FEATI UNIVERSITYHelios St., Sta Cruz Manila COLLEGE OF ENGINEERING AND TECHNOLOGY CIVIL ENGINEERING DEPARTMENT FLUID MECHANICS LABORATORY MANUAL BY ENG’R. TOMAS U. GANIRON, JR. MARCH 1997 EXPERIMENT TITLE 1 MEASUREMENT OF SPECIFIC WEIGHT AND PRESSURE INTENSITY OF WATER 2 SPECIFIC GRAVITY OF LIQUID 3 PRESSURE MEASUREMENT USING MANOMETER/PIEZOMETER 4A FALL VELOCITY OF SPHERE 4B FALLING SPHERE VISCOSITY 5A HYDROSTATIC FORCE ON PLANE SURFACES 5B DETERMINATION OF CENTER OF PRESSURE 6A BUOYANCY FORCE (ARCHIMEDES PRINCIPLE) 6B METACENTRIC HEIGHT 7 ROTATION OF LIQUID MASS (ROTATING VESSEL) 8 GRAVITY DAMS 9 DISCHARGE MEASUREMENT USING A VOLUMETRIC TANK 10 AN EXPERIMENT ON THE PRESSURE HEAD APPARATUS 11 VENTURIMETER 12 AN INVESTIGATION OF THE DARCHY WEISBACK EQUATION 13 VELOCITY MEASUREMENT BY PITOT TUBE RULES IN MAKING A REPORT 1. Report must be written in ink or 5 ½” x 11” bond paper. 2. The first few pages of a report must be detached from the manual that contain the title, object, theory, apparatus and materials, procedure and table of result. 3. The suggested arrangement of the experiment report will be as follows: Experiment No. Title Objective Theory/General Lab. Apparatus/Materials Procedure Table of Computation Discussion Sketch Conclusion Reference/s 4. use ink in making sketch and drawing of materials and / or equipment 5. In discussion, the students will cite theories and facts from which the result will be adapted. 6. Conclusion must be in the student’s own words and it must be related to the objective of the experiment. EXPERIMENT NO. 1 MEASUREMENT OF SPECIFIC WEIGHT AND PRESSURE INTENSITY OF WATER GENERAL: Specific weight is the ratio of the weight density or mass density of a substance to the weight density or mass density of water. The of fluid is its mass per unit volume. While the specific weight is its weight per unit of volume. Specific weight represented the force exerted by gravity on a unit volume of fluid and therefore must have units of force per unit volume such as pounds per cubic feet (N/M cubic in SI unit) OBJECTIVE: To establish a relation between specific weight and pressure intensity of water. Density and specific weight of fluids are as follow: Mass Density = Specific Weight Acceleration due to gravity In eqn = p = w g It should be noted that density is absolute since it depends on mass which is independent of location. Specific weight on the other hand, is not absolute for it depends on the value of the gravitational acceleration, which varies with location, primarily on latitude and elevation above main sea level. The unit pressure, meaning the intensity of pressure at any point in a fluid is the amount of pressure per unit area A, on which the total pressure is Pt. P=F/A APPARATUS: Platform balance Flow can container Ruler and water LABORATORY PROCEDURE: 1. Determine the weight of the container at its base area. 2. Place the container on the Platform balance and load it with a known quantity of water. 3. Measure the height of the water in the container. 4. Increase the amount of water in the container. 5. Make at least 5 trials. EQUATION: Volume of water = Ht. of water x Base Area Specific Weight = Weight of water Volume of water Pressure = Weight of water Base Area DATA AND COMPUTATION: Trial 1 2 3 4 5 Weight Weight Weight Ht. Base Volume Specific Pressure of of of Of Area Of H2O Weight (KPa) Contain Water Water Water (m) (m) (KPa) er and (KN) (m) (KN) Container (KN) EXPERIMENT NO. 02 DETERMINATION OF APPARATUS AND MATERIALS USED IN FLUID MECHANICS OBJECTIVE: To determine the specific gravity of liquid by means of U-tube. GENERAL: Specific gravity of liquid is the ratio of its density to that pure water. A standard temperature universally it is the ratio of the unit weight of the liquid to the unit weight of the water at 4 C or 39.2 F. Physicist use 1.0g km equivalent to 100kg/cm, and hence the specific gravity (w/c is dimensionless) has the same numerical value for a liquid as its density in that system. As the density of fluid varies with temperature, specific gravity must be determined and specified at particular temperature. In the petroleum industry, it is the customary to specific to specify the specific gravity of oil at 60 F relative to water at 60 F, indicated by 60/60 specific gravity is usually determined by reading on hydrometer standardized by American Petroleum Institute (API) w/c is graduated to read degrees (API), specific gravity at 60 F maybe obtained from degrees API at 60 F by: S = 141.5 / 131.5 + API Experimentally the specific gravity of liquid and solids can be determine by several methods. By applying the Archimedes Principle. By means of hydrostatic pressure on by the used of U-tube. By means of westhfal specific gravity balance. A glass, U-tube open to the atmosphere at both ends is a convenient instrument for determining the specific gravity of liquid provided that another non-miscible liquid of known specific gravity from one atmosphere surface to another. APPARATUS: U-tube Ruler Oil Water PROCEDURE: 1. Pour a quantity of water into the U-tube. Then pour a certain amount of oil into one leg of the U-tube. Observe the point of contact between water and oil. Then measure its height on both legs of the U-tube. Make at least three (3) trials. 2. Pour a quantity of oil on both legs of the U-tube. Do it at least three (3) trials. 3. Determine the specific gravity of oil. 4. Determine the percentage of error. DATA AND COMPUTATION: DATA 1 TRIALS HEIGHT 1 (CM) HEIGHT 2 (CM) St 1 2 3 DATA 2 TRIALS 1 2 3 DATA 1 HEIGHT 1 HEIGHT 2 (CM) HEIGHT 3 (CM) St St = H1 / H2 % ERROR = (St ave. - Ss) Ss x 100 St ave. = (St 1 + St 2 + St 3) / 3 Where: H1 H2 H3 Ss St = Height of water in 1 leg of the U-tube = Height of the oil in the other leg of U-tube = H2 – H1 = Standard Specific Gravity = Experimental Specific Gravity DATA 2 St = H3/H2 EXPERIMENT NO. 03 PRESSURE MEASUREMENT USING MANOMETER/PIEZOMETER OBJECTIVE: To measure pressure of a liquid using a manometer/piezometer, U-tube manometer, or a differential manometer. APPARATUS: Manometer/Piezometer U-tube Manometer Differential Manometer Meter Stick Foot Ruler Pipe flowing full GENERAL: P = h where: P = pressure in N/m2 or Pascal = specific weight of measuring fluid (for water, = 9,810 N/m3) = head or height, m The manometer to be made of the static pressure in a pipe. (See Figs. 2a,3b and 3c). A. Piezometer 1. Connect the piezometer to a top of pipe. 2. Turn on valve so fluid (water) will flow in pipe and will rise in the piezometer. 3. Measure the height, h of the fluid column in piezometer above the tap. This height is called the piezometer height. Pressure in the pipe at the point of tap is equal to h. 4. If tap (of piezometer) is on top of pipe, add ½ pipe diameter to h. B. U-tube Manometer’ 1. Connect U-tube manometer to tap of pipe. (Preferably, manometer fluid should be mercury, specific gravity = 13.55) 2. Turn on valve so fluid will flow in pipe. 3. Measure height, h1, and h2 (see Fig. 3b). Calculate pressure pipe. P = Hg (h2 – h1) = SHg w (h2 – h1) = C. Differential Manometer 1. Connect the two (2) arms of the differential manometer to two points (taps) along a pipeline (in this particular case, use the taps of the upstream section of the pipe and the throat of a venture meter). 2. Turn on flow. 3. Measure h , h , (see fig. 2c). Calculate pressure differences. 4. Use Formula as Shown in figure. EXPERIMENT NO. 04A FALL VELOCITY OF SPHERE OBJECTIVE: To determine the effect of three (3) different liquids w/ different mass densities on the fall velocity of the body. GENERAL: Density The density of a fluid is the mass it possesses per unit volume. Since a molecule of a substance has a certain mass regardless of its state, it then follows that the density is proportional to the number of molecules in a unit volume of the fluid. Density is vital in any problem of flow in w/c acceleration is important. APPARATUS: Stop Watch Fresh water Oil Weight Balance Meter Stick Sea water Vernier Caliper 3 Marbles 3-6inch tall transparent cylinders Graduated Cylinder PROCEDURE: 1. Weight each three (3) colored marbles diameter. 2. Fill each cylinder of the fall velocity apparatus w/ an equal and measure the height of water of cylinder A, cylinder B, and cylinder C. 3. Drop each time marble three (3) times in each cylinder and take note of the elapsed time trial w/ the use of stop watch. DATA & COMPUTATION: Diameter of Marble = ______________________mm Weight of Marble = ______________________KN Fresh water Sea Water Oil Elapsed Marble 1 A B C 2 3 1 2 3 1 2 3 Fresh Sea water water Oil EXPERIMENT NO. 05B DETERMINATION OF CENTER OF PRESSURE OBJECTIVE: To determine the depth of the center of pressure, Yc of a rectangular plane immersed in water. APPARATUS: Hydrostatic pressure apparatus and accessories (A schematic diagram of the apparatus is shown in Fig. 4) GENERAL: P = A N YO P = total pressure on rectangle A = area of rectangle Yo = depth of centroid of area W = specific weight of water FH = P FV = where V = submerged volume Description of the apparatus and how it works are given in Fig. PROCEDURE: 1. Measure L1, (QR), vertical distance Ro, EG (vertical height of rectangle, and 2. horizontal width z of rectangle). Check if beam GRS is balanced. 3. Fill tank with water to depth such that pt. E at top of rectangular are is flushed with the water surface. 4. Since the beam QRS will swing clockwise on account of the moment of the buoyant force, Fv, maintain equilibrium by adding weight on tray at Q, Record the added weight, W. COMPUTATIONS: P = A w (Yo) = FH Area = EG x z Yo = radius of quadrant minus ½ EG = Depth of centroid = Specific weight of water MR = 0 W x L1 = FV x X (FV weight of displaced volume as determined. See Fig. 4) F1 and P are equal in magnitude and collinear. Since GJ is a circular are, the pressure vector at each point is concentric at R, thus the resultant of FV and FH passes at B. Thus, moment at R as a center equals zero: FH Yc = FV X Y = FV X FH Yc is the location of the center of pressure (Refer to Fig. 4. Hydrostatic Pressure Apparatus) DABC is a rectangular tank with width AB, height DA and length perpendicular to plane of paper. A beam QRS with fulcrum at R is attached to the tank. To the left end, weight can be loaded on a tray, while on the opposite and is a counterpoise. A float in the shape of a ring sector of a quadrant of a circle with center at R is affixed to the left arm of the beam. The vertical rectangle of height EG and width perpendicular to paper has area A and centroid at 0. (EG and R are on same is balanced by adjusting the counterweight). When the foal EGJIH is immersed in the water, the beam will tilt clockwise because of the torque exerted by the buoyant forces Fv. Weight should be added to maintain equilibrium. The buoyant force Fv is equal to the weight of the displaced volume. A way of determining the submerge volume at any level of immersion of the float is to mark the depth of the water at the level. Then list the float totally out of the water and mark the new depth. The amount by which the water level subsided is the displaced volume. EXPERIMENT NO. 06 BUOYANCY FORCE (ARCHIMEDES PRINCIPLE) OBJECTIVE: To determine the buoyancy force on a floating object. GENERAL: When an object floats in liquid, the weight of the object is balanced by the buoyancy force. APPARATUS: Test tube Mate stick Sand Graduated cylinder Liquids (water, oil, kerosene) LAB. PROCEDURE: 1. Place grains of sand in the test tube, just enough so that the test tube will float upright when placed in the liquid. 2. Weigh the test tube and sand; Wo = mass of test tube and sand x gravity. 3. Fill the graduated cylinder with the liquid to about 3/4. Determine the level of the liquid in the scale. Mark level as Vi = ________________ml. 4. Allow the test tube with sand to float in the liquid. Note that the level of liquid changes. Mark new level as Vf = ________________ml. 5. Determine V = Vf – Vi in ml. Note: 1 ml. = 1cc ANALYSIS: Wo Bf when the object floats in liquid DATA AND RESULTS: WATER Water Oil Kerosene W (Dynes) V (ml) Where: Wo = weight of test tube with sand Wi = weight of displaced liquid W = DV/g V = volume displaced in liquid D = 1g/cc; g = 980 cm/s2 W (Dynes) Wo/Wi EXPERIMENT NO. 7 METACENTRIC HEIGHT OBJECTIVE : To measure metacentric height of a floating body. APPARATUS : Metacentric apparatus Plumb bomb Meter stick Protractor GENERAL: A body will be in its upright positions if the weight and the force are collinear. Due to wind or wave action, the body is made to tilt and the two forces (W and BF) are longer collinear producing a couple which is equal to W (X) or BF (X). The point of intersection between the lines of action of the BF and the axis is called the Metacenter, M and the distance from metacenter to the center of gravity of the body is the metacentric height. EQUATION: MG = Metacentric height G = Center of gravity of floating body B = Center of Buoyancy when body is in upright position B = Width of the floating body L = Length A = Depth of Floatation B = Center of buoyancy MG = MG + GB MB = b2 / 12a (1 + tan2 e/2) GB = Measure The criterion for stability of a submerged body is that the center of buoyancy must be above the center of mass of the body. PROCEDURE: 1. Fill the container with water 2. Take the following measurement. b = ________________ a = ________________ L = ________________ 3. Tilt the body and measure the angle using a protractor. Record 0 = _______________ COMPUTATION: SUMMARY: EXPERIMENT NO. 08 ROTATION OF LIQUID MASS (ROTATING VESSEL) OBJECTIVE: To determine the angular velocity of an open vessel fully and partially filled with water. GENERAL: Considering that the liquid in the open container is at rest, the free surface will assume the horizontal position MN. If the container is then rotated about its vertical axis with an angular velocity, an initial disturbance of the liquid mass is experienced but after a short time the condition of relative equilibrium is reached. The free surface is now curved and assumes the new position M’ON’. To study the form of this substance and the pressure variation in the rotated mass of liquid, we apply the same principle used in rotational motion. APPARATUS: Hydro synthetic machine with container Meter stick Stop watch Stirring rod LAB. PROCEDURE: 1. Measure the cross section of an empty container in SI units. L = _______________________cm W = _______________________cm H = _______________________cm A. OPEN VESSEL FULLY FILLED WITH WATER Run the water until the container reaches the max. ht.. Stir and rotate the water with 25 cycles. Measure the ht. of the container. Determine the angular velocity of an open container. Compute the volume of the water during and after rotation. B. OPEN VESSEL PARTIALLY FILLED WITH WATER Allow the water to run in the container until reaches 30cm. Repeat the same procedure in open vessel fully filled with water. TABULATION: Type of open Vessel 1. Fully filled w/ water 2. Partially filled w/ water Vol. of empty container (cm3) Ht. of Water (cm) Angular velocity (rad/s) Vol. of Water (cm3) PRACTICAL QUESTION: 1. How much area at the top is not covered by water during and after rotation? 2. (Refer to Procedure B) 3. Is the volume spilled out in Procedure A and B? By how much? CALCULATION: DISCUSSION: FIGURE/SKETCH: RECOMMENDATION: CONCLUSION: EXPERIMENT NO. 09 GRAVITY DAMS OBJECTIVE: To determine the stability against sliding and over turning under a. FS vs. Overturning b. FS vs. Sliding GENERAL: Any dam that does not depend on arch action to resist the various forces to which it is subjected is called gravity dams. Dams are built for the primary purpose of impounding water in the reservoir upstream of its location according, the main external forces which must be taken into consideration when designing gravity dam, the greatest is the gravity force of the dam itself. APPARATUS: 1. 2. 3. 4. Hydroelectric power plant and accessories Stop watch Meter stick Steel tape LAB. APPARATUS: 1. Measure the cross section of the electronic power plants in SI units approximate a triangle. 2. Allow the water to flow the cross section of the dam until it reaches its constant height. 3. Determine the height of the water and the hydrostatic, gravity and uplift force of dam. 4. Locate the total hydrostatic pressure above the heel of dam. This is the eccentricity (e) 5. Calculate the following: RV = RH = RM = OM = FS vs. Sliding FS vs. Overturning Where coefficient of friction is 0.75 6. Determine the point where resultant intersects the base and the maximum and minimum pressure developed in the foundation. EXPERIMENT NO. 10 DISCHARGE MEASUREMENT USING A VOLUMETRIC TANK OBJECTIVE: To measure Q which is the rate which is the rate of discharge or flow from a course in units of volume per unit time. APPARATUS: 1. 2. 3. 4. 5. Volumetric tank or container of measurable capacity Stop watch Weighing scale Water source Tape measure GENERAL: Q1 in m3/s = Total volume Elapsed time Q = volume discharge M2 = Weight Elapsed time in kg-wt/s M = mass discharge Q2 = __M__ where ρ = mass density of liquid ρ = 1 Kgm3 for water LAB. PROCEDURE: A. For Q1: 1. Measure volume of tank/container in m 2. Turn on flow reservoir or source od steady flow. 3. Catch flow into container at same time that stopwatch is started. 4. Determine time in seconds to fill tank/container. 5. Repeat at least two (2) times with different opening of pipe measure. B. For M2 (if weighing scale is available for use) 1. Place container on weighing scale and determine weight of empty container, Wo, in kg-wt. 2. Turn on flow from reservoir or source. 3. Record time that the mass-weight of container and flow reach several values of W1, W2... etc. DATA AND COMPUTATIONS: PART A: 3 Volume = ________________________ m t1 = _________________ m t2 = ______________________ s t3 = _________________ s Q1 = Vol. t1 = __________________ m3/s Q = Vol. t2 = ____________________m3/s = Vol. t3 = ___________________m3/s 2 Q3 Q = Q1 + Q2 + Q3 = ____________________m3/s 3 or Q1 1 1 1 = V (t1 + t2 + t3) = ______________________m3/s PART B: ∆W : M= : ∑ time = ∑t Wn – Wo : ∆W/∑t : Wo : : t0 = 0 : 0 ________________________________________________________________________ W1 : : t1 = : M1 = W2 : : t2 = : : t3 = : M2 = W3 : M3 = M2 = ∑M 3 = ____________________ Q = M2 = ____________________ Ρ EXPERIMENT NO. 11 AN EXPERIMENT ON THE PRESSURE HEAD APPARATUS OBJECTIVE: To determine the pressure by measurement of the head and apply Bernoulli’s equation and determining pressure in venturimeter. GENERAL: Pressure is the outward force, which a substance exerts on its surroundings. It is defined as the force on a unit surface area and is commonly measured in pounds per square inch or in dryness per square centimeter. Generally, the pressure of a gas is due to the collisions of the gas molecules with the walls of the container. For an ideal gas the pressure is directly proportional to the absolute temperature and inversely proportional to the volume. the pressure of the liquid gas that is not moving is called hydrostatic pressure and is due to the weight of the fluid and the reactive forces applied by the containing walls. Hydrostatic pressure is constant for all points at the same depth and is independent of the shape or cross section of the container. Also, pressure is important in the science of fluids in motion, or hydrodynamics. Bernoulli’s equation is the basic relation between streamline flow of an incompressible, non-viscous fluid and its pressure, velocity, crosssection, the higher velocities and lower pressures occur when the cross-section is smaller. The reduced pressure near a constriction is the basis for several types of fluid pumps, including the automobile carburetor, in which this effect is used to draw gasoline vapor. APPARATUS: Hydro synthetic machine Vernier caliper Meter stick Stop watch LAB. PROCEDURE: 1. Measure the diameter of large and small pipes. 2. Allow the water to flow through the venturimeter. Compute the rate of the volume discharge or Q. 3. After each trial, adjust the value to increase the Q. Record the data. 4. Compute the pressure from the gathered data and use of the Bernoulli’s equation. DATA AND COMPUTATIONS: Dia. big pipe = _____________________________ mm. Dia. small pipe = _____________________________ mm. No. of Trials 1 2 3 h1 h2 Q (m3/s) EXPERIMENT NO. 12 VENTURI METERS OBJECTIVE: To measure the rate of flow in a pipe and to determine the coefficient of discharge Cd. GENERAL: A contraction in a stream tube tend to produce an accelerated flow and fall of pressure which is directly related to flow rate and thus is an excellent meter in which rate of flow maybe calculated from pressure measurements. The form of the venture tube is usually a conical nozzle like reducer followed by a more general enlargement to the original size. It is generally a casting consisting of an upstream section which is the same size as the pipe, has a bronze lining, and contains a piezometer ring for measuring static pressure; a converging conical section; a short conical or cylindrical section containing a piezometer ring, and a diffuser on order to minimized head loss. The pressures at the base of the meter (section 0) and at the throat (section 2) are ontained by the piezometer rings and a differential manometer usually measures the pressure difference. The pressure at the upstream section and throat are actual pressures, the velocities from Bernoulli’s equation are theoretical velocities. If losses are considered in the energy equation, the velocities are then the actual velocities. New, from the principle of continuity, Q = AV, the actual velocity times the actual area of the throat determines the actual discharge. Because of streamlining the flow passage, any jet contraction beyond the smallest section is eliminated; consequently the coefficient of contraction has a value of unity and the basic discharge equation for the venture meter for incompressible flow is Where R = gauge difference S = specific gravity of manometer liquid Si = specific gravity of flowing liquid Note: that since contraction coefficient is unity; hence LAB. APPARATUS: Hydro synthetic machine Stop watch Ruler Container Hose PROCEDURE: 1. Run the pump to let the water flow through the pipelines. 2. Allow the liquid to collect in a container and note the rise in the liquid surfaced in a measured time. 3. Read the manometer gauge difference. 4. Make five (5) trials. DATA AND COMPUTATIONS: Trial 1 2 3 4 5 H (cm) R (cm) Time (sec) Cd R gauge difference H = height of water from base of the bucket D1 inside dia. of pipe D2 outside dia. of pipe Pipe thickness = _________________ Area of container = _________________ EXPERIMENT NO. 13 AN INVESTIGATION OF THE DARCY-WEISBACK EQUATION I. INTRODUCTION OBJECTIVE: 1. To determine the head loss using the head loss apparatus. 2. To compare the experimental head loss with the theoretical head loss. GENERAL: The flow of fluids through various conduits and element results in a friction loss. This experiment aims to examine this loss with the use of thru Friction Loss Apparatus. APPARATUS: Hydro synthetic machine Meter stick Stop watch Vernier caliper Darcy Weisback Equation h = L f V D2g LAB. APPARATUS: 1. Select the pipelines to be considered in the experiment. 2. Take note of the pipe diameter involved. 3. Measure the lengths of the pipes involved. 4. 5. Allow the water to flow. 6. Measure the head loss and determine the discharge by taking note of the volume of flow and the time taken. 7. Repeat for the other pipes selected. DATA AND COMPUTATIONS: Trial Length Dia. Velocity f Exp. hf Theo. hf % 1 2 3 The values of friction factor (f) were obtained by solving for the Reynold’s Number and assuming that the pipes were hydraulically smooth. EXPERIMENT NO. 14 VELOCITY MEASUREMENT BY PITOT TUBE OBJECTIVE: To determine velocity of flow by use of a Pitot tube. APPARATUS: Pitot tube Meter stick Equipment used in experiment work of volumetric discharge measurement Drawing a Pitot tube