Chapter2 Solutions
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Introd uction to Thermo-Fluid s System s Design , First Edition. André G. McDonald and Hugh L. Magande.©2013 André G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd. 2.1 A design engineer wishes to select an appropriate fan for the following galvanized steel duct system. Estimate the pressure loss for each branch of the duct system. Solution: There are two branches in this duct system: Branches 1-3 and 1-4. These branches are made up of multiple sections: Branch 1-3: Sections 1-2 and 2-3. Branch 1-4: Sections 1-2 and 2-4 Find the pressure loss in each duct section to determine the pressure loss in each branch. Section 1-2 This section is 50 ft long with a 10-in-diameter. The total flow rate through the section is 400 cfm. The equivalent length of this section is the sum of the actual length of the section, plus the equivalent length for the entrance from the large plenum: L1-2 = Lduct + Le,entrance From Table A.4, the equivalent length for an abrupt, 90o entrance to the 10-in-diameter circular duct is found to be 25 ft. So, L1-2 = 50 ft + 25 ft = 75 ft From the appropriate friction loss chart for round, straight galvanized steel ducts (Figure A.1), the pressure loss per 100 ft of duct is 0.09 in. of water. So, the pressure loss in this section is Introd uction to Thermo-Fluid s System s Design , First Edition. André G. McDonald and Hugh L. Magande. ©2013 André G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd. 0.09 in. water P12 75 ft 100 ft ΔP1-2 = 0.0675 in. of water Section 2-3 This section is 50 ft long with a 9-in-diameter. The total flow rate through the section is 280 cfm. The equivalent length of this section is the sum of the actual length of the section, plus the equivalent length for the straight-through tee branch fitting: L2-3 = Lduct + Le,tee-straight In Table A.4, the equivalent length for a straight-through tee branch fitting on a 9-in-diameter circular duct is not given. Therefore, choose the value for the 10-in-diameter duct, which is given as 7 ft (This will give more conservative numbers for any subsequent calculation). Thus, L2-3 = 50 ft + 7 ft = 57 ft From the friction loss chart for round, straight galvanized steel ducts, the pressure loss per 100 ft of duct is 0.078 in. of water. Therefore, the pressure loss in this section is 0.078 in. water P23 57 ft 100 ft ΔP2-3 = 0.0445 in. of water Section 2-4 This section is 40 ft long with a 6-in-diameter. The total flow rate through the section is 120 cfm. The equivalent length of this section is the sum of the actual length of the section, plus the equivalent lengths for the diverging 45o wye branch fitting, the 45o bend, and the 90o bend: L2-4 = Lduct + Le,wye + Le,45 deg bend + Le,90 deg bend Introd uction to Thermo-Fluid s System s Design , First Edition. André G. McDonald and Hugh L. Magande. ©2013 André G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd. Choose the 90o pleated elbow since it has a lower equivalent length and lower losses. The 45o elbow is also pleated. Note that only 120 cfm of fluid enters section 2-4. Therefore, the wye is a diverging branch fitting. The equivalent lengths for this 6-in-diameter circular duct section are: Le,wye = 10 ft; Le,45 deg bend = 5 ft; Le,90 deg bend = 8 ft Hence, L2-4 = 40 ft + 10 ft + 5 ft + 8 ft = 63 ft From the friction loss chart for round, straight galvanized steel ducts, the pressure loss per 100 ft of duct is 0.13 in. of water. Therefore, the pressure loss in this section is 0.13 in. water P24 63 ft 100 ft ΔP2-4 = 0.0819 in. of water The total pressure loss in each branch can be determined. Branch 1-3: ΔP1-3= ΔP1-2 + ΔP2-3 = 0.0675 in. of water + 0.0445 in. of water ΔP1-3 = 0.112 in. of water Branch 1-4: ΔP1-4 = ΔP1-2 + ΔP2-4 = 0.0675 in. of water + 0.0819 in. of water ΔP2-4 = 0.149 in. of water Magande. Magande. Design a round duct system. Preliminary Specifications and Constraints i. and 100 cfm. Published 2013 by John Wiley & Sons. The size and material of the ducts will be determined. Select a suitable duct material. The length of each duct section is given. complete with the pressure losses. 2. The system is a perimeter type located below the finished floor. The diffuser boots are shown.21 in. Detailed Design Objective To design a round air duct system. McDonald and Hugh L. The working fluid will be air. and pressure losses are constrained. bearing in mind that a total pressure of 0. McDonald and Hugh L. Ltd. ii. First Edition. This is a low-velocity air-distribution system. 120 cfm. . iv. The duct lengths. wg.2 The duct system shown is one branch of a complete low-velocity air-distribution system. iii. as shown in the drawing. ii.Introd uction to Thermo-Fluid s System s Design . The total pressure available at the plenum is restricted to 0. The air flow rates through the three diffusers are given as 80 cfm. Possible Solution: Definition Size the round ducts for the given system. ©2013 André G. wg is available at the plenum. iii. air flow rates.21 in. The duct system is connected to an air plenum. André G. Data Given or Known i. 0. The pressure losses for the three diffusers are given as 0.elbow). wg.04 in. Sketch A sketch of the system is provided to show the labels of each section of the duct system. iii. wg. McDonald and Hugh L. If the plenum is able to move air through the longest run of ductwork. Analysis In this design problem.05 in. This is required for low-velocity air-distribution systems. wg.. Total friction losses available for the ductwork should be 0.through + L3 + Lwye.21 in.. wg. . iv. It will be chosen as the material. Galvanized steel is typically used to fabricate air duct systems. wg.Introd uction to Thermo-Fluid s System s Design .036 in. The designer is required to size the ducts within this constraint. wg.21 in. This reduces noise and losses. ©2013 André G. v. Published 2013 by John Wiley & Sons. McDonald and Hugh L. The total pressure available at the plenum is 0. ii. then it will be able to move air through the side branches. The maximum air velocity is 1200 fpm. Ltd. The total equivalent length of this branch is Ltotal = LBellmouth + L1 + Ltee. and 0. The 45o elbows are pleated. First Edition. Assumptions/Limitations/Constraints i. v. André G.through + L5 + 2(L45. or less to meet the constraint at the plenum. The entrance to the system at the plenum is a Bellmouth entrance. Magande.21 in. Determine the pressure loss per 100 ft of duct The longest branch is the 1-3-5 branch. Magande. the total pressure available at the plenum is constrained to 0. iv. wg. Ltotal = 8 ft + 20 ft + 5 ft + 12 ft + 5 ft + (8 + 8 + 15) ft + 2(6 ft) = 93 ft. At this point. Magande. Therefore.. wg. .21 in. 820 fpm. Assume that the duct diameter is 8 inches to find the equivalent length of the fittings.18 in. per 100 ft duct ≈ 0. 600 fpm. Section 5: 5 inches. Section 3: 220 cfm. Published 2013 by John Wiley & Sons. The duct sizes and velocities are: Section 1: 8 inches. Ltd.21 0. 850 fpm. Section 3: 7 inches. First Edition. Apply a pressure loss of 0. ©2013 André G. x 100 ft = 0. 710 fpm. The volume flow rate through the sections of the system are: Section 1: 300 cfm. The total pressure available from the plenum is 0. 620 fpm. McDonald and Hugh L.1 can be used to size the duct sections. the diameter of the duct is not known. the duct velocity does not exceed 1200 fpm. Table A. Section 4: 120 cfm. In all the sections. For the longest branch of the duct system. Note that the equivalent lengths for the tee and the wye are for diverging branch fittings. the available pressure is the total pressure from the plenum less the pressure loss at the end of the longest branch. wg. Section 2: 80 cfm.04 in. Thus. Section 4: 6 inches. The chart shown in Figure A. Magande. for sizing the ducts. Section 2: 5 inches.2 in. per 100 ft duct 93 ft will be used.2 in. Section 5: 100 cfm. per 100 ft duct. André G.Introd uction to Thermo-Fluid s System s Design .4 gives the equivalent lengths for each circular duct fitting. wg. ΔP 0. Size the duct sections The total volume flow rate of air from the plenum is (80 + 120 + 100) cfm = 300 cfm. wg. McDonald and Hugh L. For branch 1-2: ΔP1-2 = ΔP1 + ΔP2 = (0. per 100 ft duct. wg. wg.12) in.031 + 0. = 0.031 + 0.12 in. x L1 Ltee.18 in. wg.18 in. showing the duct sizes is presented below.21 in.through x 12 5 ft = 0. Magande. wg. Section 3: ΔP3 0. wg. 100 ft 100 ft ΔP4 = 0. < 0. x L4 Lwye. wg.05 in. wg. x L2 Ltee.18 in. all the sections have lower pressure losses than that available from the plenum.036 in. = 0. wg. In this case. 0. 0..086 in. wg. Section 5: ΔP5 0. Magande.elbow ΔPdiffuser x 31 12 ft 0. Published 2013 by John Wiley & Sons. 100 ft 100 ft Section 4: ΔP4 0. André G. wg. wg. wg.196 in. McDonald and Hugh L. wg. wg. wg.21 in. < 0. wg. wg. x L3 Lwye. McDonald and Hugh L. wg.12) in..18 in.18 in. First Edition. A similar check should be conducted for the longest branch.branch ΔPdiffuser x 10 27 ft 0. With 0.21 in. wg.18 in.045 + 0.18 in.162 in. wg. For the longest branch: ΔP1-3-5 = ΔP1 + ΔP3 + ΔP5 = (0.165 in.045 + 0.18 in. 100 ft 100 ft ΔP5 = 0. wg. Drawings The final drawing.031 in. < 0.. 0.18 in. 100 ft 100 ft Section 2: ΔP2 0. wg.12 in. wg.18 in. ©2013 André G. 100 ft 100 ft ΔP2 = 0.Introd uction to Thermo-Fluid s System s Design . = 0. 0. wg. Ltd.045 + 0.through x 20 5 ft = 0. 0. wg.. the pressure drop through the sections of the duct system are: Section 1: ΔP1 0. wg.045 in. x L5 2 L45..04 in.18 in. wg.086) in. wg. For branch 1-3-4: ΔP1-3-4 = ΔP1 + ΔP3 + ΔP4 = (0. .branch ΔPdiffuser x 15 13 ft 0. A check should be conducted to ensure that the pressure loss in each of the branches does not exceed the total pressure available at the plenum. this loss is very small. Absent from the design are losses due to transitions from larger duct sizes to smaller duct sizes. In branch 1-2 and 1-3-4. of available pressure at the plenum forced a calculation of an appropriate pressure loss for the purposes of duct sizing. Conclusions Round duct sizes have been chosen for this system based on a pressure loss of 0. In all cases. per 100 ft of duct for small-sized. of pressure drop.21 in. wg. the duct would be converging (becoming smaller) in the direction of air flow. These dampers should provide about 0. First Edition. the pressure loss is lower than the main branch (branch 1-3-5). This assumption resulted in a more conservative design since lower equivalent lengths are expected for duct sizes smaller than 8 inches. This is larger than the standard 0. ©2013 André G. Published 2013 by John Wiley & Sons. Magande. The assumption of an 8-inches duct to determine the equivalent lengths of the fittings is valid. The constraint of 0. McDonald and Hugh L.Introd uction to Thermo-Fluid s System s Design .18 in. wg.1 in. Ltd. Magande. wg. wg. per 100 ft of duct. dampers may be installed to control the flow of air through these branches. In all cases. and was ignored. the duct sizes were 8 inches or less. To balance the system. with small equivalent lengths on the order of 3 ft. André G.03 in. . low-velocity duct systems. Compared to other losses in the system. McDonald and Hugh L. 1 8 850 0. First Edition.086 5 5 710 0. The following table summarizes the design results. ©2013 André G.045 2 5 600 0. McDonald and Hugh L. André G. wg. Duct Section Duct Size Duct Velocity Total Pressure Loss in. fpm in.12 . Magande.12 3 7 820 0.Introd uction to Thermo-Fluid s System s Design . Ltd. McDonald and Hugh L. Published 2013 by John Wiley & Sons.031 4 6 620 0. Magande. Published 2013 by John Wiley & Sons.Introd uction to Thermo-Fluid s System s Design . Magande. Office Space Heating Air Requirement Office 204 310 cfm Office 205 450 cfm Office 206 170 cfm Office 207 500 cfm . First Edition.3 For most building design projects. For the offices shown in the plan (complete with the occupant and work function). Ltd. McDonald and Hugh L. and they are shown in the following table. the mechanical engineering sub-consultant has expertise in the design of ductwork to transport air for the purposes of heating and/or cooling an occupied space.e. The following section of a second floor tenant plan of an office building has been given by an architect. the architect has requested the design of a ductwork system to provide air at 75oF to heat the occupied spaces. McDonald and Hugh L. In most cases. André G. 2. ©2013 André G. Magande. the architectural trade tends to be the consultant (i. the lead consultant for the project) who hires the mechanical and the electrical trades as sub-consultants on the project. A HVAC engineer has determined the amount of air required to maintain the space temperature. . The amount of air. Data Given or Known i. McDonald and Hugh L. Limit the air velocity in the ductwork to 1200 fpm. Therefore. Office 204 has a length of 18 ft and a width of 10 ft. Limit the friction loss everywhere in the duct system to approximately 0. ii. a low-velocity duct system will be designed where the maximum velocity should be 1200 fpm. André G. the engineer missed the fact that ASHRAE Standard 62 requires that 20 cfm per person of fresh outdoor air must be provided. iii. v. The fan is to be located on the roof above the offices. a) To ensure an esthetically pleasing finish in the space. Ltd. less the fresh air required by code. The fan is complete with a plenum section. Air at 75oF is required. and show the system layout. Since this is an office space. ©2013 André G. 20 cfm per person of fresh outdoor air is required. specify the minimum operating condition of the fan. wg. Published 2013 by John Wiley & Sons. a noisy. is provided by the HVAC engineer in tabular format. highvelocity duct system may not be desired.1 in. Magande. First Edition. and it will be fitted with a plenum section. However. the architect has requested the design of a ductwork system based on round ducts. Due to the fact that most of the occupants of this section of the floor are managers and/or directors in the complex hierarchy of the client’s company. b) Based on the design of the ductwork. a) Possible Solution: Detailed Design Objective To determine the sizes of round duct in a ductwork system. Assumptions/Limitations/Constraints i. iv. the architect would like to have a dedicated fan installed with the ductwork for this section of offices. ii. Magande.Introd uction to Thermo-Fluid s System s Design . McDonald and Hugh L. This is a standard industry guideline. per 100 ft of duct. wg. McDonald and Hugh L.Introd uction to Thermo-Fluid s System s Design . McDonald and Hugh L. However. complete with numbering of the branches. André G. Sketch The following sketch shows the tentative layout. from experience. Analysis The total flow rates to each of the offices shall be determined to find the duct sizes. iii. it is clear that each office will have a single full-time occupant. Magande. Diffuser boots may be needed for discharge into the office spaces. Magande. Published 2013 by John Wiley & Sons. First Edition. iv. Based on the titles for the offices. Galvanized sheet metal will be used to fabricate the duct since this is typically the material of choice for these types of applications. Including the requirement of ASHRAE Standard 62.05 in. ©2013 André G. Ltd. for a more conservative design. this magnitude of loss was found to be on the high side. the total flow rates for the offices are: . Assume that the pressure loss across the diffuser is 0. Note that this really depends on the selection of the diffuser. per 100 ft of duct and the air velocities are less than 1200 fpm.Office 206 7 750 190 0. wg. per 100 ft of duct. First Edition.Office 205 10 860 470 0.125 3-4 12 920 710 0. André G.1 in. Duct Section Duct Diameter Air Velocity Air Flow Pressure Loss in. McDonald and Hugh L. fpm cfm in. wg./100 ft 1-2 16 1090 1510 0. Magande.13 3. Published 2013 by John Wiley & Sons.1 2-3 14 1150 1180 0. ©2013 André G.Office 207 10 980 520 0.1 2.Introd uction to Thermo-Fluid s System s Design .15 In all the sections. Magande. Drawings The layout. including the sizes of the ducts. the pressure loss in the ducts is on the order of 0. wg. the actual pressure loss per 100 ft of duct and the duct velocity will be provided to ensure that the design constraints were not violated. Ltd.15 4.1 in. .Office 204 9 730 330 0. For verification. McDonald and Hugh L.11 4. is shown below. Office Space Total Air Requirement Office 204 330 cfm Office 205 470 cfm Office 206 190 cfm Office 207 520 cfm It was assumed that the pressure loss in the ductwork would be on the order of 0. The friction loss chart for round. straight galvanized steel ducts will be consulted to determine the round duct sizes. Determine the total length (straight duct length. wg. to balance the systems. ©2013 André G.Introd uction to Thermo-Fluid s System s Design . Next. The total air flow rate required for this system is 1510 cfm. First Edition. These may be increased to even numbers. The velocities in all the duct sections were less than 1200 fpm. McDonald and Hugh L. Published 2013 by John Wiley & Sons. . André G. Ltd. b) Specification of the minimum operating condition of the fan means that the minimum air flow rate and static pressure at the fan will be provided. per 100 ft of duct. McDonald and Hugh L. The friction losses were on the order of 0. if desired. determine the total pressure drop in the longest branch of the duct system. Some odd duct sizes are present. However. The longest branch is labelled 1-2-3-4-5-Office 207. Magande. Conclusion The ductwork system has been designed as specified with round ducts.1 in. dampers may be needed in the branches at the diffusers. Magande. plus equivalent lengths of fittings) of this branch (LLB). ΔPduct 0.thru.thru. LLB Lentrance L12 Ltee. wg. x 156 ft 0. ΔPstatic. wg. Accordingly. André G. McDonald and Hugh L.5 L5-207 Assumptions will be made regarding the length of the duct sections. the Le/D ratio will be used to find the equivalent lengths. Magande. the minimum operating condition of the fan is: 1510 cfm at 0.21 in. LLB = (40 + 5 + 11 + 10 + 10 + 10 + 8 + 15 + 33 + 14) ft ≈ 156 ft. and are negligible. given in the problem statement.22 in.1 in. 100 ft There is also a pressure loss across the diffuser to Office 207.05) in. First Edition. ©2013 André G.156 + 0. wg.fan = (0. This will ensure that the fan is a bit larger.fan = 0. For duct sizes larger than 12 in.21 in. the total pressure required at the fan and plenum is ΔPstatic.branch.. wg. Published 2013 by John Wiley & Sons. Assume that the entrance to the duct from the plenum is an abrupt 90o entrance. Therefore.thru. . Duct contractions typically produce low losses. wg. Thus.Introd uction to Thermo-Fluid s System s Design .2 L23 Ltee.156 in. Note that including losses due to the duct contractions would have increased the pressure loss to approximately 0. Magande.4 L45 Ltee. McDonald and Hugh L.3 L34 Ltee. Hence. Ltd. wg. These lengths will be based on the length and width of Office 204. wg. . McDonald and Hugh L. of total pressure at the required design flows. wg. Ltd. iv. McDonald and Hugh L. The air flow rates through the diffuser boots are given. iv.. Design a round ductwork system. The duct system is connected to an air handling unit (AHU). the heating/cooling coil section has a pressure loss of 0.20 in. The pressure losses in the AHU are given. 2. wg. The AHU is a modular unit complete with a fan that can produce 0. for the design flows given..05 in. ©2013 André G.60 in. wg. the filter section has a pressure loss of 0. iii. ii. and the casing has a miscellaneous loss of 0. André G.10 in. Magande. The total pressure available from the fan is 0. The size and material of the ducts will be determined. ensuring that the location of and pressure drops across appropriate dampers for balancing the system is clear for the convenience of the mechanical contractor and the client. The length of each duct section is given. Magande. First Edition.4 A draw-through air handling unit (AHU) will be used to supply conditioned air as shown in the schematic below.60 in.Introd uction to Thermo-Fluid s System s Design . wg. Data Given or Known i. Published 2013 by John Wiley & Sons. Possible Solution: Detailed Design Objective To design a round air duct system. Within the AHU assembly. Introd uction to Thermo-Fluid s System s Design . First Edition. The elbows are pleated. v. the diameter of the duct is not known. McDonald and Hugh L. The designer is required to size the ducts within this constraint. the total pressure available at the fan is constrained to 0. or less to meet the constraint at the fan. At this point. Table A.through). This reduces noise and losses. wg. Magande.60 in. Another sketch will be provided that clearly shows the locations of the appropriate dampers (if needed). then it will be able to move air through the side branches. ©2013 André G. Galvanized steel is typically used to fabricate air duct systems. Analysis In this design problem. Total friction losses available for the ductwork and component losses should be 0. iii. The maximum air velocity will be 1200 fpm. Sketch A sketch of the system has been provided that shows the labels of each section of the duct system. Ltd. Published 2013 by John Wiley & Sons. This assumption will be used to find the equivalent lengths of the fittings.4 gives the equivalent lengths of the fittings in circular ducts. Assumptions/Limitations/Constraints i. ii. André G. Note that the equivalent lengths for the wye are for diverging branch fittings. 12 inches was chosen because the total flow rate of air is large at 845 cfm. with the typical boot equivalent length given as 20 ft. Determine the pressure loss per 100 ft of duct The longest branch is the 1-2-3-4-9 branch. It will be chosen as the material. McDonald and Hugh L. The entrance to the system at the plenum is a Bellmouth entrance. Ltotal = 12 ft + 21 ft + 10 ft + 8 ft + 10 ft + 29 ft + 3(15 ft) + 4(8 ft) = 167 ft. The pressure loss at the diffuser boots are given.60 in. If the fan is able to move air through the longest run of ductwork. . This is typical for low-velocity air-distribution systems. Magande. wg. The total equivalent length of this branch is Ltotal = LBellmouth + L1 + L2 + L3 + L4 + L9+ 3(L90. Assume that the duct diameter is 12 inches. v. iv. Therefore.elbow) + 4(Lwye. Low velocities will be chosen to ensure that the available total pressure from the fan is not exceeded. Section 5: 6 inches. Section 6: 8 inches. the duct velocity does not exceed 1200 fpm. the available pressure is the total pressure from the fan less the pressure losses through the diffuser at the end of the longest branch and the losses in the AHU. Section 2: 595 cfm. Section 2: 10 inches. wg.Introd uction to Thermo-Fluid s System s Design .. Section 4: 275 cfm.18 in. wg. 610 fpm.1 can be used to size the duct sections. velocities.19 in. wg.15 in./100 ft. wg. 900 fpm. wg. 0. Published 2013 by John Wiley & Sons.. 850 fpm..12 in. per 100 ft duct ≈ 0. For the longest branch of the duct system. In all the sections. Magande. wg. wg. per 100 ft duct will be used. Section 3: 395 cfm. Section 8: 6 inches.15 in. 610 fpm. wg. Section 4: 8 inches./100 ft. 1100 fpm. 0. for sizing the ducts. per 100 ft duct./100 ft.20 0. 710 fpm. Section 9: 6 inches. and actual pressure drops are: Section 1: 12 inches./100 ft.15 in.04 0. 0. ©2013 André G. Section 7: 7 inches. Thus./100 ft.15 in. 1100 fpm. wg. .13 in. 0.13 in. The chart shown in Figure A. 760 fpm... The total pressure available from the fan is 0. McDonald and Hugh L. McDonald and Hugh L. wg. 750 fpm.. Section 3: 9 inches. 0. André G.60 0. ΔP 0. 0. Apply a pressure loss of 0. Ltd. x 100 ft 167 ft ΔP = 0. The volume flow rate through the sections of the main branch are: Section 1: 845 cfm. wg. First Edition.15 in. Magande. 0.60 in../100 ft./100 ft.13 in. Size the duct sections The total volume flow rate of air from the fan is (250 + 120 + 150 + 200 + 125) cfm = 845 cfm.10 0. 0. The duct sizes.05 in. wg.15 in. 0./100 ft. wg./100 ft.. wg. wg. 0.branch ΔPdiffuser x 14 13 ft 0.075 in. wg. wg. 100 ft 100 ft Section 3: ΔP3 0. wg.19 in. wg.branch ΔPdiffuser x 20 10 ft 0. ©2013 André G.branch ΔPdiffuser x 22 13 ft 0. wg. wg.13 in. wg.through x 8 7 ft = 0. x L6 Lwy e.072 in. 100 ft 100 ft Section 2: ΔP2 0. Section 6: ΔP6 0. First Edition. Ltd. McDonald and Hugh L. 0.13 in. x L1 Lbellmouth 2 L90.095 in. wg.15 in. 100 ft 100 ft Section 7: ΔP7 0. 0.. Magande.. 100 ft 100 ft Section 4: ΔP4 0.. wg. . 0. wg. A similar check should be conducted for the longest branch. 100 ft 100 ft . x L7 Lwy e.04 in. wg.023 in.Introd uction to Thermo-Fluid s System s Design .19 in. wg. 0. 0. wg. wg.092 in.023 in.15 in. x L8 Lwye. wg. 0.05 in.12 in. 100 ft 100 ft Section 5: ΔP5 0. A check should be conducted to ensure that the pressure loss in each of the branches does not exceed the total pressure available at the fan. McDonald and Hugh L. Magande. 0.elbow ΔPdiffuser x 17 10 5 ft 0.elbow x 21 12 2 *15 ft 0.15 in. Published 2013 by John Wiley & Sons.15 in. wg. x L4 Lwy e. wg. wg. 100 ft 100 ft Section 8: ΔP8 0. 0.032 in. wg.through x 10 5 ft = 0.03 in.081 in. wg.15 in. wg. The pressure drop through the sections of the duct system are: Section 1: ΔP1 0. wg.13 in.through x 10 7 ft 0.12 in.15 in. André G. wg. 0.036 in.15 in. wg. x L2 Lwy e. x L3 Lwy e. 0. wg. wg.13 in.15 in. x L5 Lwye.branch L45. wg. 100 ft 100 ft ΔP5 = 0. ©2013 André G. McDonald and Hugh L.25 + 0.072) in.54 in. Dampers with the specified pressure drops are required to balance the system on each section: Section 6: 0. < 0. wg. wg. wg.60 in. André G. For branch 1-2-3-4-5: ΔP1-2-3-4-5 = ΔPAHU + ΔP1 + ΔP2 + ΔP3 + ΔP4 + ΔP5 = (0. wg.through L90.10 in.18 in. it is shown that all the sections have lower pressure losses than that available from the fan. < 0. wg. 100 ft 100 ft ΔP9 = 0. For branch 1-2-7: ΔP1-2-7 = ΔPAHU + ΔP1 + ΔP2 + ΔP7 = (0. Section 5: 0. Published 2013 by John Wiley & Sons.023 + 0. = 0. Magande.60 in.023 + 0. wg.095 + 0. wg. For branch 1-2-3-8: ΔP1-2-3-8 = ΔPAHU + ΔP1 + ΔP2 + ΔP3 + ΔP8 = (0. wg.081) in. Section 9: ΔP9 0. wg.023 + 0. 0.60 in.095 + 0. wg.25 + 0. = 0.032 + 0. = 0. wg.075) in.12 in. = 0.18 in.032 + 0. < 0.092) in.16 in. = 0. wg.elbow ΔPdiffuser x 28 4 8 ft 0. x L9 Lwy e.60 in. wg. From the above calculations. wg. McDonald and Hugh L.095 + 0. First Edition. wg.60 in.112 in.023 + 0. For branch 1-6: ΔP = ΔPAHU + ΔP1 + ΔP6 = (0. < 0.04 in. < 0.25 + 0.032 + 0.Introd uction to Thermo-Fluid s System s Design . wg. For the longest branch (1-2-3-4-9): ΔP = ΔPAHU + ΔP1 + ΔP2 + ΔP3 + ΔP4 + ΔP9 ΔP = (0.023 + 0.095 + 0. wg. Section 8: 0.. wg.032 + 0. wg.112) in. Section 7: 0.25 + 0. wg. Ltd.46 in. wg.48 in.095 + 0. wg.25 + 0. wg.44 in.50 in.14 in. . Magande. The following table summarizes the design results. This assumption resulted in a more conservative design since. André G. wg.Introd uction to Thermo-Fluid s System s Design . Published 2013 by John Wiley & Sons. The constraint of 0. Absent from the design are losses due to transitions from larger duct sizes to smaller duct sizes. Drawings The drawing shows the duct sizes and the damper locations. Conclusions Round duct sizes have been chosen for this system based on a pressure loss of 0. This is close to the standard 0. and was ignored. .13 in. The assumption of a 12-inches duct to determine the equivalent lengths of the fittings is valid. low-velocity duct systems. Magande. Ltd. wg. Compared to other losses in the system. First Edition. the duct would be converging (becoming smaller) in the direction of air flow. lower equivalent lengths are expected for duct sizes smaller than 12 inches. the duct sizes were 12 inches or less.60 in. of available pressure at the fan forced a calculation of an appropriate pressure loss for the purposes of duct sizing. In all cases.1 in. this loss is very small. Magande. wg. per 100 ft of duct for small-sized. for the most part. McDonald and Hugh L. with small equivalent lengths on the order of 3 – 4 ft. ©2013 André G. In all cases. per 100 ft of duct. McDonald and Hugh L. 19 3 9 900 0. Published 2013 by John Wiley & Sons.13 9 6 760 0. Magande. André G. 1 12 1100 0. wg.15 2 10 1100 0. McDonald and Hugh L.15 8 6 610 0. First Edition.13 6 8 710 0. Duct Section Duct Size Duct Velocity Total Pressure Loss in.15 4 8 850 0. McDonald and Hugh L.12 7 7 750 0. Magande.15 5 6 610 0. Ltd. ©2013 André G.Introd uction to Thermo-Fluid s System s Design .18 . fpm in. Introd uction to Thermo-Fluid s System s Design , First Edition. André G. McDonald and Hugh L. Magande. ©2013 André G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd. 2.5 A small-duct high-velocity system is to be developed to distribute conditioned air to a factory. This type of air distribution system results in smaller duct sizes, and is desired due to space limits and high construction costs. As a guide, Section 3.11 of the Air-Conditioning, Heating, and Refrigeration Institute (AHRI) Standard 210/240-2005 [10] requires that a cooling product contain a blower that produces at least 1.2 in. wg. of external static pressure when operating at the certified air flow rate of 220 to 350 cfm per rated ton of cooling. For high-velocity systems, a maximum velocity of 5000 fpm has been recommended [11]. Terminal boxes will be introduced at the duct exit to the space to throttle the air to a low velocity, control the air flow, and reduce noise. The terminal boxes are usually designed to operate at a minimum pressure loss of about 0.25 to 1.0 in. wg., that is, the branch pressure loss should be on the order of at least 0.25 to 1.0 in. wg. The cooling product is an air-handling unit, capable of producing 5 tons of cooling. Based on the sketch provided below, design a round duct, high-velocity system to distribute air in the factory. Will the pressure drops across the terminal boxes be sufficient to balance the system? Make appropriate recommendations to the client. Possible Solution: Definition Size the round ducts for the given high-velocity system. Preliminary Specifications and Constraints i. The working fluid will be air. ii. This is a high-velocity air-distribution system. Introd uction to Thermo-Fluid s System s Design , First Edition. André G. McDonald and Hugh L. Magande. ©2013 André G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd. iii. AHRI Standard 210/240-2005 specifies that a high-velocity blower should produce at least 1.2 in. wg. of external static pressure at 220 to 350 cfm per rated ton of cooling. iv. The air velocity should not exceed 5000 fpm. v. The branch pressure losses should be on the order of at least 0.25 to 1.0 in. wg. vi. The duct lengths, air flow rates, and pressure losses across the terminal boxes are constrained, as shown in the drawing. Detailed Design Objective To design a round air duct system. The size and material of the ducts will be determined. Data Given or Known i. The length of each duct section is given. ii. The air flow rate through the three diffusers is given as 460 cfm, 590 cfm, and 550 cfm. iii. The duct system is connected to an air handling unit. iv. The blower should produce at least 1.2 in. wg. of external static pressure at 220 to 350 cfm per rated ton of cooling. v. The air handling unit produces 5 tons of cooling. vi. The pressure losses across the three terminal boxes are given as 0.07 in. wg., 0.056 in. wg., and 0.06 in. wg. Assumptions/Limitations/Constraints i. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material. ii. The entrance to the system at the air handling unit will be a Bellmouth entrance. This reduces noise and losses. iii. The 45o elbows will be pleated. Sketch A sketch of the system is provided to show the labeling of each section to be evaluated. Introd uction to Thermo-Fluid s System s Design , First Edition. André G. McDonald and Hugh L. Magande. ©2013 André G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd. Analysis Determine the maximum air velocity in the system According to the problem preamble, the air velocity in the duct cannot exceed 5000 fpm. From Table 2.3 and for high-velocity duct systems, air flow rates between 1000 cfm and 3000 cfm require a maximum air velocity of 2500 fpm. Even though the volume flow rate in section 5 and the branch take-offs are lower than 1000 cfm, a maximum velocity of 2500 fpm will be used to size the round ducts. Size the duct sections The total volume flow rate of air from the air handling unit is (460 + 590 + 550) cfm = 1600 cfm. The volume flow rates through the sections of the system are: Section 1: 1600 cfm, Section 2: 460 cfm, Section 3: 1140 cfm, Section 4: 590 cfm, Section 5: 550 cfm. The chart shown in Figure A.1 can be used to size the duct sections. Use the maximum velocity constraint of 2500 fpm as a guide. The duct sizes, velocities, and pressure losses are: Section 1: 11 inches, 2500 fpm, 0.8 in. wg. per 100 ft, Section 2: 6 inches, 2500 fpm, 1.45 in. wg. per 100 ft, Section 3: 10 inches, 2050 fpm, 0.6 in. wg. per 100 ft, Section 4: 7 inches, 2250 fpm, 1.2 in. wg. per 100 ft, wg. 100 ft 100 ft Section 5: ΔP5 0. . 100 ft 100 ft Section 3: ΔP3 0. wg. wg.114 in. wg. wg. Section 1: ΔP1 0..2 in. x L2 Ltee.through x 20 8 ft 0. Ltd.80 in. > 0. 100 ft 100 ft For the longest branch: ΔP1-3-5 = ΔP1 + ΔP3 + ΔP5 = (0. 100 ft 100 ft Section 4: ΔP4 1. wg.elbow x 31 12 ft 0.114 + 0. For a more conservative analysis. In all the sections. .60 in. McDonald and Hugh L. the pressure drop across the terminal boxes themselves will not be included. Magande.336 in.409 in.95 in.224 + 0.409) in. .747 in. wg.45 in. wg. Higher pressure losses per 100 ft of duct in the shorter branch sections should facilitate system balancing (to prevent excess air from flooding branches with low pressure losses or low frictional resistances). per 100 ft. wg.25 in. 1. Magande. Published 2013 by John Wiley & Sons. 0.branch x 10 20 ft 0. .60 in.45 in. x L1 Ltee.branch x 15 13 ft 0. McDonald and Hugh L. the duct velocity does not exceed 2500 fpm.through x 12 7 ft 0.25 to 1. wg.2 in. . wg. wg. wg. wg. wg. wg. First Edition. 1. 2050 fpm. as required for operation of the terminal boxes. Section 5: 7 inches. 0.0 in. x L5 2 L45. 100 ft 100 ft Section 2: ΔP2 1.80 in. 0. Check the branch pressure losses to confirm minimum requirement for terminal box operation A check should be conducted to ensure that the pressure loss in each of the branches is at least 0. wg. x L4 Lwy e. André G. ©2013 André G. wg. wg.95 in.224 in. wg.95 in.435 in. = 0.Introd uction to Thermo-Fluid s System s Design . 0. x L3 Lwy e. For branch 1-3-4: ΔP1-3-4 = ΔP1 + ΔP3 + ΔP4 = (0.total .114 + 0.25 in. wg.ΔP1-3-4 = (0. Magande. wg. of external static pressure. = 0. at 1. > 0. In addition. = 0. wg. . Magande. Therefore.Introd uction to Thermo-Fluid s System s Design .659 in. wg. wg..674) in. showing the duct sizes is presented below. of external static pressure should be provided by the blower. wg. Based on AHRI Standard 210/240-2005 at least 1. This will be sufficient to meet the pressure loss requirement (0. = 0. Published 2013 by John Wiley & Sons. ΔPbox4 = ΔP1-3-5. wg. wg. McDonald and Hugh L.06 in. First Edition. wg. all the branch sections have pressure losses that are greater than 0. it may be necessary to select different terminal boxes that will produce larger pressure losses in branches 1-2 and 1-3-4.2 in. ©2013 André G.807 in. the total pressure loss in the longest branch is ΔP1-3-5. The pressure drops required across the other terminal boxes are ΔPbox2 = ΔP1-3-5.2 in.224 + 0.674 in. Ltd.total = (0. Pressure drops across the terminal boxes Based on these calculations of branch pressure losses. McDonald and Hugh L.807 – 0.336) in. wg.807 – 0.06) in.total . Given that 1600 cfm will be delivered by the blower on the 5 ton air handling unit. which is required for operation of the terminal boxes. wg.) of the longest branch and the rest of the system. = 0.81 in.13 in.25 in. wg.ΔP1-2 = (0. In this case.224 + 0. = 0.15 in. > 0. The pressure drop across the terminal box in the longest branch will be held at 0. Drawings The final drawing. the blower will not be greatly over-sized for this application.747 + 0. 320 cfm per ton will be required.435) in. without the pressure drops across the terminal boxes. wg. The pressure drops across the terminal boxes have also been modified to reflect the results of the analysis. wg. wg. For branch 1-2: ΔP1-2 = ΔP1 + ΔP2 = (0. André G.659) in. wg. wg.25 in. the client may consider installing dampers in the branches to control air flow and increase the duct pressure losses. Magande. However. and space requirements. Conclusions Round duct sizes have been chosen for this high-velocity system based on a maximum air velocity of 2500 fpm. which would have produced high velocities in excess of the 2500 fpm design constraint. the pressure drop across the terminal boxes was increased. McDonald and Hugh L. caution was taken to avoid under-sizing the ducts. To balance the system. Absent are the losses when the duct converges to smaller diameters. Decisions were made throughout the analysis to ensure that this constraint was not violated. . Effort was taken to size the branch ducts such that the pressure loss per 100 ft of duct was larger than the main branch. The final decision would depend on the preference of the client. the pressure loss is lower than the main branch (branch 1-3-5). The pressure drops could remain the same (as given in the original problem). McDonald and Hugh L. and appropriate balancing dampers could be installed. cost. ©2013 André G. André G. Ltd. This also presents another viable alternative to increasing the size and pressure drop across the terminal boxes. First Edition. Published 2013 by John Wiley & Sons. Magande. These losses are small compared to the others and were ignored. In branch 1-2 and 1-3-4. This helped to reduce the pressure drop requirement across the terminal boxes.Introd uction to Thermo-Fluid s System s Design . Given that the blower is slightly oversized for this application. 60 4 7 2250 1. The following table summarizes the design results.Introd uction to Thermo-Fluid s System s Design .95 . Duct Section Duct Size Duct Velocity Total Pressure Loss in. 1 11 2500 0. André G. Ltd.20 5 7 2050 0. McDonald and Hugh L.80 2 6 2500 1. Published 2013 by John Wiley & Sons. McDonald and Hugh L. Magande.45 3 10 2050 0. First Edition. Magande. wg. ©2013 André G. fpm in. Magande. The working fluid will be air. accessories. The air will be drawn through a hood and filter system. To that end.Introd uction to Thermo-Fluid s System s Design . First Edition. 2. The layout. McDonald and Hugh L. Specify an appropriate fan. to design a high-velocity duct system for a Farr® Gold Series 10 dust collector. Preliminary Specifications and Constraints i. w. Possible Solution: Definition Size the round duct for a dust collector system. as shown. A commercial shop environment will be provided by the Council. Magande. and fittings that are chosen should be such that losses are kept at a minimum. the Council has contracted the services of Alliance Engineering Corp. The dust collector will draw 4000 cfm of air in an effort to eliminate any powder particles from the space. André G. Published 2013 by John Wiley & Sons.g. the designer may consider specification of a utility or industrial centrifugal fan.6 The National Research Council has decided to pursue research in the area of spray-dried agglomeration of nano-sized powder particles to produce micron-sized powder particles. Size and specify the round ductwork between the hood and the duct collector. High efficiency. ©2013 André G. Ltd. Further Information: Given that this is an industrial application. open-pleat style cartridge filters with flame-retardant media and average pressure loss of 2. in which the maximum duct velocity can be on the order of 2500 to 6000 fpm. were used. McDonald and Hugh L. .7 in. Safety and health regulations permit only a limited amount of these particles to escape into the ambient air of the space. Data Given or Known i. André G. The layout.Introd uction to Thermo-Fluid s System s Design . McDonald and Hugh L. This reduces noise and losses.g. The entrance to the system at the hood will be a Bellmouth entrance. Ltd. Any 90o elbows will be 5-piece. ii. ii. Galvanized steel is typically used to fabricate air duct systems. First Edition. Detailed Design Objective To design a round air duct. The air pressure loss across the filters is 2. iii. This is a high-velocity air duct system. The final drawing will show the final duct layout and size. as shown in the sketch. Analysis Determine the maximum air velocity in the system According to the problem statement. The maximum air flow rate is 4000 cfm. with R/D = 1. ii. This will be the velocity constraint in this design. iii. From Table 2. Published 2013 by John Wiley & Sons. Magande. ©2013 André G. Pleated or mitered with vanes will be avoided to prevent accumulation of powder particles in the duct. the maximum air flow rate in the duct will be 4000 cfm. Assumptions/Limitations/Constraints i. The exit to the dust collector will also be a Bellmouth shape. iv. accessories. The equipment dimensions and maximum air flow rate are constrained. iii. The size and material of the duct will be determined. Sketch A sketch of the system is not required here for this analysis. w. . and fittings that are chosen should be such that losses are kept at a minimum. The dimensions of equipment and distances between equipment are given. McDonald and Hugh L. It will be chosen as the material. an air flow rate 4000 cfm will require a maximum air velocity of 3000 fpm.7 in. The air velocity should be between 2500 to 6000 fpm.3 and for high-velocity duct systems. Magande.5. The chart shown in Figure A. air velocity. Thus. and pressure loss are: 16 inches. the duct velocity does not exceed 3000 fpm. 100 ft D D D The length of straight duct is approximately. The duct size. Lstraight = 50 in.33 ft 12 1.7 in. McDonald and Hugh L. wg.Introd uction to Thermo-Fluid s System s Design . wg. wg. 2810 fpm. 0. L L x Lstraight D entrance D 90 bend D exit . + 24 in.1 will be used to size the duct. In this case. wg. Magande.g. Magande.2 in. per 100 ft.33 ft 12 100 ft ΔP 3. Ltd. Size the duct The total volume flow rate of air and the maximum velocity will be used to guide the sizing of the duct. André G. 0. wg. ΔP Pfilter 0. Table A. x27 ft 1. respectively.60 in. Determine the pressure losses in the duct system The total pressure loss in the duct system will be required to specify the requirements of the dust collector fan. ΔP 2. x Lstraight Lentrance L90o bend Lexit 100 ft ΔP Pfilter L o 0. First Edition. wg. w. ©2013 André G.6 in.2 in.4 presents the equivalent lengths of the fittings for round ducts. Therefore.60 in. . Published 2013 by John Wiley & Sons.60 in. McDonald and Hugh L. + 20 ft = 27 ft. the fan should be able to move 4000 cfm of air and provide an external static pressure of 3.33 ft 12 1. In this case. From the performance curves for the Greenheck 15 BISW fan.Introd uction to Thermo-Fluid s System s Design . McDonald and Hugh L.g. a 2830 rpm speed and a 4. The specifications are shown in the catalog sheet. A Greenheck single-width industrial centrifugal belt drive fan will be selected for this application. Magande. First Edition. w. McDonald and Hugh L. Published 2013 by John Wiley & Sons.83 hp motor is selected. The fan should provide at least 4000 cfm of air over at least 3. ©2013 André G.2 in. of external static pressure. Ltd. . André G. Magande. ©2013 André G. Magande. Source: Greenheck Fan. Corp. André G. McDonald and Hugh L. Magande. (Reprinted with permission) .Introd uction to Thermo-Fluid s System s Design . First Edition. McDonald and Hugh L. Published 2013 by John Wiley & Sons. Ltd. ©2013 André G. This will prevent the accumulation of powder particles in the duct.Introd uction to Thermo-Fluid s System s Design . which may be difficult to clean or pose a risk of explosion. Conclusions A round duct has been chosen for this high-velocity system based on a maximum air velocity of 3000 fpm. In this application. McDonald and Hugh L. the fan was slightly oversized. André G. . Throughout the design. Drawings The final drawing. McDonald and Hugh L. Decisions were made throughout the analysis to ensure that this constraint was not violated and that the system losses were kept low. Magande. First Edition. it was decided to avoid the use of any fittings that produced abrupt changes in the duct or flow pattern. showing the duct size is presented below. Published 2013 by John Wiley & Sons. Magande. Ltd. 036 in. The length of each duct section is given. 120 cfm. Galvanized steel is typically used to fabricate air duct systems.04 in.21 in. and 100 cfm. wg.05 in.21 in. v. or less to meet the constraint at the plenum. This is a low-velocity air-distribution system. . McDonald and Hugh L. This reduces noise and losses. wg. The 45o elbows are pleated. iii. The maximum air velocity will be 1200 fpm. 2. First Edition. Magande. ii. and 0.21 in. The working fluid will be air. Magande.2 and redesign the system with rectangular ducts. It will be chosen as the material. iv. iv.. iii. as shown in the drawing. Preliminary Specifications and Constraints i. This is required for low-velocity air-distribution systems. ©2013 André G. air flow rates. wg. The air flow rate through the three diffusers is given as 80 cfm. wg. 0. The entrance to the system at the plenum is a Bellmouth entrance. v. The duct lengths. The size and material of the ducts will be determined. The duct system is connected to an air plenum. The total pressure available at the plenum is 0. Assumptions/Limitations/Constraints i. iv.. ii. Possible Solution: Definition Size the rectangular ducts for the given system.7 Refer to Problem 2. Ltd. Detailed Design Objective To design a rectangular air duct system. André G. Select a suitable duct material. ii. The pressure loss at the three diffusers are given as 0. Data Given or Known i. wg.Introd uction to Thermo-Fluid s System s Design . wg. McDonald and Hugh L. Total friction losses available for the ductwork should be 0. Published 2013 by John Wiley & Sons. and pressure losses are constrained. iii. The total pressure available at the plenum is restricted to 0. through + L3 + Lwye.Introd uction to Thermo-Fluid s System s Design . Published 2013 by John Wiley & Sons. Magande.4 gives the equivalent lengths of the fittings in circular ducts. ©2013 André G.through + L5 + 2(L45. André G. wg. Magande. Ltd.21 in. Assume that the duct diameter is 8 inches to find the equivalents of the fittings. the diameter of the duct is not known. Analysis In this design problem. . At this point. If the plenum is able to move air through the longest run of ductwork. First Edition. Sketch A sketch of the system will be provided to show the labeling of each section of the duct system. Determine the pressure loss per 100 ft of duct The longest branch is the 1-3-5 branch. Table A.elbow).21 in. Therefore. the available pressure is the total pressure from the plenum less the pressure loss at the end of the longest branch. wg. For the longest branch of the duct system. The total pressure available from the plenum is 0. Ltotal = 8 ft + 20 ft + 5 ft + 12 ft + 5 ft + (8 + 8 + 15) ft + 2(6 ft) = 93 ft. then it will be able to move air through the side branches. McDonald and Hugh L. The designer is required to size the ducts within this constraint. The total equivalent length of this branch is Ltotal = LBellmouth + L1 + Ltee. Note that the equivalent lengths for the tee and the wye are for diverging branch fittings. McDonald and Hugh L. the total pressure available at the plenum is constrained to 0. Section 3: 220 cfm. 0. Magande.. x L2 Ltee. Apply a pressure loss of 0. wg. A similar check should be conducted for the longest branch. Section 2: 80 cfm. Ltd.2 in.045 in. 0. Published 2013 by John Wiley & Sons. wg. A check should be conducted to ensure that the pressure loss in each of the branches does not exceed the total pressure available at the plenum. for sizing the ducts.18 in.18 in. 600 fpm. The duct sizes and velocities are: Section 1: 8 inches. The chart shown in Figure A. x L1 Ltee. wg. wg. x 100 ft = 0. 710 fpm.through x 20 5 ft = 0. With 0. McDonald and Hugh L.12 in.2 in. ©2013 André G. wg. per 100 ft duct 93 ft will be used.18 in.Introd uction to Thermo-Fluid s System s Design . Section 5: 100 cfm. McDonald and Hugh L. Magande. per 100 ft duct ≈ 0.04 in. Section 4: 120 cfm.18 in. 100 ft 100 ft Section 2: ΔP2 0.1 can be used to size the duct sections. 820 fpm. wg. .18 in. wg. André G. Size the duct sections as circular ducts The total volume flow rate of air from the plenum is (80 + 120 + 100) cfm = 300 cfm.branch ΔPdiffuser x 10 27 ft 0. wg. First Edition. 620 fpm.21 0. Section 2: 5 inches. 850 fpm. wg. the duct velocity does not exceed 1200 fpm. wg. In all the sections. Section 3: 7 inches.18 in. wg. Section 4: 6 inches. the pressure drop through the sections of the duct system are: Section 1: ΔP1 0. ΔP 0. per 100 ft duct. per 100 ft duct. 100 ft 100 ft ΔP2 = 0. wg. Section 5: 5 inches. The volume flow rate through the sections of the system are: Section 1: 300 cfm.05 in. Therefore.. Introd uction to Thermo-Fluid s System s Design . Section 2: 6 in.12) in.21 in. < 0. 0.162 in. wg. Section 4: 6 in. wg. wg. x 6 in.17). Ltd. Section 3: 7 in.branch ΔPdiffuser x 15 13 ft 0.086 in.031 + 0.18 in..00).18 in. This is gives an equivalent diameter of 6. (aspect ratio: 1.. Size the duct sections as rectangular ducts The equal friction and capacity chart (Table A. McDonald and Hugh L.18 in. The aspect ratio will be 4 or lower.21 in.031 in. (aspect ratio: 1.00).045 + 0. wg.036 in. x 7 in. 100 ft 100 ft ΔP5 = 0. In this case. wg. Section 5: ΔP5 0.3) will be used to select an appropriate rectangular duct equivalent for the circular ducts.18 in.04 in.6 in. (aspect ratio: 1. wg. First Edition. x L3 Lwye.. For branch 1-2: ΔP1-2 = ΔP1 + ΔP2 = (0. wg. wg. 0. 100 ft 100 ft Section 4: ΔP4 0. wg.18 in. wg. x 6 in. x 6 in. wg. (aspect ratio: 1. Magande.14). wg. the pressure loss will be lower than the design equivalent diameters of 5 in. For branch 1-3-4: ΔP1-3-4 = ΔP1 + ΔP3 + ΔP4 = (0. Magande.086) in. wg.00). x L4 Lwye. < 0. At this diameter. wg. and 6 . McDonald and Hugh L.3 is 6 in. Section 3: ΔP3 0. André G. x L5 2 L45. 0. Section 1: 8 in. wg.12) in. The smallest size available from Table A. wg. x 6 in. ©2013 André G.196 in.through x 12 5 ft = 0.045 + 0.18 in.elbow ΔPdiffuser x 31 12 ft 0.165 in.031 + 0. For the longest branch: ΔP1-3-5 = ΔP1 + ΔP3 + ΔP5 = (0.12 in. Published 2013 by John Wiley & Sons. = 0.21 in. wg. Therefore. = 0. Section 5: 6 in. x 6 in. = 0. (aspect ratio: 1. wg. < 0. wg.045 + 0. all the sections have lower pressure losses than that available from the plenum. 100 ft 100 ft ΔP4 = 0. wg. in. the duct would be converging (becoming smaller) in the direction of air flow. While the aspect ratios of the ducts are close to 1. wg. Ltd.21 in. Conclusions Rectangular duct sizes have been chosen for this system based on a pressure loss of 0. This assumption resulted in a more conservative design since lower equivalent lengths are expected for duct sizes smaller than 8 inches. In all cases.18 in. duct in Section 1 and a 7 in. In all cases. Magande. First Edition. The assumption of an 8-inches duct to determine the equivalent lengths of the fittings is valid. wg. Compared to other losses in the system. while producing a duct aspect ratio of 1 and lower pressure drops. Magande. per 100 ft of duct for small-sized.1 in. this loss is very small. Drawings The final drawing. André G. The increase in material is small. installers in the field would likely install an 8 in. and was ignored. ©2013 André G. The constraint of 0. This is larger than the standard 0. Published 2013 by John Wiley & Sons. This would result in marginal increase in duct material. This should be acceptable from a cost and installation perspective. per 100 ft of duct. lowvelocity duct systems. of available pressure at the plenum forced a calculation of an appropriate pressure loss for the purposes of duct sizing. Absent from the design are losses due to transitions from larger duct sizes to smaller duct sizes. x 8 in. duct in Section 3. showing the duct sizes is presented below. resulting in a system pressure loss. . McDonald and Hugh L. x 7 in.Introd uction to Thermo-Fluid s System s Design . the duct sizes were 8 inches or less.. wg. McDonald and Hugh L. with small equivalent lengths on the order of 3 ft. 03 in. Magande. Published 2013 by John Wiley & Sons. These dampers should provide about 0. In branch 1-2 and 1-3-4. wg. To balance the system.045 2 6x6 600 0. fpm in. The following table summarizes the design results. Duct Section Duct Size Duct Velocity Total Pressure Loss in. of pressure drop.031 4 6x6 620 0. ©2013 André G. McDonald and Hugh L. Ltd.Introd uction to Thermo-Fluid s System s Design . André G. dampers may be installed to control the flow of air through these branches. McDonald and Hugh L. 1 8x7 850 0.12 3 7x6 820 0. wg. Magande.12 .086 5 6x6 710 0. the pressure loss is lower than the main branch (branch 1-3-5). First Edition. iv.8 Refer to Problem 2. The entrance to the system at the plenum is a Bellmouth entrance. for the design flows given. with the typical boot equivalent length given as 20 ft. . ©2013 André G. The air flow rate through the diffusers boots is given. Proposed Solution: Detailed Design Objective To design a rectangular air duct system and select a fan. Total friction losses available for the ductwork and component losses should be 0. McDonald and Hugh L.4 and redesign the system with rectangular ducts. Ltd. It will be chosen as the material. iii. Low velocities will be chosen to ensure that the available total pressure from the fan is not exceeded. Assumptions/Limitations/Constraints i. First Edition. The maximum air velocity will be 1200 fpm. The pressure loss at the diffuser boots are given. The elbows are pleated. The total pressure available from the fan is 0.60 in. Magande. This reduces noise and losses. iii. Data Given or Known i. iv. Published 2013 by John Wiley & Sons. The duct system is connected to an air handling unit (AHU). This is typical for low-velocity air-distribution systems. wg. ii. The length of each duct section is given. iv. 2. Sketch A sketch of the system has been provided that shows the labels of each section of the duct system. ii. v. or less to meet the constraint at the fan. Galvanized steel is typically used to fabricate air duct systems. André G. v. The size and material of the ducts will be determined. wg. Magande.Introd uction to Thermo-Fluid s System s Design . Another sketch will be provided that clearly shows the locations of the appropriate dampers (if needed).60 in. The pressure losses in the AHU are given. McDonald and Hugh L. Specify a fan from a manufacturer’s catalog. 05 in. the available pressure is the total pressure from the plenum less the pressure losses through the diffuser at the end of the longest branch and the losses in the AHU. Section 3: 395 cfm. for sizing the ducts. Ltd. per 100 ft duct will be used. The designer is required to size the ducts within this constraint. x 100 ft 167 ft ΔP = 0.Introd uction to Thermo-Fluid s System s Design . At this point. Note that the equivalent lengths for the wye are for diverging branch fittings. . The total pressure available from the fan is 0. Ltotal = 12 ft + 21 ft + 10 ft + 8 ft + 10 ft + 29 ft + 3(15 ft) + 4(8 ft) = 167 ft.elbow) + 4(Lwye. then it will be able to move air through the side branches. Section 4: 275 cfm. wg. wg.13 in. Analysis In this design problem. wg.60 0. the diameter of the duct is not known. Section 2: 595 cfm. First Edition. If the fan is able to move air through the longest run of ductwork. The volume flow rate through the sections of the main branch are: Section 1: 845 cfm. wg. Table A. per 100 ft duct ≈ 0. Hence.60 in. ©2013 André G. ΔP 0. Therefore. For the longest branch of the duct system.10 0.through). Size the duct sections as circular ducts The total volume flow rate of air from the fan is (250 + 120 + 150 + 200 + 125) cfm = 845 cfm. Assume that the duct diameter is 12 inches to find the equivalent lengths of the fittings. Determine the pressure loss per 100 ft of duct The longest branch is the 1-2-3-4-9 branch. McDonald and Hugh L. André G. the total pressure available at the fan is constrained to 0. McDonald and Hugh L. Magande.60 in.4 gives the equivalent lengths of the fittings in circular ducts.20 0. Magande. 12 inches was chosen since the total flow rate of air is large at 845 cfm. wg. The total equivalent length of this branch is Ltotal = LBellmouth + L1 + L2 + L3 + L4 + L9+ 3(L90.04 0. Published 2013 by John Wiley & Sons.15 in. 1 can be used to size the duct sections. wg.15 in./100 ft.13 in.15 in. The chart shown in Figure A./100 ft. In all the sections. André G. Section 3: 9 inches. x L1 Lbellmouth 2 L90. per 100 ft duct. wg. x L2 Lwy e. A similar check should be conducted for the longest branch. Section 9: 6 inches. the duct velocity does not exceed 1200 fpm.023 in. x L3 Lwy e. wg./100 ft. Ltd. wg.15 in. Section 8: 6 inches. Section 7: 7 inches. Section 2: 10 inches. First Edition. wg.through x 10 5 ft = 0.15 in. 0. wg. wg. 0. 1100 fpm./100 ft. 100 ft 100 ft Section 4: ΔP4 0. 0... 0.. Section 4: 8 inches. wg. 610 fpm. wg. 0.15 in. A check should be conducted to ensure that the pressure loss in each of the branches does not exceed the total pressure available at the fan... 100 ft 100 ft Section 2: ΔP2 0. 610 fpm. wg.15 in./100 ft. x L4 Lwy e.. wg. 710 fpm.032 in. wg. 100 ft 100 ft . 0. Apply a pressure loss of 0. 0.095 in. 0. wg. The duct sizes. and actual pressure drops are: Section 1: 12 inches.15 in. wg. 1100 fpm. ©2013 André G.elbow x 21 12 2 *15 ft 0. McDonald and Hugh L.. Magande. 850 fpm. wg. 0. 0. 100 ft 100 ft Section 3: ΔP3 0.18 in. Magande./100 ft. ./100 ft..023 in.15 in. Published 2013 by John Wiley & Sons. 750 fpm. wg./100 ft. wg. wg. 900 fpm.19 in.through x 8 7 ft = 0.through x 10 7 ft 0. wg.15 in..13 in. wg.19 in./100 ft. Section 6: 8 inches.19 in.Introd uction to Thermo-Fluid s System s Design .15 in.15 in. wg. McDonald and Hugh L. 760 fpm. 0. 0.. velocities.12 in. 0. wg. The pressure drop through the sections of the duct system are: Section 1: ΔP1 0. Section 5: 6 inches. 44 in. wg. < 0. McDonald and Hugh L.023 + 0.095 + 0.15 in. Magande. wg. x L8 Lwye. André G.03 in.branch ΔPdiffuser x 20 10 ft 0.036 in.072 in. 0. wg. wg. . wg.15 in. wg. < 0. wg.095 + 0. wg. wg. wg. Ltd.05 in.. Magande. First Edition. x L7 Lwy e. wg.25 + 0. 0.13 in.023 + 0. 0.112 in. 100 ft 100 ft Section 7: ΔP7 0. x L5 Lwye. = 0.46 in. < 0. = 0. wg. wg.elbow ΔPdiffuser x 28 4 8 ft 0.12 in.04 in. Published 2013 by John Wiley & Sons.081 in. 100 ft 100 ft Section 9: ΔP9 0. wg.13 in. McDonald and Hugh L. 100 ft 100 ft ΔP9 = 0.092 in.092) in.081) in. 0. 0. 100 ft 100 ft Section 8: ΔP8 0.112) in. wg. wg.032 + 0.60 in. x L6 Lwy e. wg.. wg. Section 5: ΔP5 0.branch L45. wg.60 in.60 in. wg. wg. wg.04 in. wg. 100 ft 100 ft ΔP5 = 0.Introd uction to Thermo-Fluid s System s Design . wg. 0.18 in. For branch 1-6: ΔP = ΔPAHU + ΔP1 + ΔP6 = (0. ©2013 André G.branch ΔPdiffuser x 14 13 ft 0. = 0. For branch 1-2-7: ΔP1-2-7 = ΔPAHU + ΔP1 + ΔP2 + ΔP7 = (0.branch ΔPdiffuser x 22 13 ft 0. Section 6: ΔP6 0.25 + 0.through L90.075 in. 0. 0.13 in. wg.18 in. wg.13 in.032 + 0.54 in.095 + 0. wg. x L9 Lwy e.12 in.elbow ΔPdiffuser x 17 10 5 ft 0. wg.25 + 0. For the longest branch (1-2-3-4-9): ΔP = ΔPAHU + ΔP1 + ΔP2 + ΔP3 + ΔP4 + ΔP9 ΔP = (0. wg. 16 in. wg. Published 2013 by John Wiley & Sons. Magande. = 0.48 in.17). In this case. < 0. = 0. (aspect ratio: 1. Ltd.00). (aspect ratio: 1. ©2013 André G.00).075) in.12 in. Size the duct sections as rectangular ducts The equal friction and capacity chart (Figure A. wg. x 6 in. McDonald and Hugh L. Section 9: 6 in. (aspect ratio: 1. . (aspect ratio: 1.50 in. (aspect ratio: 1.1) will be used to select an appropriate rectangular duct equivalent for the circular ducts. Section 1: 11 in. (aspect ratio: 1. Section 8: 6 in.14 in.032 + 0. For branch 1-2-3-8: ΔP1-2-3-8 = ΔPAHU + ΔP1 + ΔP2 + ΔP3 + ΔP8 = (0. Magande. all the sections have lower pressure losses than that available from the fan. The aspect ratio will be 4 or lower. wg. Section 3: 8 in. Section 4: 8 in. x 7 in. Section 2: 9 in.Introd uction to Thermo-Fluid s System s Design .25 + 0. Drawings The drawing shows the duct sizes and the damper locations. Section 6: 8 in. wg. Section 7: 7 in. wg. wg. x 6 in. wg.00). x 6 in.072) in. Section 5: 0.00). Section 7: 0.25 + 0.023 + 0.00). x 11 in. wg. x 6 in. x 7 in. wg. Dampers with the specified pressure drops are required to balance the system on each section: Section 6: 0. Section 8: 0. Section 5: 6 in. First Edition. McDonald and Hugh L. So. (aspect ratio: 1.60 in.023 + 0. x 8 in.023 + 0.095 + 0.60 in.095 + 0. x 9 in. André G. (aspect ratio: 1. wg.00).032 + 0. For branch 1-2-3-4-5: ΔP1-2-3-4-5 = ΔPAHU + ΔP1 + ΔP2 + ΔP3 + ΔP4 + ΔP5 = (0. (aspect ratio: 1.14).14). < 0.10 in. Magande. ©2013 André G. McDonald and Hugh L. André G.60 in. of external static pressure. The specifications are shown in the following catalog sheet. This fan will be able to provide 0. a 2212 rpm speed and a 0. w. w.g. McDonald and Hugh L. . Magande.Introd uction to Thermo-Fluid s System s Design . A Greenheck single-width industrial centrifugal belt drive fan will be selected for this application. Fan selection The AHU should include a fan that is capable of moving 845 cfm of air and provide at least 0. of external static pressure. From the performance curves for the Greenheck 9 BISW fan. Ltd.75 in.g. First Edition. Published 2013 by John Wiley & Sons.29 hp motor is selected. André G. Magande. (Reprinted with permission) . Source: Greenheck Fan.Introd uction to Thermo-Fluid s System s Design . Magande. McDonald and Hugh L. Ltd. ©2013 André G. First Edition. McDonald and Hugh L. Published 2013 by John Wiley & Sons. Corp. In all cases.60 in. Absent from the design are losses due to transitions from larger duct sizes to smaller duct sizes. lower equivalent lengths are expected for duct sizes smaller than 12 inches. fpm in. Conclusions Rectangular duct sizes have been chosen for this system based on a pressure loss of 0. the duct sizes were 12 inches or less. w.18 . per 100 ft of duct for small-sized. with small equivalent lengths on the order of 3 – 4 ft.75 in. the duct would be converging (becoming smaller) in the direction of air flow.g. ©2013 André G.19 3 8x8 900 0. The assumption of a 12-inches duct to determine the equivalent lengths of the fittings is valid.13 in. This assumption resulted in a more conservative design since. which meets the requirements of the designed system.13 6 8x7 710 0. This is close to the standard 0. In all cases. McDonald and Hugh L. André G. of available pressure at the fan forced a calculation of an appropriate pressure loss for the purposes of duct sizing. First Edition. for the most part. wg.12 7 7x6 750 0.15 2 9x9 1100 0. of external static pressure.15 5 6x6 610 0. The following table summarizes the design results. per 100 ft of duct. McDonald and Hugh L. wg. Ltd. Magande. 1 11 x 11 1100 0. Magande.Introd uction to Thermo-Fluid s System s Design . wg. wg.15 8 6x6 610 0.13 9 6x6 760 0. and was ignored.1 in.15 4 8x7 850 0. this loss is very small. The constraint of 0. low-velocity duct systems. Published 2013 by John Wiley & Sons. Compared to other losses in the system. Duct Section Duct Size Duct Velocity Total Pressure Loss in. The fan selected will be able to deliver a maximum of 850 cfm at 0. Section 4.3. . André G. iv. McDonald and Hugh L. the maximum length of straight duct will depend on the fact that the burner blower cannot provide more than 0. Preliminary Specifications and Constraints i. of pressure. oil-burning equipment must be installed so that a minimum 3 ft separation is maintained from any electrical panel-board.Introd uction to Thermo-Fluid s System s Design . iii. Ltd. The layout. The client failed to provide specific information regarding the heat exchanger and conduct verification of the presence of electronics and electrical boards on the unit. The burner blower cannot provide more than 0. and fittings will be chosen. The material of the duct will be selected. of pressure. accessories. Design and layout a low-velocity rectangular duct system. and protection. First Edition.000 lb/hr of corrosive combustion gases at 600oF will be transported through the duct after combustion with a low air/fuel ratio. Section 4. It is expected that 25. The design strategy will be to connect a duct to the burner and route it to the bottom of the heat exchanger. To facilitate operation and maintenance of the two units. As per the 2006 National Fire Protection Association (NFPA) Standard 31. Magande. 2. McDonald and Hugh L. they have been separated and installed individually.3. v. NFPA Standard 31. wg. Further Information: For the system designed. Magande. The duct should be routed through the concrete slab of the floor. ii.6 require a minimum 3 ft separation between the burner and the heat exchanger.35 in. Detailed Design Objective To size a rectangular duct. The duct will be routed through the concrete slab of the floor in a trench to provide insulation. Possible Solution: Definition Design a rectangular duct system to transport hot combustion gases between a burner and a heat exchanger. ©2013 André G. Published 2013 by John Wiley & Sons. This is a low-velocity duct system.6.35 in.9 Hot combustion gases from a large burner are being considered to heat cold water in a heat exchanger. wg. support. The working fluid will be combustion gases. McDonald and Hugh L. ©2013 André G. McDonald and Hugh L. iii. The flow rate of the combustion gases will be 25. high-temperature filters should be placed in the burner to ensure that ash particulates do not enter and accumulate in the duct. The entrance and exit to the duct will be a Bellmouth shaped. Assume that the combustion gases have the same properties as air since the air/fuel ratio is low. iv.000 lb/hr. For industrial applications. Sketch Below is a sketch of the system. Magande. Ltd. Any 90o elbows will be mitered with turning vanes. The temperature of the combustion gases will be 600oF. Assumptions/Limitations/Constraints i. The final drawing will show the final duct layout and size. Another alternative may be to use stainless steel. especially to install. ii. In that case. This will reduce noise and losses. v. rising gases will enter the duct. . Let the gas velocity in the duct be no more than 2200 fpm. The duct will be connected to the bottom of the heat exchanger. Data Given or Known i.Introd uction to Thermo-Fluid s System s Design . given the corrosive nature of the combustion gases. First Edition. Stainless steel duct lined with a Halar coating is also an option. the maximum velocity for low-velocity ducts should be 1300 to 2200 fpm. André G. ii. vi. iii. This may be expensive. Magande. Published 2013 by John Wiley & Sons. The duct will be connected close to the top of the burner to ensure that the hot. Fiber-reinforced polymer (FRP) will be selected as the duct material. from the mass flow rate. McDonald and Hugh L. Ltd.132 cfm . per 100 ft. and pressure loss are: 30 inches. With the total length known. McDonald and Hugh L. Hence. In this case. the layout of the system can be fully presented. First Edition. coupled with the maximum velocity will be needed to size the duct.18 in. the duct velocity does not exceed 2200 fpm. wg.1 will be used to size the duct. L L x Lstraight D entrance 4 D 90 bend D exit . wg.Introd uction to Thermo-Fluid s System s Design . The chart shown in Figure A.03743 lb/ft 60 min The properties are those of air at 600oF. x 24 in. based on the sketch. 3 0. the aspect ratio is 1. wg.3 and the equivalent circular duct diameter is 30. Determine the length of duct The total pressure available from the blower will be used to specify the total length of duct.1 in. Determine the size of an equivalent rectangular duct With the circular duct size known. 2200 fpm. André G. 100 ft D D D .18 in. In this case. m 25. and 0. Published 2013 by John Wiley & Sons. ©2013 André G. Therefore. The duct size.3. x Lstraight Lentrance 4 L90o bend Lexit 100 ft ΔP L o 0.18 in. The dimensions will be chosen so that the aspect ratio will be 4 or less. Choose: 32 in.000 lb/hr 1 hr V x 11. Analysis Determine the flow rate of the gases The flow rate of the gases. respectively. a rectangular duct with equivalent friction and capacity will be selected from Table A. Magande. Magande. air velocity. Size the round duct The total volume flow rate of air and the maximum velocity will be used to guide the sizing of the duct. ΔP 0. McDonald and Hugh L. Therefore. 0. Ltd. The length of straight duct cannot exceed 34 ft. 0. Note that the total length of straight duct is 30 ft. wg. Drawings The final drawing. Published 2013 by John Wiley & Sons. Table A. André G. Conclusions A rectangular duct has been chosen for the transport of hot corrosive gases from a burner to a heat exchanger. x Lstraight 2. ©2013 André G. restrict the duct length to 30 ft.5 ft 12 42. McDonald and Hugh L.35 in. Magande.5 ft 12 100 ft Lstraight 34 ft . showing the duct size and length is presented below.18 in.4 presents the equivalent lengths of the fittings in round ducts. For this design.Introd uction to Thermo-Fluid s System s Design . two pieces of 4 ft sections of duct were allocated for attachment to the burner and heat exchanger to facilitate installation. while avoiding adverse impact on the performance of the burner blower in terms of its ability to produce sufficient pressure to . First Edition. Magande.5 ft 10 2. wg. An analysis was conducted to determine the maximum length of duct required. Note that since the dimensions of the duct are on the order of 24 to 32 inches. Ltd. McDonald and Hugh L. Published 2013 by John Wiley & Sons. McDonald and Hugh L. . ©2013 André G. André G.Introd uction to Thermo-Fluid s System s Design . Magande. especially when additional information regarding the dimensions of the burner and heat exchanger are known. The final lengths of the duct sections in the drawing will need to be confirmed during the installation stage of the project. First Edition. Magande. move the gases through the duct. vii. as shown in the drawing. First Edition. Specify dampers. The duct lengths. The client has decided to upgrade the factory space that is serviced by the small-duct high velocity system such that it will be classified as a clean room space for use in fabrication of microelectronic devices. 2. Terminal ceiling filter modules based on HEPA or ultra-low penetration air (ULPA) technology should be used. The air velocity should not exceed 5000 fpm. Details on the recommendation of filter modules should be provided for review by the client. v.Introd uction to Thermo-Fluid s System s Design . The working fluid will be air. What impact will this have on operation of the fan? Will it stall? Comment.5 is included here) Definition Specify and select an appropriate fan and terminal filter modules for the given high-velocity system. ©2013 André G. . Detailed Design Objective To design a round air duct system and select an appropriate fan and filter modules. Magande. air flow rates. Possible Solution: (Note that the analysis for Problem 2. ii. iv. Preliminary Specifications and Constraints i. McDonald and Hugh L. Specify and select an appropriate fan from a manufacturer’s catalog for this application. new filters. vi.10 Refer to Problem 2. iii. of external static pressure at 220 to 350 cfm per rated ton of cooling. To that end. Published 2013 by John Wiley & Sons. Ltd. This is a high-velocity air-distribution system. McDonald and Hugh L. and pressure losses across the terminal boxes are constrained. the client wishes to replace the existing terminal boxes with replaceable terminal ceiling filter modules based on HEPA or ultra-low penetration air (ULPA) technology. Magande. The length of each duct section is given.2 in. AHRI Standard 210/240-2005 specifies a blower that produces at least 1. to balance the air flow in the system. The space will be a clean room for use in fabrication of microelectronic devices. Static pressure loss increases as the particulate matter accumulates on the filter over time. Most manufacturers may provide static pressure loss data for clean. André G. wg. Data Given or Known i.5. where required. ©2013 André G. Analysis Determine the maximum air velocity in the system According to the preamble of Problem 2. The air handling unit produces 5 tons of cooling. Galvanized steel is typically used to fabricate air duct systems.3 and for high-velocity duct systems. air flow rates between 1000 cfm and 3000 cfm require a maximum air velocity of 2500 fpm. Even though the volume flow rate in section 5 and the branch . iv. v. wg. The maximum pressure loss across the filters will occur when they are blocked by particles. Published 2013 by John Wiley & Sons. The air flow rates through the three diffusers are given as 460 cfm. The duct system is connected to an air handling unit. The 45o elbows will be pleated. The entrance to the system at the air handling unit will be a Bellmouth entrance. Since the pressure drops across the terminal filter modules are not yet known. Ltd. of external static pressure when 220 to 350 cfm per rated ton of cooling will be produced. First Edition. they are not specified in the subsequent drawing. Assumptions/Limitations/Constraints i. iii.2 in. McDonald and Hugh L. From Table 2. The blower should produce at least 1.5.Introd uction to Thermo-Fluid s System s Design . It will be chosen as the material. the air velocity in the duct cannot exceed 5000 fpm. André G. and 550 cfm. This reduces noise and losses. ii. Sketch A sketch of the system is provided to show the labeling of each section of the duct system. iv. 590 cfm. iii. Magande. Magande. ii. McDonald and Hugh L. 2500 fpm. The chart shown in Figure A. the design criteria for noise should be NC 45 – 55. wg. Magande. For a factory-type setting (similar to a testing laboratory).1 can be used to size the duct sections. per 100 ft. Section 4: 7 inches. Section 5: 7 inches. Ltd. Section 2: 6 inches.2 in. wg. wg. 0. wide module will be chosen. 0. First Edition. wg. Given that all the velocities in the duct are less than 2600. It is expected that the velocity across the filters will be between 70 and 110 fpm (see catalog sheets).45 in. Magande. 1. Section 2: 460 cfm.95 in.6 in. For circular ducts. 0. An excerpt of their catalog is shown below. Published 2013 by John Wiley & Sons. Size the duct sections The total volume flow rate of air from the air handling unit is (460 + 590 + 550) cfm = 1600 cfm. wg. Select the terminal filter modules Flanders Filters is one manufacturer of replaceable terminal HEPA/ULPA filter modules that can be specified for this application.Introd uction to Thermo-Fluid s System s Design . In all the sections. 1. the 48 in. the duct velocity does not exceed 2500 fpm. . Use the maximum velocity constraint of 2500 fpm as a guide. velocities. André G. Section 3: 1140 cfm. Higher pressure losses per 100 ft of duct in the shorter branch sections should facilitate system balancing (to prevent excess air from flooding branches with low pressure losses or low frictional resistances). per 100 ft. For this application. 2050 fpm. McDonald and Hugh L. 2250 fpm. take-offs are lower than 1000 cfm. The duct sizes. it is expected that the noise levels will be lower than the NC 45 – 55 criterion. McDonald and Hugh L. per 100 ft. long x 24 in. 2050 fpm. The volume flow rates through the sections of the system are: Section 1: 1600 cfm. Section 5: 550 cfm. and pressure losses are: Section 1: 11 inches. per 100 ft. ©2013 André G. a maximum velocity of 2600 fpm will produce NC 35 for an occupied space. per 100 ft. Section 4: 590 cfm. 2500 fpm. a maximum velocity of 2500 fpm will be used to size the round ducts. and given that the flow rates are greater than 440 cfm.8 in. Section 3: 10 inches. the pressure drop may be as high as 2. (see catalog sheets). McDonald and Hugh L. Thus. It is expected that the static pressure loss will increase as the particulate matter accumulates on the filter over time. McDonald and Hugh L.0 in. the static pressure loss will be taken to be 0.g. choose filter model number PF-GS591-2448. w. This is larger than the pressure drop of the clean filters at 0. a conservative approach will be to choose a filter capable of removing 99. For these filters.9995% of particles with sizes of 0. First Edition. Magande.Introd uction to Thermo-Fluid s System s Design . Published 2013 by John Wiley & Sons.65 in.g. w. w.0 in.12 microns and larger.65 in. This suggests that as particulate matter accumulates on the filters. This will have an impact on the fan and the air flow rates that it will draw. This choice will result in larger pressure drops across the filters. Ltd. Magande. . which will serve to avoid filter damage.g. André G.g. w. standard construction allows the modules to be operated at a pressure drop of 2. Given that the flow rates through the filter modules in the longest run of duct is 550 cfm. Given that specifications on the type of solid particulates were not provided. ©2013 André G. McDonald and Hugh L. ©2013 André G. McDonald and Hugh L. . André G.Introd uction to Thermo-Fluid s System s Design . Magande. Published 2013 by John Wiley & Sons. Ltd. First Edition. Magande. Magande.Introd uction to Thermo-Fluid s System s Design . McDonald and Hugh L. (Reprinted with permission) . Magande. André G. Source: Flanders. Published 2013 by John Wiley & Sons. Corp. ©2013 André G. First Edition. Ltd. McDonald and Hugh L. 31 in. In this case. wg. wg.through x 20 8 ft 0.336 in.65) in. André G.60 in. 1. 100 ft 100 ft Section 3: ΔP3 0.224 + 0.336 + 0.45 in. wg. Published 2013 by John Wiley & Sons. wg.80 in.branch x 15 13 ft 0.through x 12 7 ft 0.95 in. McDonald and Hugh L.Introd uction to Thermo-Fluid s System s Design . First Edition.435 + 0.65) in.2 in. wg. wg. wg. . x L5 2 L45. wg. Ltd.40 in. 100 ft 100 ft Section 5: ΔP5 0. 0. Magande.114 + 0. wg. wg.224 + 0. x L1 Ltee. McDonald and Hugh L. wg. 0. . x L4 Lwy e.409 + 0. Check the branch pressure losses for fan sizing and balancing A check should be conducted of the pressure loss in each of the branches.95 in. .114 + 0. wg. For branch 1-3-4: ΔP1-3-4 = ΔP1 + ΔP3 + ΔP4 + ΔPfilter = (0. = 1. the minimum pressure loss requirement for operation of the terminal boxes is no longer applicable because the boxes have been replaced with terminal filter modules. 1.32 in.elbow x 31 12 ft 0. ©2013 André G. 0. wg.65) in. x L3 Lwy e.2 in.60 in.45 in. 100 ft 100 ft For the longest branch: ΔP1-3-5 = ΔP1 + ΔP3 + ΔP5 + ΔPfilter = (0.409 in.80 in. wg. wg.435 in. wg. wg. 100 ft 100 ft Section 2: ΔP2 1.branch x 10 20 ft 0. wg. wg. wg. Section 1: ΔP1 0.114 in. = 1. = 1. For branch 1-2: ΔP1-2 = ΔP1 + ΔP2 + ΔPfilter = (0. wg. x L2 Ltee. .224 in.224 + 0. Magande. Since the longest branch . 100 ft 100 ft Section 4: ΔP4 1. From the performance curves for the Greenheck 10 BISW fan. of external static pressure loss.g. Also. w. will require 1. Fan selection The AHU includes a fan that is capable of moving 1600 cfm of air and provide 1. In that case.40 in. Magande. w.g. of external static pressure).5 required a fan to produce 1.g. of external static pressure.Introd uction to Thermo-Fluid s System s Design . If the filter module has collected particulates such that the pressure drop is 2. of external static pressure.08 in. a new fan will be needed (Example 2. For branch 1-3-4: 0.09 in. First Edition.98 hp motor is selected. ©2013 André G. w.g. the fan will be required to provide 2. McDonald and Hugh L. w. Magande. André G. . of external static pressure. w. the fan will only be able to provide approximately 1100 cfm of air at the same motor horsepower. Though the flow rate would be lower.g.g. A Greenheck single-width industrial centrifugal belt drive fan will be selected for this application. Therefore. Published 2013 by John Wiley & Sons.40 in.75 in. McDonald and Hugh L.g.. w.40 in. w.g.2 in. w. Damper sizes In order to balance the system. the operation of the fan would be well outside the stalling region and far from the free delivery point. The specifications are shown in the catalog sheet. the pressure drops across the dampers are For branch 1-2: 0. Ltd. this larger value of static pressure satisfies the requirements of AHRI Standard 210/240-2005. This fan will be able to provide 1. dampers will be needed in branches 1-2 and 1-3-4 since the pressure losses in those branches are less than 1. w.50 in.g.0 in. a 3118 rpm speed and a 0. . First Edition. Published 2013 by John Wiley & Sons. McDonald and Hugh L.Introd uction to Thermo-Fluid s System s Design . Ltd. ©2013 André G. Magande. Magande. André G. McDonald and Hugh L. Magande. (Reprinted with permission) . McDonald and Hugh L. Ltd. First Edition. ©2013 André G. McDonald and Hugh L. André G. Magande. Source: Greenheck Fan. Published 2013 by John Wiley & Sons. Corp.Introd uction to Thermo-Fluid s System s Design . they will not contribute to decreasing the static pressure difference between the branches.Introd uction to Thermo-Fluid s System s Design . To balance the system. Conclusions Round duct sizes have been chosen for this high-velocity system based on a maximum air velocity of 2500 fpm. Magande. showing the duct sizes is presented below. McDonald and Hugh L. the pressure loss is lower than the main branch (branch 1-3-5). It should be noted that dampers are also available with the terminal filter modules. In branch 1-2 and 1-3-4. Effort was taken to size the branch ducts such that the pressure loss per 100 ft of duct was larger than the main branch. Published 2013 by John Wiley & Sons. the additional dampers will be required in branches 1-2 and 1-3-4. Magande. First Edition. dampers were installed. André G. Decisions were made throughout the analysis to ensure that this constraint was not violated. McDonald and Hugh L. Absent are the losses when the duct converges to smaller diameters. . Ltd. since they are included with all the modules. However. The effect of including the filter modules based on HEPA or ultra-low penetration air (ULPA) technology to meet the client’s requirements was an increase in the size of the fan required for this application. The pressure drops across the terminal boxes have also been modified to reflect the results of the analysis. These losses are small compared to the others and were ignored. ©2013 André G. Therefore. Drawings The final drawing. Four 10 in.11 A researcher at a local university has decided to install new equipment in a laboratory booth that will be used to fabricate fiber-reinforced polymer (FRP) composites for the construction industry on a pilot scale. The elevation plan. The tentative location of the exhaust fan has also been specified by the client in the drawing. and a damper at the inlet to the fan.Introd uction to Thermo-Fluid s System s Design . ©2013 André G. complete with a fan and other accessories such as dampers and filters. complete with the equipment. The researcher has engaged a mechanical engineer to design and layout a circular duct exhaust system. Magande. and as such. The researcher is also an engineer and has requested the use of HEPA filters to protect the fan from particle damage and to avoid their discharge to the open external ambient. diameter openings in the top of the booth were provided to allow installation of ductwork. the International Mechanical Code and NFPA Standard 704. a sidewall mounted exhaust fan. Published 2013 by John Wiley & Sons. Static pressure loss increases as the particulate matter accumulates on the filter over time. André G. new filters. McDonald and Hugh L. Ltd. has been provided by the researcher. Magande. . Design the required system by referring to the client-supplied drawing of the elevation plan and through consultation with the International Building Code. Most manufacturers may provide static pressure loss data for clean. VOC’s) and non-flammable small-particle contaminants (carbon fiber particles) that will need to be exhausted. McDonald and Hugh L. What impact will this have on operation of the fan? Will it stall? Comment. selection of the hoods is outside the scope of this problem. The client will supply 4 exhaust hoods (dimensions: 5 ft long by 3 ft wide opening) for connection to the ductwork system. The production process will produce gases (volatile organic compounds. 2. First Edition. ©2013 André G. v. The working fluid will be air that is contaminated with VOC’s and non-flammable small-particle contaminants. . An exhaust fan will be selected. McDonald and Hugh L.Introd uction to Thermo-Fluid s System s Design . In this case. for a booth in a laboratory. iii. The dimensions of equipment and the space are given. Magande. complete with a fan. McDonald and Hugh L. Detailed Design Objective To size a circular air duct. iv. Possible Solution: Definition Design a circular duct exhaust system. the International Mechanical Code. André G. The size and material of the duct will be determined. and fittings that are chosen should be such that losses are kept at a minimum. The layout. Magande. Galvanized steel is typically used to fabricate air and exhaust duct systems. it will be chosen as the material since excessive amounts of water will likely not be present in the exhaust gases to induce corrosion. Constraints on the dimensions of the space and booth were provided by the client. Published 2013 by John Wiley & Sons. ii. ii. Preliminary Specifications and Constraints i. A HEPA filter and a damper must be installed. and damper. diameter openings in the roof of the booth are provided to facilitate the installation of the ductwork. filter. The client will supply 4 exhaust hoods. The design should be constrained by the requirements of the International Building Code. Assumptions/Limitations/Constraints i. and NFPA Standard 704. Four 10 in. accessories. Data Given or Known i. Ltd. The fan must be a sidewall mounted fan. iii. First Edition. In this case. the gas velocity should be at least 500 fpm. The entrance to the system at the hood will be a Bellmouth entrance. ©2013 André G.5. ii. The final drawing will show the final layout and duct sizes. The total friction losses available for the ductwork should be about 0. Therefore. Based on experience with NFPA Standard 96 for commercial cooking exhaust systems. the gas velocity should not exceed 2200 fpm in the main duct and 1800 fpm in the branch duct. as per industry standard. .Introd uction to Thermo-Fluid s System s Design . lowvibration ductwork system. vi. André G. iii. Ltd. with R/D = 1. Pleated or mitered elbows with vanes will be avoided to prevent accumulation of powder particles in the duct. Assume that this problem falls in an industrial setting. McDonald and Hugh L. The exit to the dust collector will also be a Bellmouth shape. a target maximum velocity of 1800 fpm will be chosen for the duct system for a conservative design approach. Magande. the fan will be sized after the ductwork system has been designed. of water per 100 ft of ductwork. Sketch A sketch of the system is shown below. Published 2013 by John Wiley & Sons. iv. Magande. McDonald and Hugh L.1 in. v. First Edition. In order to maintain a low-noise. the codes do not provide much guidance regarding gas flow velocity in the ducts. This reduces noise and losses. For non-flammable exhaust materials. Any 90o elbows will be 5-piece. Note that each section of the duct has been labeled. Thus. per 100 ft of ductwork and the target maximum velocity will be 1800 fpm. 9 in. diameter. Section d-e: 1120 cfm. pressure losses. Section a-b: 280 cfm. this industry standard will be used. straight galvanized steel ducts (Figure A. the amount of air that is exhausted will be increased.Introd uction to Thermo-Fluid s System s Design . 830 fpm. 1100 fpm.1). w. 1000 fpm. Consequently. as required for a low-velocity. Magande. the requirement will be met in the most conservative case when only one hood is operational. Section 502. 630 fpm. Ltd. at least 6 complete air changes per hour (ACH) be provided for an exhausted enclosure similar to the booth in this problem. It was assumed that the pressure loss in the system will be guided by a value of 0. André G.g. 12 in. 11 in.11 in. 0. low-noise. Note that since the designer will size and select a fan as a part of this problem solution.g. ©2013 André G. the minimum volume flow rate of exhaust that needs to be removed is 6 air changes 6 air changes 1 hour Vmin x space volume x 50 ft 8 ft 7 ft x 280 cfm . The approximate diameter of the circular ducts will be found by using the flow rates. Section c-d: 840 cfm. per 100 ft (typical of 4) Section b-c: 560 cfm. w. diameter. . 1 hour 1 hour 60 min To give the client some flexibility. w. diameter. Analysis Determine flow rates in the duct system It can be inferred from the problem preamble that the researcher will likely generate most of the VOC’s and particulate contaminants during operation of the system. 0. per 100 ft. Note that the velocities of the exhaust gas in each section of the ductwork system are less than 1800 fpm.08 in. 0. It is possible that vapors may also be generated even when the system is not operating. wg. An air change is a complete change of the total volume of air in a space. Therefore. First Edition.1 of the International Mechanical Code requires that for hazardous production materials. per 100 ft.g. Hence. 1120 cfm of exhaust gas will be removed from the booth enclosure.g. and the appropriate friction loss chart for round. 14 in. 0.15 in.10. Published 2013 by John Wiley & Sons. McDonald and Hugh L.12 in. low-vibration duct system. McDonald and Hugh L. diameter. w. The system will be designed such that each hood will be able to meet the minimum requirement of the code. Size the circular duct The flow rate through each section of the ductwork system can be calculated.1 in. Magande. per 100 ft. Magande. the external static pressure requirement of the fan will be increased. Therefore.0 in. the static pressure drop across the filter could be as high as 1.) doubles. Since the pressure drop across the filter will increase as particulates accumulate.5 in.Introd uction to Thermo-Fluid s System s Design . Published 2013 by John Wiley & Sons. The Camfil Farr Filtra 2000 Absolute filter will be selected. . Ltd.g. it is recommended that the filter be changed when the initial pressure (0. Given that the total volume flow rate is 1120 cfm. w. For this filter. McDonald and Hugh L. McDonald and Hugh L. André G. the FA 1563-03-01 filter will be chosen.g. This will have an impact on the operation of the fan. w.5 in. Choose a HEPA filter The client has requested that a HEPA filter be installed in the system.g. First Edition. w. ©2013 André G. It will withstand a maximum of 1500 cfm and produce a pressure loss of 0. and in an effort to keep the system static pressure loss low. Magande. An excerpt from the catalog is shown. Introd uction to Thermo-Fluid s System s Design . Ltd. Published 2013 by John Wiley & Sons. André G. Source: Camfil Farr (Reprinted with permission) . Magande. ©2013 André G. McDonald and Hugh L. First Edition. McDonald and Hugh L. Magande. wg. the tees will be through and converging as noted from the sketch provided by the client. It would also be acceptable to use the pressure loss for each section and the length of straight duct for each section to determine the pressure loss.g. From the performance curves for the Greenheck CW-141HP-A sidewall direct drive fan.g. x Lstraight Lhood L90o bend Ltee.converge 0.g.15 in. per 100 ft of duct. w. Also. L .75 in. McDonald and Hugh L.5 in. Determine the pressure losses in the duct system to size the exhaust fan The total pressure loss in the duct system will be required to specify the requirements of the dust collector fan. The pressure loss in the longest run of duct will be used to size the fan. The specifications are shown in the catalog sheet.15 in. wg. This would yield a more conservative estimate of the pressure loss and fan size. w.15 in. In this case.75 ft 1. wg. converge 100 ft ΔP Pfilter L o Ltee. ΔP Pfilter 0. the longest run of duct is branch a-b-c-d-e. First Edition. Thus.15 in. w.75 ft 12 100 ft ΔP 0. x Lstraight D hood D 90 bend D 100 ft D D D It should be noted that as the diameter of the duct changes the equivalent lengths of the fittings will also change and will be different.2 ft 1. It will come complete with a damper.4 presents the equivalent lengths of the fittings in round ducts. 0. the fan should be able to move 1120 cfm of air and provide an external static pressure of 0.Introd uction to Thermo-Fluid s System s Design . ΔP 0. A Greenheck centrifugal sidewall exhaust fan with direct drive will be selected for this application. Magande. a 1725 rpm speed . In this case. wg. the length of straight duct is approximately Lstraight = 40 ft + 22 ft + 15 ft + 12 ft = 89 ft.75 in. The pressure loss in the duct varies between 0.15 in. Published 2013 by John Wiley & Sons.75 ft 12 0. It would be acceptable to use a pressure loss of 0. Therefore.08 and 0. ©2013 André G.2 ft 12 30. Magande. McDonald and Hugh L. Table A. wg. André G. per 100 ft of duct to determine the static pressure loss in all the duct sections. Also from the sketch. x 89 ft 0. Ltd. of external static pressure.Introd uction to Thermo-Fluid s System s Design .g. Magande. The shape of the fan curve suggests that operating the fan at around 2.g. and 0 to 500 cfm would produce stalling. w. the operation of the fan would be well outside the stalling region and far from the free delivery point. Ltd. Magande. This fan will be able to draw 1178 cfm of exhaust gas at 0. the fan will be required to provide 1. If the filter module has collected particulates such that the pressure drop is 1. For the selected forward-curved fan.0 in. w.0 in. André G. w. Published 2013 by John Wiley & Sons. In that case. of external static pressure. and should be avoided.25 in. the fan will only be able to draw 999 cfm of exhaust gas. Though the flow rate would be lower. McDonald and Hugh L.75 in. . the stalling region is approximately between 0 and 420 cfm (30% of 1394 cfm). ©2013 André G.g.. w. McDonald and Hugh L.g. First Edition. and a ½ hp motor is selected. Ltd. McDonald and Hugh L.Introd uction to Thermo-Fluid s System s Design . Magande. ©2013 André G. Published 2013 by John Wiley & Sons. Magande. Corp. André G. (Reprinted with permission) . McDonald and Hugh L. First Edition. Source: Greenheck Fan. pressure loss higher than 1. The clearance needs to be at least 21 in. Thus.5 x 14 in. from the wall to provide sufficient space for curvature of the 5-piece 90o bend at the connection to the fan. taking into consideration the appropriate codes and standards. First Edition.Introd uction to Thermo-Fluid s System s Design . Magande. The pressure drops through the ductwork.0 in.g. The exhaust outlet to the fan will be rectangular. and components were used to size and select a fan from a manufacturer’s catalog. A maintenance program will be required to ensure frequent filter changes. Conclusions The exhaust system has been sized. which will maintain a low-velocity. maintaining the integrity of the system.). McDonald and Hugh L. Ltd. Therefore. lowvibration duct system. Galvanized steel will be used to fabricate the exhaust system based on circular ducts. fittings. Drawings The final drawing. .. André G. McDonald and Hugh L. Published 2013 by John Wiley & Sons. Magande. filter. w. low-noise. The air velocities in each section of the duct are less than 1800 fpm. (R = 1. it will be necessary to transition from the rectangular exhaust outlet on the fan to the circular duct.5 x D = 1.e. Care should be taken to ensure that the filter does not accumulate excess particulate material to avoid excessive pressure loss (i. showing the duct sizes and layout. Note that the vertical section of duct is 24 in. ©2013 André G. is presented below.) for installation of the 5-piece 90o bend.
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