. What is a venturimeter. Calculate the discharge of the oil.* A 0. Distinguish between orifices and notches. * Mention the advantages of V-notch over rectangular notch. * Derive Euler's equation along a streamline and reduce it to Bernoulli's equation. (4) 3.G. (6) 10. Dia of jet at vena-contracta =78.*Derive Bernoulli’s equation using an infinitesimal stream tube.62kN/m3. 0. A 30 mm X 15 mm venturimeter is provided in a vertical pipeline carrying oil of S. Write Bernoulli’s equation of motion. (6) 6. 6 litres 17. Determine the discharge through the pipe if f = 0.* Derive the head vs. State all the assumption made. when the head over the notch is 0. * What are minor and major losses? Derive an expression to evaluate the loss of head due to sudden contraction. *Define Reynolds' Number.E. based on the following points (a) Cost and ease of manufacture (b) Accuracy (c) Energy loss (d) Sensitivity ( output manometer deflection per unit flow rate) (4) 19. (4) 16. * For turbulent flow through a pipe. Write the expressions for the loss of head due to the following in pipes: Entrance to the pipe. (6) 20. sudden expansion. (10) 5. Write short notes on Water hammer. Determine the pressure gradient. (4) 14.9m dia. Derive an expression for the equivalent size of a compound pipe. discharge relation equation for a V notch.5m. mean velocity and Reynolds' number.s N/m2.225m in diameter the difference in water levels being 7. Find the depth and top width of a V-notch capable of discharging a maximum 0. 4. What is a compound pipe. Determine the flow through the pipe in litres / min if f = 0. sudden contraction.03. Mechanical 4 Semester Course Information . It is found that the depth of water in the tank increases by 0. * Distinguish between Laminar and Turbulent flow. The pressure intensity at the inlet is 140 kPa while at the throat is 80kPa. (6) 9.225m in diameter the difference in water levels being 7. Derive an expression for the loss of head due to friction for the laminar flow between two parallel plates. Assume that 2% of the differential head is lost between the inlet and the throat. / s. (6) 10. Determine the Cd of the notch. (5) 6. (6) 3. Two reservoirs are connected by a pipe 2250m long and 0. 2d & 3d respectively and they are of the same length l. In an experiment on a 900 V-notch .5m.65m in 16. (6) 12.*The inlet and throat diameters of a vertically mounted venturimeter are 300mm and 100mm respectively. (8) Chapter-VII: Flow through pipes & Chapter-VIII: Laminar & Viscous Flow PESIT 1. The throat is below the inlet at a distance of 100mm.407 H5/2. Two reservoirs are connected by a pipe 2250m long and 0. (3) 13. the flow is collected in a vertical cylindrical tank 0. Assuming f to be the same for all pipes. (4) 7. *Compare a Venturimeter and an orifice plate. (6) 18. It’s Cd is same as that of a similar (in material and sharpness of edges only) right angled V-notch for which Q=1.8s. (8) 11. Pipe fittings. Calculate the flow rate. (6) 8. Also find the % increase in the discharge if for the last 600m a second pipe of the same diameter is laid alongside the first. their diameters being d. Exit from the pipe.0075.7m3/s and such that head the head shall be 75mm for a discharge of 5.2m. What is its physical significance? (4) 2. For the flow of fluid through a circular pipe show that the friction factor f = 16/Re. Two reservoirs are connected by three pipes laid in parallel. The mass density of the liquid is 900kg/m3. * Explain the terms (i) Critical Reynolds number Critical velocity (ii) (iii) Transition Zone (6) th B. A horizontal pipe 50mm diameter carrying glycerine has shear stress at the pipe boundary as 196.15. derive Darcy’s equation for the head loss. determine the discharge through each of the larger pipes if the smallest pipe is (6) discharging 1m3/s. R and S.01 poise. 4. laminar.4. the pressure loss per unit length. Define Mach No. What should be the dia of the supply pipe. What is its significance. Shear stress at the plates.2 m/s.4 for air. Water at 15o C flows between two parallel plates at a distance of 1. fully developed flow of an incompressible fluid in a circular pipe.6 mm apart.* Derive the Darcy Weisbach equation for the loss of head due to friction in a pipe 16. Determine the maximum velocity .14 J/ kg o K and k = 1. 17. Take Chezy’s constant as 45. (8) 5. The value is kept half open and the entry loss into the pipe is negligible PESIT Ho smooth pipe Rough pipe Vexit Value kept half Chapter X: Introduction to compressible flow & Chapter IX: Flow past immersed bodies 1. Derive an expression for velocity of sound in a fluid in terms of bulk modulus. The viscosity of water at 15o C is given as 0. The loss of head due to friction in the pipe line is 12m.*Water is supplied to a town having a population of 1 lakh from a reservoir 6 km away from the town and it is stipulated that half of the daily supply of 150 litres per head should be delivered in 8 hours. Assume temperature of air as 15o C.065 N/m2 and temperature . (4) 2. (8) B.*Starting from an appropriate control volume derive the expression for the velocity distribution for steady.*What are hydraulic gradient and total energy lines. show that the friction factor ƒ=2gDhf/LV2 is 64/Re for this flow. find the velocity of projectile. (4) 6. (2) 19. (8) 18. if the average velocity is 0.*In the Chezy equation V=C(RS)1/2.15. 21. (4) 3. A projectile travels in air of pressure 0.*Derive the expression for the energy loss due to a sudden expansion in a pipe from area A1 to area A2(>A1). in terms of the inlet dynamic pressure ½ ρV12 Clearly state all the assumption made. Find the velocity of bullet in standard air if the Mach angle is 30o. Derive an expression for the compressible flow of a fluid for (i) Isothermal process (ii) Adiabatic process.E. Mechanical 4th Semester Course Information . (6) 20. K = 1.*For the system shown below qualitatively sketch the hydraulic and energy grade lines. If the Mach angle is 300C. (10) Further. R = 287 J / Kg K. Take R = 287. explain the physical meaning of the terms C.70C. 282 N/m3 The plate is kept at such an angle that the coefficient of lift and drag are 0. determine the speed of the aeroplane.15 respectively. The specific weight of air is 11.75 And 0.E. Determine: (a) Lift force (b) Drag force (c) Resultant force (d) Power excited by air stream on the plate. L B. (b) Lift force and drag force (c) The physical significance of displacement thickness and momentum thickness. * Explain the effect of area variation on one dimensional compressible fluid flow. Momentum thickness.8 Mach at an altitude of 20Km above the ground How far ahead the plane will be when one hears the sonic boom on the Ground? (8) 19. 20.4 and R = 2875/ kg-K.1. drag and skin friction drag. (6) (b) Calculate the pressure felt at the nose of the aircraft. (6) 8. Assuming R = 1. Mechanical 4th Semester Course Information .7.4.(6) * These questions have appeared in past VTU question paper PESIT KINEMATICS OF MACHINE–ME 44 Faculty: Sunith Babu. An aeroplane is flying at an altitude of 15 Km where the temperature is -500. Define [a] Drag [b] Lift [c] Drag Co-efficient [d] Lift Co-efficient 14.6. Displacement thickness. the air is isentropically brought to rest at the Nose.*The velocity distribution in a boundary-layer is given by: u=U∝sin(π/2y/δ) 0≤y≤δ u=U∝ y≥δ (a) Determine the displacement and momentum thickness if δ=cm and U∝=10m/s (b) What would happen to the answer of part (a) above. The speed of the plane corresponds to a Mach No. in the Reference frames of the planes.0 is observed directly over head at a height of 10 km.*Experiment were conducted in a wild tunnel with a wind speed of 50 km/hr on a flat plate of size 2m long and 1m wide. 16.6kg/m3 respectively.*Distinguish between the following: (a) form. (8) 11. if the shape of the Velocity profile remains the same and δ remains at 1cm but U∝ is doubled. * Explain (i) Lift (ii) Drag (iii) Wake region (iv) Boundary layer separation (8) 13. *Sketch the nature of propagation of disturbance in compressible flow when Mach number is more than one and hence define mach angle and mach cone. Derive an expression for velocity of propagation of elastic wave in an isothermal medium. The density and pressure at that altitude are 0. γ is 1. assuming that.(10) 18. (6) 9. Define [a] Aero foil [b] Cord length [c] Angle of attack (5) 15. (6) 10. (6) 17. *Distinguish between friction drag and pressure drag.*A Supersonic plane travels at 1. * A jet fighter flying at Mach number 2. Define : Boundary layer thickness. (4) 21. How much distance it would cover before the sonic boom is heard on the ground? 12. (a) How long after it flies directly overhead will the sonic boom be heard? R for air is 287 J/kg/K and the ratio of specific heats.*An aircraft is flying at a uniform speed of 1Km/s at a height of 2 Km. 21. (IV) Toggle mechanism.0 Kinematic chain and Inversion T1: 20 .0 Topics to be covered Definition – Link or element. 2. 11.PESIT Class # Chapter Title / Reference Literature Chapter #: 1. 5 6.30 R1: 15 . 17. Grubler’s criterion (without derivation). 3. Mechanical 4th Semester Course Information .0 Velocity and Acceleration Analysis of Mechanisms T1: 31 . Machine Kinematic Chain and Inversion: Kinematic chain with three lower pairs. 8. 12.52 R1: 21 . Introduction T1: 1 . Inversion. Four bar chain. 15. Mechanism. Single slider crank chain & Double slider crank chain and % Of Portions Covered 1. (III) Intermittent motion mechanisms – Geneva mechanism and Ratchet & Pawl mechanism. 20. Hooke’s joint and Ackerman steering mechanism 13 % 25 % Chapter #: 2. 14. 18. Pantograph. 7.30 R1: 95 . 13. 19.19 R1: 3 – 14 Chapter #: 1.123 Chapter #: 3. Mobility of Mechanism.0 Mechanism T1: 22 . 9. Whitworth mechanism and Crank & slotted lever mechanism. Kinematic chain. 16. Paring of element with degrees of freedom. 10. (II) Straight line motion mechanisms – Peacellier’s mechanism and Roberts’s mechanism. Coriolis components of acceleration 15 % 40 % B.21 4% 4% 8% 12 % Their inversions Mechanisms: (I) Quick return mechanisms – Drag link mechanism.E. 4.23 Velocity and Acceleration Analysis of Mechanisms (Graphical Methods): Velocity and Acceleration Analysis by vector polygons – Relative velocity and acceleration of particles in a common link. Relative velocity and accelerations of coincident particles on separate links. 26. 38. Tooth load and torque Calculations in epicyclic gear trains. 25. 35. Epicyclic gear trains.383 R1: 163 – 187 Simple gear trains.73 R1: 24 – 71 Definition. Chapter #: 5. Interference in involute gears. 23.0 Velocity Analysis by Instantaneous center method & Klein’s construction T1: 53 . Comparison of involute and cycloidal teeth 15 % 75 % T1: 326 . 31. 24. 32. 44.PESIT 22. 39. 37. 34. 42. Characteristics of involute action. Definitions. 29.0 Gear Trains Chapter #: 6. Back lash. Arc of Contact. Mechanical 4th Semester Course Information .221 Chapter #: 7. 36. 41. 27. Path of Contact. Kennedy’s Theorem Determination of velocity using instantaneous center method Analysis of Velocity and Acceleration of single slider crank mechanism by using Klein’s construction 12 % 52 % Velocity Analysis by Complex No And Loop Closure Equation R2: Velocity and Acceleration Analysis by Complex Numbers: Analysis of A) Single slider crank mechanism by 1) Loop closure equations 2) Complex numbers B) Four Bar mechanism 1) Loop closure equations 2) Complex numbers 8 % 60 % 30. Differential mechanism of an automobile 12 % 87 % B. 40. T1: 383 .0 Spur Gears Law of gearing.E. 43. Algebraic and tabular methods of finding velocity ratio of epicyclic gear trains.414 R1: 201 . Involutometry. Compound gear trains for large speed reduction.0 Chapter #: 4. Contact ratio. 33. 28. Methods of avoiding interference. Rattan Tata Mc Graw Hill / Eighteen / 1998 T2. 51. Chapter #: 8. Uniform acceleration & retardation and cycloidal motion 13 % 100 % Learning Resources for the Subject Prescribed Text Books: Code T1. 46. S. Mechanical 4th Semester Course Information .162 Types of followers. 50. 47. 49.238 R1: 124 . Disc cam with reciprocating follower having knife edge. Title Author(s) Publisher / Edition / Year Theory of Machines – S. Roller and flat faced follower. 48. S. Kinematics of Machines A.0 Cams T1: 195 .PESIT 45. 52. Velocity and Acceleration time curves for cam profiles. Displacement.E. Uniform velocity. Mechanism and machine J. Rao New Age / Second / 2003 Prescribed Reference Books: R1. disc cam with oscillating roller follower. Follower motions including SHM.S Ravindran Sudha Publication / Fourth / 2004 Guidelines for Quick Study* [ACTUAL EXAM PATTERN MAY VARY] Chapters 1 and 2 are theory type hence maintain descriptive answers in the exams with neat sketches Chapters 3 and 8 are to be solved in the Drawing Sheets hence practice problems in Drawing Sheet only Chapters 4 5 6 7 mainly contains problems of 15 to 20 marks while theory only 5 marks B. Explain the construction of Oldham’s coupling and state for what purpose it is used* (6) 12. Describe Peacellier’s mechanism with a suitable sketch* (6) 15. What is a Pantograph and what are its uses? With neat sketches explain its working principle * (6) (iii) Double slider crank chain and its inversions (iii) Crank and slotted lever mechanism 17.PESIT QUESTION BANK LINKAGES AND MECHANISMS: 1. State and prove the condition that must satisfy by the steering mechanism of a car in order that the wheel may have pure rolling motion when rounding a curve? (10) Describe toggle mechanism. Mechanical 4th Semester Course Information 23. . * 3. Distinguish between complete. Define a Kinematic pair.E. c) Sketch & explain the working of a ratchet Mechanism (10) 25. The driving shaft rotates at a uniform speed of 120 rpm. Acceleration. Define mobility of a mechanism and write the Grubler’s mobility equation for planar mechanism* (4) 8. What are its uses * (4) What is a double Hooke’s joint? (4) 22. The driving shaft rotates at a uniform speed of 300 rpm and the angle between the shafts is 200. Two shafts are connected by a Hooke’s joint. Explain the various types of Kinematic pairs. Explain the working of an Ellipse Trammel and show how is it useful in drawing an ellipse (10) 11. 21. Find the maximum torque which will B. 19. Describe the following quick return mechanism* (10) (i) Drag Link (ii) Witworth 13. The driven shaft operates against a study torque of 150 Nm and carries a flywheel whose mass is 45 kg and the radius of gyration is 140 mm. Describe Roberts approximate straight line motion mechanism with suitable sketches* (4) 16. What are straight-line motion mechanisms? How are they classified* (6) 14. Explain the following terms with examples (i) Element (ii) Link (iii) Kinematic pair (iv) Mechanism (v) Inversion (vi) Machine (vii) Mobility (viii) Degree of Freedom* (16) (4) 2. Differentiate between (i) Machine and Mechanism (ii) Machine and structure*(8) 7. A Hooke’s joint connects two shafts whose axes are inclined at 1500. Define the following (i) Lower pair (ii) Higher pair* (4) (4) 5. 19. 20. Find the maximum and minimum speed of the driven shaft and its max. Sketch and explain the following* (12) (i) Four Bar Chain and its inversions (ii) Single slider crank chain and its inversions 10. Define Kinematic chain and how does it differ from a mechanism * 6. Write short notes on Kinematic chain with three lower pairs* (6) 9. incomplete and successful constraint of the relative motion between the two links (4) 4. State the condition to be satisfied in double Hooke’s joint in order to provide a uniform velocity ratio (8) Write short notes on Ackermann steering gear * What is Hooke’s joint and what are its application* (6) (4) What is intermittent mechanism? Explain the following intermittent motion Mechanism (i) Geneva (ii) Ratchet* (6) 24. (10) For the four bar mechanism shown in figure – 3. The crank rotates at 400 rpm. position of the crank = 45 degree with IDC. determine the acceleration of the slider. BC & CD are 90mm. 180mm & 180mm long respectively. which is 250 mm long. The driving rank AB = 0. RS = 430mm. In a slider crank mechanism. The crank is rotating at a speed of 10 rad/s and the crank is at 450 from IDC. . The crank is 150mm and the connecting rod is 600mm long. Find the velocity and acceleration of point ‘P’ midway between B and C When the angle BAD =1350 and AB rotates at a speed of 300 rpm. b) The crank of a reciprocating engine is 60mm long and connecting rod is 240 mm long. Find the velocity and acceleration of both piston and the angular velocity and angular acceleration of the connecting rod when the crank is 300 from IDC by Klein’s construction method. OP = 240mm. A link ABC of a mechanism shown in figure – 4 is in motion. The crank rotates at 150rpm. the crank is 50mm long and the connecting rod is 150mm long. rotates at 20 radians per second.VELOCITY AND ACCELERATION IN MECHANISMS: PESIT be exerted by the driving shaft. The crank AB rotates at 100 rpm and an angular acceleration 100rad/sec2 at the instant when the crank AB makes an angle of 600 to the horizontal. a reciprocating engine mechanism. angular acceleration of link 3 when crank 2.5 rad/sec & has an angular acceleration of 20 rad/sec2. (10) which the crank makes with the IDC. The Follower link CD = 0. At the instant shown. a reference line (08) 10.5cm x-x is parallel to AB.3m. At what value of ‘α‘ will the total fluctuation of speed of the driven shaft be limited to 24 rpm (12) 26. The links AB. speed of the engine = 450rpm CW. * (08) Determine the velocity and acceleration of the piston by “Kleins Construction” for a 6.E. is 300. AR = 165mm. (10) Derive analytically the expression for the velocity and the acceleration of the piston in 7. (15) th B. (16) A four bar chain mechanism ABCD is made up of 4 links pin jointed at ends.6 m/s in the direction shown and ‘B’ moves with a speed of 0. AB = BC = AC = 0. (4) b) A four bar chain ABCD as a fixed link AD = 1m. By kleins construction determine: i) Velocity of piston ii) Acceleration of the piston iii) Angular acceleration of the Connecting rod. at a crank angle of 450 from IDC position. 9. AD is fixed 4. determine the acceleration of C and 5. (10) 8. Find the degree of freedom of the following mechanism shown in figure – 1 * (4) 27. the angular acceleration of the link AR. (16) 2. OA = 150mm. Mechanical 4 Semester Course Information 1. Determine (I) linear velocity and acceleration of the mid point of the connecting rod (ii) Angular velocity and acceleration of the connecting rod. ‘A’ moves with 0. Find the velocity and the acceleration of the piston and angular velocity and angular acceleration of the connecting rod when the angle. The crank of a slider crank mechanism rotates CW at a constant speed of 300 rpm. In a with worth quick return mechanism as shown in figure – 2. link.2m. steam engine for the following specification: Stroke of piston = 600mm.5 m/s/ find the magnitude and direction of (i) Velocity of C and (ii) angular velocity of ABC. Derive analytical expressions for velocity and acceleration of the piston in a reciprocating engine mechanism.6 m and the connecting link BC = 1. Find the angular velocities and angular accelerations of links BC & CD. Ratio of length o connecting rod to crank length = 5. (10) a) Write a brief note an instantaneous center of rotation. If the crank OP rotates at an angular velocity of 2. The crank of a reciprocating engine is 90mm long and the connecting rod is 360mm long. RS. (10) 3. by KLEIN’S construction. Find the velocity and acceleration of the piston and the angular velocity and angular acceleration of the connecting rod. when the crank is 30 degrees from inner dead center. What is instantaneous center? Locate all the instantaneous center for a single slider crank mechanism and show how velocity of slider is determined? (08) Velocity and acceleration analysis by complex method: 11.10 is rotating clockwise at a constant speed of 100 rad/sec. BC = 180 mm CD = 180 mm. The driving rank AB = 0. determine I) the acceleration of the point c. The crank of an engine is 20cm long and connecting rod length to crank radius is 4. crank rotates at 3000rpm. PESIT B. Velocity of A3 a point on the system iii. The crank rotates at 400rpm.E. Determine the following when the crank is at 60 degree from the inner dead center 1) Velocity of slider 2) Angular velocity of connecting rod 3) The Position and velocity of a point P on the connecting rod having at least absolute velocity.6 m and the connecting link BC = 1. direction and sense. Is increasing or decreasing at the instant A3 & A4 are coincident points of piston & A3B=400mm. The crank O2B rotates at 300rpm (ccw). For the four bar mechanism shown in figure – 12 determine the acceleration of C and angular acceleration of link 3 when crank 2. AD is fixed link. The crank of a reciprocating engine is 60mm long and connecting rod is 240mm long. (15) cylinder respectively. 180mm & 180mm long respectively. The crank AB rotates at 100 rpm and an angular acceleration 100rad/sec2 at the instant when the crank AB makes an angle of 600 to the horizontal. (10) 19. Mechanical 4th Semester Course Information . rotates at 20 radians / sec* (10) 23. The crank is rotating at a speed of 10 rad/s and the crank is at 450 from IDC. (10) 18. What is Coriolis component? Derive the expression for the same * (06) 24. The crank 02A of the four bar mechanism shown in figure .(16) 14. Find the velocity and acceleration of point ‘P’ midway between B and C When the angle BAD =1350 and AB rotates at a speed of 300 rpm. II) the angular acceleration of link 3 and 4.An oscillatory cylinder mechanism is shown in the figure 5. Also state whether the magnitude of angular velocity. Find also the angular acceleration of link 3. Angular velocity of cylinder ii. The links AB. Determine the acceleration of the piston when the crank has turned through 45 Degree from the inner dead center position and moving towards center at 240 rpm by the following methods 1) complex algebra analysis 2) Klein’s construction and compare the values and get the error % figure – 11 * (20) 22. By kleins construction determine: Velocity of piston ii) Acceleration of the piston iii) Angular acceleration of i) the Connecting rod * (15) 20. The Follower link CD = 0. Locate all the instantaneous centers and find the angular velocity of link BC and Linear velocity of link CD. In a slider crank mechanism. O2O4=600mm. 12. Determine the velocity of point K in the mechanism shown in figure –8 (6) 16. A four bar chain ABCD has a fixed link AD = 1m. LINK AB = 150mm. Find the acceleration of the point c in magnitude. Link AB makes 60 degree with Link AD and rotates uniformly at 100 rpm. * (12) 25. (15) 13. For the phase. A four bar chain mechanism ABCD is made up of 4 links pin jointed at ends. the crank is 50mm long and the connecting rod is 150mm long. shown in figure.6. (10) 17. O2B=150mm.3m. The crank of a slider crank mechanism is 480 mm long and rotates at 20 rad/sec in the counter clockwise direction. which is 250 mm long. Locate all the instantaneous centers for the toggle mechanism shown in figure –7 (4) 15.2m. Determine the magnitude & direction of I. It has a connecting rod of 160mm long. and the fixed Link AD = 300 mm. In the mechanism shown in figure – 9. BC & CD are 90mm. Angular acceleration of the cylinder. Find the angular velocities and angular accelerations of links BC & CD * (20) 21. A pin jointed 4-bar mechanism ABCD is shown in figure . The teeth have 200 involute pressure angle and module is 5mm.E. The AB has an angular velocity of 10rad/sec and angular acceleration of 30rad/sec2 both clock wise. The number of teeth on each of two equal spur gears is mesh each other are 40. * (20) PESIT SPUR GEAR 1. The angle of link AB with fixed is 60degree. Derive an expression for minimum number of teeth necessary for a pinion to avoid interference.CD=360mm and the fixed link AD=600mm. In an internal combustion engine mechanism. (15) In a 4 bar mechanism ABCD link. 5. The following are the particulars of a single reduction spur gear the gear ratio is 10: 1 and the center distance is 275mm. The teeth's are of involute form with standard addendum of 1 module and pressure angle is 22. and the addendum is 4. calculate the length of action and contact ratio. at the pitch point. Find (I) the nearest B. (6) What are the general Characteristics of spur gearing* (4) Draw a neat sketch of spur gear and explain the various terms (6) Define the following (i) Pitch circle diameter (ii) Circular Pitch (iii) Module (iv) Addendum (v) Dedendum (vi) Pressure angle* . the crank radius is 100mm and the length of the connecting rod is 450 mm. What is Backlash? Derive an expression for backlash if the center distance is pulled apart at a distance Δc. Derive the formula for the length of arc of contact for two meshing spur Gears of involute profile* (6) 12. State the condition for no Interference (4) 13. addendum length is 5mm and the module is 5mm (20) 20. The pinion transmits 375 KW at 1800 rpm.50. 2. Determine the velocity of sliding between the gear teeth faces at the point of engagement. 10. If the arc of contact is 1. 9. (10) 18. 7.1. AB=300mm. if the tooth thickness at some other point is known (10) 17. Derive an expression for the length of path of contact for a pinion on rack (6) 16. 4. at the point of disengagement if the smaller gear is the driver. Normal tooth pressure is not to exceed 9810N/cm width. the crank is rotating at 10 rad/sec. Two equal spur gears of 48 teeth mesh together with pitch radii of 100 mm. 3. Explain the phenomenon of interference.25 mm. 6. in (CCW) direction. 2. Describe the various methods of avoiding interference (4) 14. A pair of gears having 40 and 20 teeth are rotating in mesh the speed of smaller being 1800rpm. Find the addendum (10) 21. 8.BC=360mm. If the pressure angle is 200. What is Involutometry? Derive an expression for the tooth thickness at any point on the involute. Assume the gear teeth 200 involute form. Sketch the different types of gear trains and explain briefly (20) 19. Determine the angular velocity and angular acceleration of link BC and CD by RAVEN’S approach. Mechanical 4th Semester Course Information What are toothed gears? State their uses* (4) What are the advantages and disadvantages of gear drives (4) How are gears classified* (4) State and prove “Law of gearing”* (6) What are the common curves used for tooth profile* (2) Discuss the merits and demerits of involute curve and cycloidal curve for the profile of gear tooth.75 times the circular pitch. Define the following (i) Path of Contact (ii) Arc of Contact (iii) Contact Ratio* (12) 11. (10) 15. Determine the magnitude and direction of 1) Velocity of the piston 2) The angular velocity of the connecting rod when crank is at 45 degree from the inner dead center by complex algebra method verify the same by Klein’s construction. three in number has 45 teeth's gears with fixed annulus ‘A’ and rotates on a spindle cared by an arm which is fixed to the output shaft. The compound wheel revolves freely on a pin. module 12mm. 24. a module 12. if the motor transmits 2Kw. Find the torque required to fit the annulus.5 degrees. In a reverted epicyclic gear train the arm A carries two wheels B & C and a compound wheel DE. Calculate the path of contact and arc of contact. Find the maximum velocity of sliding during approach and the recess and the length of arc of contact. which projects from a disc keyed to a shaft A co-axial with F. find the backlash between the gears. C&D are 4th Semester Course Information 10. (20) An internal wheel B with 80teeth is keyed to shaft F. 26. What do you understand by gear trains (2) Explain Train Value? How is it related to velocity ratio? * (4) Name different types of Gear Trains and give examples (4) Explain Simple. 4. The planet ‘P’ also gears with the sun wheel ‘S’ Find the speed of the output shaft. 2. * (08) PESIT GEAR TRAINS 1. Compounded & Reverted gear trains * (6) Explain Epicyclic gear trains (2) Explain Bevel gear differential* (4) Explain Spur gear differential (4) Obtain the expression for the length of path of contact for two involute profile gears in mesh (10) In an epicyclic gear train of ‘ SUN & PLANET’ type the sun wheel has 15 teeth and is fixed to the motor shaft rotating at 1500 rpm. If the pressure angle is 180 and the pinion rotates at 90 rpm. 8. and the standard addendum is one module.5 mm an addendum 12. 9. The teeth are of involute form of module 6mm. 3. 6.E. Number of teeth on the pinion is 20.5mm and a pressure angle 14. gear ratio is 2. * (14) A pair of gear has 16 teeth and 18 teeth. The spur gear in mesh with it is 250 mm in dia. Mechanical . 7. The number of teeth on wheel B. 27. 11. If the wheels have the same pitch and the shaft A makes 800rpm.22. 23. Show the forces action on the wheels separately. * (5) Two Gear wheels mesh externally and are to give a velocity ratio of 3. A fixed internal wheel C with 82 teeth is concentric with B. The pressure angle is 200. * (15) The following data refers to two mating involute gears of 200 pressure angle. the pressure angle is 20 degree. 5. Determine the tangential force FT and the separating force FR. B. The wheel C gears with wheel D. A compound wheel DE gears with the two internal wheels: D has 28 teeth and gears with C while E gears with B. Derive the expression used. (15) Two spur gears wheels have 24 and 30 teeth and a standard addendum of 1 module. speed of the pinion is 250rpm. The planet P. 25. Determine the minimum number of teeth and the velocity ratio to avoid interference. Find i) The minimum number of teeth on each wheel to avoid interference. Prove that gears have interference. standard diameter pitch if no interference is to occur (ii) the number of teeth in each wheel (iii) the width of pinion* (20) A spur Pinion 100 mm in diameter has a torque of 200Nm applied to it. The length of path of contact iii) The maximum velocity of sliding iv) number of pairs of teeth in contact* (16) The following data refers to two mating involute gears of 200 pressure angle: Number of teeth on pinion – 20 Module – 12mm If the center distance between the gears is increased by 2mm. If the addendum on each wheel is such that the path of approach and the path of recess on each side are half of the maximum permissible length. What is the speed of the (15) shaft F. Sketch the arrangement. 15. & the gear F is connected to the output shaft. 2. Fand the compound wheels C. the internal wheel A and B the compound wheel C and D rotate independently about axis O. E gears with A and C and F gears with B and D. 75. find B speed iii) iv) If the arm G makes 100 rpm CW and wheel A makes 10rpm. TD=48. The gear C is free to rotate on an arm driven by shaft S1 & meshes externally with the casing D & internally with pinion B. The wheel C is fixed. The wheel E and F rotate on pins fixed to the arm G. If the input speed is 100rpm(ccw) when see from right. Of teeth TB=24. 4. (10) In an epicycle gear train. C = 28. iii) Follower to dwell for the remaining 30 degree of cam 4th Semester Course Information 8. 5. turns freely on the output shaft. find the speed of F when I) Wheel A is fixed and II) Wheel A makes 15rpm (CCW) by tabular column method. When the arm rotates at 30rpm. 16. The arm A. 3. D rotate about the axis O. (ii) When the contact is on circular nose (10) B. 6. Tf = 18. Find the speed and directions of the wheel C when wheel B is (15) fixed and the arm A makes 100rpm clockwise In a planetary gear system of sun and planet type. CCW find speed of B PESIT CAMS 1. The wheels have same pitch and the number of teeth on B and E are 18. determine the speed planet gear B (10) Figure – 13 shows an epicyclic gear train Wheel E is fixed and Wheel C and D are integrally cast and mounted on the same pin.16 the internal wheels A. Determine the speed of output shaft. The arms C with Planet gear wheel B with 40 teeth revolve about the gear wheel A. Mechanical . The No of teeth on each gear is indicated in the fig. 7. The wheels B and E rotate on a pin fixed to the arm L. If arm A makes 1 revolution/ sec (CCW).t. D = 26. TC=32 & 40.r.E. All wheels have the same module and the number of teeth are Tc = 28. has teeth cut both internally & externally. Td = 26. Ratio between S1 & S2 when D is fixed S1 & D when D is fixed (15) In an epicyclic gear train shown in figure . 14.5kW* (20) In the epicyclic gear train shown in figure . 17.The gears have the following No. If the arm L makes 150rpm clockwise.15 A gear C. Cams a) Base Circle b) Pitch circle 3) Pressure angle (6) What are the different types of follower motions (4) Derive an expression for velocity acceleration & displacement when the circular arc cam is operating on an flat faced follower (i) When the contact is on the circular flank Derive an expression for velocity acceleration & displacement when the tangent cam is operating on an radial translating roller follower When the contact is on straight flank When the contact is on circular nose (4) Draw the outline of a cam which will transmit motion to a roller follower in the following manner I) the follower to move outwards through a distance of 65 mm during 180 degree of cam rotation. carrying the compound wheels D & E. ii) Follower to return to its initial position during 150 degree of cam rotation. 9. Sketch the arrangement i) ii) Find the number of teeth on A and B If the arm G makes 100rpm clock wise and A is fixed. determine the speed and direction of the wheels B and F. the sun wheel A has 20 teeth and is fixed to the frame. (15) In the gear train shown in figure – 14.12. Determine the vel. 13. Find the output torque & the holding torque to keep the wheel C fixed if the input power is 7. Give the classification of cams and follower* (4) Discuss the types of follower displacement diagrams* (4) Write short notes on cams and follower * (4) Why a roller follower is preferred to that of Knife edge follower (4) Explain w. the gear B is connected to the input shaft. 30 & 90 respectively. then allows the follower to drop suddenly halfway & further return the follower with UARM during the remaining 180 degree cam rotation. (iii) Follower to return to its starting position during 1200 of cam rotation with SHM. The follower then descends with UARM during 0. * (8) Draw the profile of the cam to give the following motion to the follower—Follower to move through 30mm.R. the acceleration during outstroke of the follower.05 sec at the upper position.The time of lift is 0.A. The roller diameter is 10mm & the follower axis is offset by 10mm from the axis of the shaft. When in its lowest position. Roller dia is 10mm. Details of the cam & the follower motion are the following: Roller dia = 10mm. (iv) Follower to dwell for the rest of cam rotation* (15) Draw the full size cam profile for a cam with roller of 25mm dia attached to the follower to give a lift of 35mm.M. 13.E. rotation. 11. the deceleration period being 1/2 the acceleration period . i) Follower to move outward through an angular displacement of 20 degree during 900 of cam rotation ii) Follower to dwell for 45 degree of cam rotation . During 180oof cam rotation with cycloidal motion. * (20) Draw the cam profile for the cam with reciprocating follower . B. The motion of the follower is to take place with SHM during outstroke and with UARM during return stroke. Axis of the follower is offset to right of cam axis by 18mm.The minimum radius of the cam is 25 mm.The least radius of the cam is 30 mm. 12. then dwells for 30 degree of cam rotation and finally descends with UARM during 90 degree of cam rotation. * (15) A cam rotating clockwise at uniform speed of 300rpm operates a reciprocating follower through a roller 10mm dia the follower motion is defined: (I) Follower to move outwards during 1200 of the cam rotation with equal uniform acceleration and deacceleration. 16.0125sec.It rises 25 mm with SHM during 600 of cam rotation. if the cam speed is 1200rpm. when cam rotates at 2000rpm.125sec and the Mechanical 4th Semester Course Information PESIT .M motion through 30 mm in 1/3 rd revolution.15 sec & the time of fall is 0.iii) Follower to dwell for the remaining period of the revolution of the cam . Calculate the maximum velocity & acceleration of the follower during outstroke (20) A push rod operated by a cam is to rise and fall with SHM along an inclined path.10 sec with a period of rest of 0. Keep it fully raised through 1/6th revolution & to lower it with S.The location of the pivot is 70mm to the left and 50mm above the axis of the cam.The cam has to lift the follower with SHM during 180 degree of cam rotation. The least radius of the cam is 30 mm and push rod is fitted at its lower end with a roller 15 mm diameter.the axis of the roller is offset by 8mm to the right. 14. 18. Displacement of the follower is 40 mm in a direction 30 degree to the right of the vertical . * (8) A disc cam is required to lift a flat-faced follower with U.05sec follower by a period of rest of 0. (10) It is required to set out the profile of a cam for the following data.iv) Follower to return to its initial position of zero displacement in 5 degree of cam rotation. (20) A knife edged follower for the fuel valve of a four stroke diesel engine has its center line coincident with the vertical center line of the cam . 15. Determine the maximum velocity and acceleration of the follower during the outstroke.10.H. Base circle dia. the roller center is above the cam axis. draw the graphical cam profile.The axis of the follower passes through the axis of the cam. Total lift = 25 mm . The minimum radius of the cam is 30 mm & the displacement of the follower is to take place with cycloidal motion both during outward & return strokes. in 1/3rd revolution and to dwell during rest of the revolution .The cam rotates at 100 rpm in a clockwise direction . minimum radius of cam is 30mm . The max. Draw the profile of the cam to full size. of the cam is 30mm and the roller dia of the follower is 10mm. Draw the cam profile & also determine the maximum velocity & acceleration of the follower during and return strokes if the cam rotates at 200 rpm clockwise. 17. minimum radius of the cam = 22 mm. (ii) Follower to dwell in the lifted position for the next 300 of cam rotation. Follower to return with cycloidal motion during 180o of cam rotation. * (20) The distance between the pivot center and the roller follower center is 70mm. Ascend of the follower takes place with SHM in 0. The cam rotates in CCW direction at a constant speed of 240rpm and the base radius is 50mm (20) * Questions appeared in VTU examinations METROLOGY & MEASUREMENTS – IP42 B Faculty: S.7-Transfer from line standard to end standard 1. The cam rotates in clockwise direction.6-Comparison 1. The duration of the dwell before and after the rise is 300.50 180 3. M-112) 4th Semester Course Information 8 . * (20) 0 0 30 0.the base circle radius of the cam is 3cm. The outward and inward displacement of the follower each occupying 120 degree cam rotation and there is no dwell in the lifted position. Draw the displacement diagram of the follower. which makes contact with the cam.87 300 0.75 21 0 3. remaining period rest at the minimum lifted position. the acceleration being ¾ times retardation.5 240 2.10-Wringing phenomena 1. The cam rotates in CCW direction at a constant speed 240rpm and the base radius is 50mm*(20) A translating roller follower has lift of 4cm. Draw the full size cam profile for a cam with roller of 25mm diameter attached to the follower to give a lift of 35mm.1-Definition and objectives of metrology 1.19. The follower is fitted with a roller of 20mm diameter.83 270 1.V.125sec and the remaining period as rest in the minimum lifted position. The axis of fulcrum is 80mm from the axis of cam and the least distance of roller axis from cam axis is 40mm* (20) A roller follower is offset to the left by 1. Do not draw the cam profile* (20) A cam rotates at a uniform speed of 300 rpm clock wise and gives an oscillating follower 75mm long. Mechanical 1. The follower moves through out by SHM. The Follower then descends with UARM during 0. 21. 20.8-Calibration of end bars (numericals) 1. an angular displacement of 30 degree in each stroke.9-Slip gauges 1.92 330 0.25 60 0.4-Subdivision of standards 1.Satish/ Mukesh Patil Class # Chapter title / Reference Literature Standards Measurement: R1:34-40 R2:311 of Portions to be covered PART-A % Covered 1–4 B. wave length standard 1.the desired displacement of the follower Y for any cam rotation θ is listed in the table given below.25 PESIT Cam rotation θo Follower (cm) Y displacement 22. And during return the duration of acceleration is twice the duration of retardation. Ascent of the follower takes place with SHM 0.05sec followed by a period of set 0.5-Line and end standards 1. The acceleration being 3/5 times retardation. Axis of the follower is offset to right of cam axis is 18mm. How ever during the rise acceleration is twice the retardation.E.11-Indian Standards (M-87. The angle of rotation of cam during rise and return is 1500 each.3-Imperial standard yard.2cm. Layout the cam profile if the radius of roller follower is 1cm.83 150 3.international prototype meter 1. The follower has a uniform acceleration and retardation motion for both rise and return phases.2-Standards of length .87 120 2.125sec.92 90 1. 8-Gear terminology 5.5-Autocollimeter 4.4-optical comparators-principles 3.Sigma comparators . calibration.5-Zeiss ultra optimeter 3.3-Clinometers 4.6-Optical flats 5.1-Introduction to comparator 3.9-Definition of fits 2.2-Measurement of major diameter 5.3-Definition and concept of accuracy 6.4-Principle of Interferometry 4. ring gauge. Sine center.18-Gauge materials 3.E. threshold.8-Accumulation of tolerances 2.12-Positional tolerances 2.17-Types of gauges -Plain plug gauge.PESIT 5 – 13 System of Limits. Mechanical .4-Limits of size 2.10-Types of fits and their designation (IS 919-1963) 2.6-Electric and electronic comparators-principles 3.8-pneumatic comparators 3.Dial indicator 3.2-Sine principle.4-Precision.12-Numerical problems on building of slip gauges 2.9-Use of gear tooth Vernier caliper 5.2-Generalised measurement system 6.11-Geometrical tolerance 2.5-Angle and effective diameter of screw threads by 2wire & 3-wire methods 5.3-Minor diameter 5.Johnson mikrokator .2-Characteristics and classification of comparators 3. limit gauge 2. Tolerances and gauging: R1: 73-110 R2: 312-446 1. Sine bar.4-Pitch 5. Fits.10-Solex comparators 4.10-Use of gear tooth micrometer 26 14 – 18 Comparators: R1 : 63-70 R2: 447 .1-Definition of tolerance 2.724 Screw thread and Gear measurement R1 : 174. Angle gauges (numericals on building of angles) 4.14-Classification of gauges 2.190 R2 : 879 -1008 44 23 – 26 52 PART-B 26 – 31 Measurements Measurement systems R1: 268-270 & 6.5-Indian standards 2.7-Compound tolerances 2.9-Back pressure gauges 3. snap gauge. sensitivity.7-Tool makers microscope 5.2-Specification in assembly 2.1-Terminology of screw threads 5.3-Principle of interchangeability and selective assembly 2.6-Best size wire 5.16-Wear allowance on gauges 2.1-Bevel protractor 4.7-LVDT 3.3-Mechanical comparators .15-Brief concept of design of gauges (Taylor’s principle) 2.13-Hole basis system and shaft basis system 2. 4th Semester Course Information 62 B.6-Concept of limits of size and tolerances 2.1-Definition and Significance of measurement 6.519 38 19 – 22 Angular measurements and Interferometer R1 : 111 – 127 R2 : 654 . 3-Platform balance 10.3-Oscillographs 9.3-Gauge factor 13. Engineering Metrology. Mechanical Measurements .2-Preparation and mounting of strain gauges 13.3-Mechanical.C.1-Transfer efficiency 7.2-Analytical balance 10.Shotbolt 5. Mechanical Measurements – Holeman 2. Mechanical Measurements – Sirohi & Radhakrishna 3.2-Use of elastic members 11.1-Mechanical systems 8.5-Pirani gauge 12.K.R.Hydraulic dynamometer 11.2-Cathode Ray Oscilloscope 9.D.2-Primary and secondary transducers 7. loading effect -System response.Prony brake dynamometer .5-Ballast circuit 8. Mechanical 4th Semester Course Information . time delay -Errors in measurements.4-Proving ring 10.4-Input circuitry 8.6-Optical pyrometer 13.F.Marangoni & Lienhard 2.1-Mechanical 9.2-Inherent problems 8.4-Advantages of each type transducers 8.3-Bridgeman gauge 11.4-X-Y Plotters 10.R.5-Torque measurement: . Metrology for engineers-J.6-Electronic amplifiers and telemetry 9.Galyer & C.1-Principle 11.Jain Scheme of examination: B. classification of errors 7. repeatability linearity.2-Thermocouple 12.PESIT -hysteresis.Faulk 6.1-Strain gauge 13. Engineering Metrology .1-Principle 10.Beckwith .I. electronic transducer 7. Industrial Instrumentation-Alsutko & Jerry.E.4-Materials used for construction of thermocouple 12.5-pyrometer 12.4-Mcleod gauge 11.4-Methods of strain measurement 32 – 35 Transducers R1:271-314 Intermediate modifying devices R1: 315-326 70 36 – 38 76 39 – 40 Terminating Devices Measurement force & torque R1:368-379 of 80 41 – 43 86 44 – 46 Pressure measurements R1:380-418 Temperature measurement R1:419-455 92 47 – 49 98 50– 52 Strain measurement R1:275-312 100 Text Books: 1. Mechanical measurements-Doblin 4.1-Resistance thermometers 12.3-Electrical intermediate modifying devices 8.3-Laws of thermocouple 12. Electrical.Gupta Reference Books: 1. Write neat sketches and explain 'go' and 'Nogo' gauges. clearance.001D* 4. 2. Sketch the fit and mark the dimensions clearly. Define Metrology. 7. their tolerances. QUESTION BANK PART-A Chapter 1: Standards of Measurement PESIT 1. 10. Diameter step (50-80) Fundamental deviation for e shaft = -11D0.E. Differentiate between: i) Tolerance and allowance ii) Hole basis system and shaft basis system * 11.The following assumptions may be made.where D=Diameter(mm)falling in the step 18-30mm. Explain different types of fits.IT8=25i.The standard tolerance is given by i=0. Fits. What are Airy points? How do they differ from the points of minimum deflection.41 IT7=16i.Upper deviation for “d”shaft is –16D0.* Chapter 2: System of Limits.* 4. A shaft-hole pair is designated as H7d8. Determine the shaft and hole dimensions. Tolerances and Gauging 1. after deciding the fundamental deviations and tolerances in the following: Fit Ø 70H9e7.44.50mm falls in the diameter step of 30-50mm. * B. Briefly explain interchangeability. Calculate the dimensions of plug and ring gauges to control the production of 50mm shaft and hole pair of H7d8. Explain what is meant by: i) Interchangeable part ii) Universal interchangeability iii) Local interchangeability* 3. Determine the type of fit. Enumerate the advantages of using wavelength standard as a basic unit to define primary standards.453√D+0. Explain Taylor's principle for 'go' and 'Nogo' gauges.* 5. 3 IT7=16i. Illustrate with examples: i) Geometrical tolerance ii) Dimensional tolerance iii) Positional tolerance 13. * 12.001D. 8. What do you understand by line and end standards? Discuss their relative characteristics. Mechanical 4th Semester Course Information . Briefly explain selective assembly. interference and the class of fit.Four questions to be set from Metrology – Part A Four questions to be set from Measurements – Part B Answer any five questions taking at least TWO questions from each part. What is the difference between unilateral and bilateral tolerances? Why unilateral tolerance is preferred over bilateral tolerance?* 2.001D * 5. IT9=40i i=0. 9.44 Take wear allowance as 10% of the gauge tolerance. 6.453√D+0. i=0. Explain Taylor’s principle for the design of limit gauges.45 √D+0. Explain the NPL method of deriving end standards from line standards. Explain various standards of length.* 3.The fundamental deviation for fit d is given by –16D0. 7. What are the required characteristics of comparators?* 2. PART-B Chapter 6: Measurements and measurement systems B. 2. 5.Chapter 3: Comparators 1. 4. With a neat sketch explain Universal Protactor. 4. What are the advantages of electrical comparator over mechanical comparator? 3. How do you find effective diameter of a screw thread using two-wire method. Show the arrangement of gauges. Explain the terminology of a simple Spur gear 11. Select the sizes of angle gauges required to build the following angles: i)31deg29min24sec ii)102deg8min42sec * Chapter 5: Screw thread and Gear measurement PESIT 1. 6. Sketch and label the parts of a Vernier bevel protractor.* 5. Explain the working of Sigma comparator with neat sketches. How is setup of angular gauges different from simple gauges? Explain with an example. Describe a Gear Tooth Vernier caliper and show how this is used for checking gear. Explain the working of Optical comparator with neat sketches. Mechanical 4th Semester Course Information . * 10. * 8. What are the two corrections applied in the measurement of effective diameter by the method of wires?* 4. * 9. What is the difference between a comparator and a measuring instrument? * Chapter 4: Angular Measurements 1. 8. Compare profile projector with tool makers microscope.E. 7. With a neat sketch explain Bevel protractor. Explain how Gear Tooth Vernier is used for gear measurement. 6.* 2. ii)12o20’36” * i)57o 34’9” 3. Explain the working of Brook level comparator with neat sketches. Write neat sketch and explain the principle of working of Auto Collimeter. 5. * 12. Explain the working of Jhonson's Microkrater with neat sketches. Describe screw thread terminology with sketch. * 9. How do you measure the following in case of a spur gear: i) Runout ii) Tooth thickness iii) Backlash * 10. Distinguish between 2 wire and 3 wire methods of measuring and suggest the best one. Explain how sine bars are used for measurement of angle. Give the procedure to measure major and pitch diameter using 3 wire method. Distinguish between: i) Sine bar and sine center ii) Angle gauges and slip gauges. 6. What are the various types of pitch errors on threads and explain the reasons for the same. 3. Give the significance of Clinometer in angular measurement. Explain why it is preferred not to use a sine bar for generating angles larger than 45oif high accuracy is desired. Explain the working principle of Tool Makers Microscope. 7. slowly than a less sensitive instrument. Define transfer efficiency. What are the sources of errors in instruments? Explain* 4. Explain briefly the different types of errors encountered during measurement. Describe with a neat sketch the ionization transducer. Explain with an example the various stages of a generalized measurement system. a more sensitive instrument oscillates more 11. Draw the displacement time characteristics for damped motion and explain the importance of damping. 13.* 2. Explain the following: i) Zero drift and sensitivity drift ii) Threshold. What are the parameters on which capacitive transducers are developed. i) Hysteresis ii) Threshold iii) Repeatability iv) Sensitivity drift * Chapter 7: Transducers 1. Explain any one type of elastic transducer with a neat sketch. 12. Distinguish between: i) Digital and Analog measurement ii) Direct reading and null balancing * For Oscillating systems. 6. What are the requirements and objectives of measurement? State and explain the various forms of input to the instrument. With the help of examples. State the three basic elements of a measuring system and give an example to each of the basic elements. show that. Explain the principle of working of a linear variable differential transducer with a neat sketch and illustrate its characteristics. Draw a block diagram of a generalized measurement system and explain the salient feature of each stage. PESIT B. 11. 7. Resolution and Hysteresis* 3. Mention six mechanical elements used as detector transducers and indicate the operations. Draw a block diagram of generalized measurement systems and explain the salient features of each stage. 15. Mention the advantages of electrical primary detector transducer elements over other types. Discuss the relative merits and demerits of mechanical and electrical transducers.1. 8.E. * Explain with sketches: 19. Write a brief note an treatment of multisampling data. 18. 7. distinguish between the two fundamental methods of measurement.* 4. Mechanical 4th Semester Course Information . What is a measurement? 5. 9. 10. Explain the following: i) Accuracy ii) Sensitivity iii) Precision 14. 8. What do you understand by active and passive transducers? Give examples. 9. With a neat sketch explain the working of a transducer using electro kinetic phenomenon and indicate its applications. Explain the following with neat sketches: i)Mutual inductance transducer ii)Piezo electric transducer* 3. which they perform. Explain the working of a pickup used for determining the level of liquid nitrogen with a neat sketch. 16. Define the word Transducer. Draw a neat block diagram of measurement system employed for measuring acceleration. 6. 17. 5. 10. What do you mean by static calibration? Sketch the calibration curve of an instrument and explain how it is obtained?* 2. With the help of a neat sketch explain the working of a prony brake dynamometer. How resistance thermometer is used to measure temperature with advantages. Explain the principle of variable inductance transducer with a neat sketch. Explain with a neat sketch ballast circuit. * Chapter 8: Intermediate modifying devices 1. 4. 17. * 6. Mechanical 4th Semester Course Information PESIT . What are active and passive transducers. 3. 18. What are primary and secondary transducers? Explain with examples.12. Give the advantages of electrical modifying devices compared to mechanical ones. 2. 2.* 4. Explain with a neat sketch the analytical balance. With a neat sketch explain the construction and working of Cathode ray oscilloscope. 14. 3. Discuss briefly with sketches two types of elastic pressure transducers. What are the relative merits and demerits of electrical transducers over mechanical transducers? 13. Differentiate between radiation and pressure thermometer. Explain with neat sketch the working of any one device used for measurement for high pressure.* 2. Write short notes on: i) Electronic amplifiers ii) Telemetry Chapter 9:Terminating Devices 1. Write a note on hydraulic dynamometer 4. How is electric dynamometer different from mechanical ones? 5. Distinguish between active and passive transducers. With a neat sketch explain bi-metal strip thermometer. * B. With a neat sketch explain resistance thermometer. 2. What are pyrometers? Explain any one. Explain with a neat sketch the working and application of a Bridgeman gauge. What are photoelectric transducers? Explain any one type with a neat sketch. 4. * 3. Write short notes on: i) Oscillographs ii) X-Y Plotters Chapter 10: Measurement of force and torque 1. explain the working principle of : i) Mcleod gauge ii) Knuolsm gauge * Chapter 12: Temperature measurement 1. * 21. the method of torque measurement of rotating shafts using strain gauges. 6. Explain in brief inherent problems encountered in mechanical systems as intermediate modifying devices. 20. 2. With neat sketches. 16. Explain the principle of working of a piezoelectric transducer with a neat sketch. Explain with neat sketches the following: i) Piezo electric transducer ii) Ionization transducer * 11. 15. * Chapter 11:Pressure measurements 1. Explain with sketches the proper orientation of strain gauges for measurement of (i) Bending strain (ii) Torsional strain (iii) Axial strain. Explain the thermocouple way of measuring temperature.* 5. 3. With neat sketches explain Mcleod and Pirani gauges. Explain with a neat sketch.E. Explain the working of a electronic transducer with a neat sketch. How do you define high pressure range and low pressure range. 5. give examples. Explain the principle of variable resistance transducers with a neat sketch. 19. Write a note on thermocouple materials and some forms of thermocouple construction.E. Enumerate the necessary precautions to be taken while mounting a strain gauge on a test piece. * Chapter 13: Strain measurement 1. How do you calibrate the given strain gauge? * 5. * 3. Write a note on bonding materials of strain gauges. * 4. Mechanical 4th Semester Course Information . Explain with respect to strain gauges: i) Cross sentivity ii) Temperature compensation iii) Positioning of gauges to measure torsional strain 2. * *Appeared in VTU exam papers PESIT B.7. What is temperature sensitivity? Explain how is it compensated.