Gate valve; Globe valve; Ball valve; Butterfly valve; Swing-check valve; Angle valve

Transcription

1 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3. A junior engineer consults a senior engineer regarding a piping design problem. The junior engineer has determined the size of a pump to be 3-½ hp. However, to avoid motor overloading due to small spikes in the design flow rate, they have chosen a 5-hp pump. The 5-hp pump is fully capable of providing higher flow rates, which may be detrimental to the process for which the piping system is designed. The senior engineer suggests using valves to control and reduce the flow. Which of the following valves would be best suited for this purpose, even when it is fully opened? Justify your response. Choices Gate valve; Globe valve; Ball valve; Butterfly valve; Swing-check valve; Angle valve Solution: Reduction of the flow would require an increase in the resistance to flow. This can be accomplished by increasing the head loss. The choices given above will increase the minor head loss. Minor head loss (in units of length) is ave H lm KL or g L equiv ave H lm f. D g Assuming that for each choice of valve, the average velocity and diameter remain constant, the best suited valve would be the one that has the highest loss coefficient (K L ) or equivalent length (L equiv ) when fully opened. Thus, when fully opened, Gate valve: K L = 0. Globe valve: K L = 0 Ball valve: K L = 0.05 Butterfly valve: K L ~ Swing-check valve: K L = Angle valve: K L = 5 Of all the choices, the globe valve has the highest loss coefficient, and would probably be best suited for this application.

2 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3. Cooling water is pumped from a reservoir for equipment at a construction job site by using the pipe system shown. The flow rate required is 600 gpm and water must leave the spray nozzle at 0 fps. Determine the minimum pressure needed at the pump outlet. Estimate the required motor power if the pump efficiency is 75 percent. Note that aluminum pipes have similar average roughness as drawn tubing. The diameter shown is the pipe inner diameter. Solution: The energy equation will be used to find the minimum pressure needed at the pump outlet. The general form of the energy equation is given as: h pump p ave, p ave, HlT z z. g g g g Let Point be at the surface of the water in the reservoir and Point be in the spray jet just outside the pipe. Therefore, p = p = p atm, ave, = z = 0, and ave, = j. Therefore, j hpump H lt z. g

3 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The total head loss is the sum of the major and minor head losses: H lt f L D ave g K L ave g f L equiv D ave g f L D ave g K L f L equiv D ave g In this case, ave = pipe (pipe velocity). So, H lt L Lequiv pipe f K L f D. D g 4 Noting that the volume flow rate is constant and known: pipe D H L D 8 gd equiv lt f K L f. 4 L D. So, The pump head is: L Lequiv 8 j hpump f K L f 4 z D D. gd g A value for the friction factor, f is needed. The Reynolds number and the relative roughness of the aluminum pipe are needed to find f. For properties, assume that the water temperature is 70 o F. The Reynolds number for flow in the pipe is: Re 4 D lbm/ft 600 gpm x 0 lbm/ft-s 4 in ft 7.48 gal min 60 sec in ft 3 5 pipe x x x 4.85 x 0 The flow is turbulent ft The relative roughness of the galvanized iron pipe is: d ft From a Moody chart, f ~ 0.04.

4 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. A value for the kinetic energy coefficient in the spray jet, α is needed. The Reynolds number of flow in the spray jet is needed to find α. For properties, assume that the water temperature is 70 o F. The Reynolds number for this flow is: d j 4 j gpm 0 ft/s 3 ft x 7.48 gal jd Re j min x 60 sec j 0.9 ft, where d j is the jet diameter. The jet diameter is: So, lbm/ft 0 ft/s 0.9 ft jd j Re j.36 x x 0 lbm/ft-s 6 The flow is turbulent. Thus, α =.05. For the minor losses, the loss coefficients (K L ) and appropriate equivalent lengths (L equiv ) are: 5 joints: K joint = each Reentrant pipe inlet: K inlet = flanged 90 o bends: K 90 deg bend = 0.30 each (Note: There are two 90 o bends on the suction and discharge pipes attached to the pump) Fully open gate valve: K gate valve = 0.0 standard 45 o bends: L equiv /D = 6 each The total K L value is: K L,total = 5K joint + K inlet + 3K 90 deg bend + K gate valve = 5() (0.30) = 6.9 The pump head is: L Lequiv 8 j hpump f K L f 4 z D D gd g

5 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. h pump 700 ft gpm ft 3. ft/s ft 0 ft/s ft 3. ft/s 4 3 ft x 7.48 gal x min 60 sec h pump ft h pump = 806 ft. The required power input (bhp) for a pump efficiency of 70% is: gh bhp pump pump lbm/ft 600 gpm 3. ft/s 806 ft ft x 7.48 gal min x 60 sec bhp 3.09 x 0 6 lbm-ft s 3 lbf x 3. lbm-ft/s x hp 550 lbf-ft/s bhp = 75 hp The pump head (h pump ) can be used to calculate the minimum pressure needed at the pump outlet. Consider the pump enclosed in a control volume. There are no elevation changes and the velocity through the pump control volume is constant because the suction and discharge pipes have equal diameters. Also, the head loss in the pump is zero. The general form of the energy equation becomes: h pump p ave, p ave, HlT z z g g g g h pump p p. g g Assume that since the suction line is much shorter than the discharge line, the pressure in that part of the system will be atmospheric pressure. Therefore, p = p atm. Let point be at the pump entrance and point be at the pump exit. Hence,

6 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. h pump p p p p patm,gage. g g g The minimum pressure at the pump exit is: p gh,gage pump 3.3 lbm/ft 3. ft/s 806 ft lbf ft 6 3. lbm-ft/s in p,gage = 349 lbf/in gage = 349 psig

7 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.3 When operated at 70 rpm, a centrifugal pump, with impeller diameter of 8 in., has a shutoff head of 5.0 ft of water. At the same operating speed, best efficiency occurs at 300 gpm, where the head is.9 ft of water. Specify the discharge and head for the pump when it is operated at 750 rpm at both the shutoff and best efficiency points. Solution: The pump remains the same, so the two flow conditions are geometrically similar. If no cavitation occurs, the flows will also be kinematically similar. Let condition be at 70 rpm and condition be at 750 rpm. For the flow rates (discharge) Note that ω = πn. Thus, Since D = D, At the shutoff point: C Q = C Q 3 D 3 D. 3 3 N N D D N N N N 0 gpm 750 rpm 70 rpm 0 gpm At the best efficiency point: 750 rpm 300 gpm 70 rpm 449 gpm

8 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For the head C H = C H Note that ω = πn. Therefore, Since D = D, At the shutoff point: gh D gh gh D N D N D H N H H N N H N gh. H 750 rpm 5.0 ft 70 rpm H = 55.9 ft At the best efficiency point: H 750 rpm.9 ft 70 rpm H = 49.0 ft

9 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.4 MDM Consulting Engineers, Inc. has prepared the following piping schematic to supply water to a chemical plant. The lengths shown are in feet. Piping is Schedule 40, commercial steel. Circuit Flow Rate, gpm Control alve Head Loss, Ft A B C Complete the design of the primary circuit piping system. Possible Solution: Definition Size the piping and specify the pumping requirements for a partially designed water piping system provided by MDM Consulting Engineers, Inc. Preliminary Specifications and Constraints i. The working fluid is cold water due to the presence of a chiller in the system

10 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. ii. This is a system with parallel piping, valves, and a pump. iii. The lengths of the pipe sections are constrained to those given in the drawing. Detailed Design Objective To size the pipes in the system and to size and select an appropriate pump. Data Given or Known i. Length of the pipe sections ii. The flow rates through sections A, B, and C are 60, 70, and 70 gpm, respectively. iii. Head losses through the control valves are given. iv. The piping material is schedule 40, commercial steel. v. Preliminary layout of the piping system was provided. Assumptions/Limitations/Constraints i. No information was provided regarding the location of the system. Therefore, care will be taken to ensure that the system operates quitely. ii. Let the flow velocity be about 5 fps. This is below the erosion limit of water in low carbon steel piping (0 fps). iii. Limit pipe frictional losses (major losses) to 3 ft of water per 00 ft of pipe. This is an industry standard/guideline. iv. Pipe changes should be gradual to reduce losses. v. All bends will be 90 o threaded (screwed) regular bends. For smaller pipes (order of 4 in. diameters or less), threaded bends are typically used. vi. Branch and line flow tees are threaded. vii. Negligible elevation head. Assume that all components are on the same level. viii. Assume that the valve between points and 5 on the drawing is a ball valve (see sketch below).

11 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Sketch The pipe sections are labeled and shown on the layout provided by MDM Consulting Engineers. Analysis Bear the following points in mind for this design problem: i. Pipe sizing for this system can be done quickly by using the appropriate friction loss charts for Schedule 40 pipe. However, if the required sizes, flow rates, velocities, etc. are not included on the published charts or if the design is based on a specialized pipe material, then the designer should use Colebrook s equation (or other correlation equation) to find the friction factor (f) and iterate to find the pipe diameters. ii. Assign larger head losses per 00 ft of pipe to shorter pipe sections. The designer should attempt to have a constant velocity throughout the system (approximately). Pipe sections The pipe sections in this design are:

12 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Sections -, -3, -4, 3-4, 3-5, 4-5, 5- (See sketch) Consider Section 3-5. It has one of the shortest pipe lengths (00 ft) and a low flow rate (70 gpm). Assume that the frictional loss in this pipe section is close to 3 ft of water per 00 ft of pipe. Based on the friction loss and the flow rate, the friction loss chart for Schedule 40, commercial steel pipe in a closed piping system (Figure A.4) is consulted to find suitable pipe data: Nominal pipe size: ½ in (A slightly smaller standard pipe size was chosen) Water velocity: 4.8 fps Lost head: 3.5 ft per 00 ft of pipe Major head loss: 3. 5 ft x 00 ft 7.0 ft 00 ft The pipe system flow velocity should be close to 5 fps. This information will be used to size pipes in the other sections. See the Pipe Data table (below) for the pipe sizes. Now that the pipe diameter is known, the minor losses for each section can be estimated. The loss coefficients for the bends, fittings, and area changes are given below (see Table A.4) for a ½ in diameter pipe (data for a in. diameter pipe was used). Globe valve: K globe = 6.9 Threaded 90 o regular bends: K 90 deg bend = 0.95 Line tee: K line tee = 0.90 Pipe contraction: K contraction = 0.07 for a contraction angle of 60 o Pipe expansion: K expansion = 0.30 for d/d = 0. K expansion = 0.5 for d/d = 0.4 K expansion = 0.5 for d/d = 0.6 K expansion = 0.0 for d/d = 0.8 Minor Loss: threaded 90 o regular bend: K 90 deg bend = 0.95 globe valve: K globe = 6.9

13 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 4 line tees: K line tee = 0.90 pipe contraction from a 3-in. diameter pipe in section -3 to a ½-in. diameter in section 3-5: K contraction = 0.07 pipe expansion from a ½-in. diameter pipe in section 3-5 to a 4-in. diameter in section 3-5 (for d/d = 0.6): K expansion = 0.5 Therefore, ave 4. 8 ft/s Hlm K L ft g 3. ft/s The total head loss in the Section 3-5 is: H lt H H 7. 0 ft 4.8ft. ft l lm A similar procedure is followed for the other pipe sections. The charts below show the results of all the analyses. Pipe Section No. Globe alve, K L Ball alves, K L 90 o Bend, K L MINOR LOSSES Tees- Branch, K L Tees- Line, K L Gradual Expansion, K L Gradual Contraction, K L = 0.07 Total Minor Loss, ft (one) 0.64 (one) (one) 0.07 (one) (one) 0.95 (one).4 (one) 0.9 (two) 0.07 (one) (one).4 (two) 0.9 (two) (one) 0.9 (one) 0. (one) (one) 0.95 (one) 0.9 (four) 0.5 (one) 0.07 (one) (four) 0.9 (five).87 Pipe Section No. Pipe Length, ft Flow Rate, gpm PIPE DATA Lost Head, ft/00 ft Fluid elocity, ft/s Nominal Size, in. Minor Losses, ft Total Head Loss, ft ½

14 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd ½ ½ At this point in the design analysis, it is important to note that the sizing of the pipes and the determination of the minor head losses were done simultaneously. Next, consider the lost head for each of the three parallel circuits. Let: circuit A include sections -, -4, 4-5, 5-, and the control valve A. circuit B include sections -, -3, 3-4, 4-5, 5-, and the control valve B. circuit C include sections -, -3, 3-5, 5-, and the control valve C. The circuit head losses are: H A = H + H 4 + H 45 + H 5 +H cv_a = 7.8 ft ft + 8. ft ft + 40 ft = 79.9 ft H B = H + H 3 + H 34 + H 45 + H 5 + H cv_b = 7.8 ft ft ft + 8. ft ft + 50 ft = 95.4 ft H C = H + H 3 + H 35 + H 5 + H cv_c = 7.8 ft ft +. ft ft + 50 ft = 90.8 ft The system will be balanced by installing additional balancing valves in circuits A and C to increase the head to 95.4 ft (for circuit B). The head loss for circuit B will be used to find the pump head (h pump ). For this closed-loop system, let the starting and ending point be point. Therefore, the pump head is: h pump p g g p z g g z H lt H lt H B Then: h pump = 95.4 ft h pump ~ 96 ft of water

15 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For this system, a pump that is rated to produce 00 gpm at 96 ft of head is required. Use manufacturer s charts to select an appropriate pump. The pump head and flow rate are large. Hence, a base-mounted pump could be a good choice. The performance of a small in-line pump may not be sufficient for this application. A review of the various Taco pumps ( shows that a CI series based-mounted pump is suitable. The pump performance plot is shown below. The model 5 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is: 3 in. x.5 in. x.0 in. casing 0.50 in. impeller diameter 8.75 hp motor 760 rpm speed Note that to-the-point design was avoided, and a slightly larger size and power were chosen.

16 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

17 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

18 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Drawings The drawing showing the pipe sizes is presented below. Conclusions The piping system has been designed. All the pipe sizes are known, and the piping material has been selected. A pump has been specified and selected. The pipe data and pump schedule are shown below. It should be noted that in some sections of the piping system, the major head loss exceeded 3 ft per 00 ft of pipe. The junior engineer knows that this standard is a guideline for the design of piping systems. It is acceptable to be slightly above or below this value. It should be noted that 4 in. x 3 in. and 4 in. x ½ in. reducing fittings will be required on the pump suction and discharge, respectively for installation of the pump. The pump suction velocity should not be much larger than 5 fps. In this case, the velocity will be about 5 fps (see section 5-).

19 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Pipe Section No. Pipe Length, ft Flow Rate, gpm PIPE DATA Lost Head, ft/00 ft Fluid elocity, ft/s Nominal Size, in. Minor Losses, ft Total Head Loss, ft ½ ½ ½ TAG P- MANUFACTURER AND MODEL NUMBER TACO, FI/CI SERIES 5, OR EQUAL TYPE CENTRIFUGAL, BASED- MOUNTED PUMP SCHEDULE CONSTRUCTION CAST IRON 3 X.5 X.0 CASING, 0.5 FLOW RATE (GPM) FLUID WORKING FLUID HEAD LOSS (FT) MOTOR SIZE (HP) ELECTRICAL MOTOR OLT/PH SPEED /HZ (RPM) 00 WATER /3/60

20 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.5 The owner of a small office building has decided to design and install a piping network that includes 5 tankless water heaters to heat and transport water. The owner currently requires 8 gpm of hot water service. Cold water (feedwater) from the City will be supplied to each heater, and the piping connections were previously installed by the building contractor. The hot water, at 60 o F, from the heaters will be transported through a main header for distribution in the rest of the building. Each heater has been specified to provide a maximum of 4.6 gpm of water. The heater unit has a dedicated pump that serves only to circulate the cold water through its internal finned-coil system. Unfortunately, the City supplies the feedwater at a low pressure of 40 psia, and the owner needs hot water at 80 psia for complete distribution though the building. Based on the sketch provided below, complete the design of the hot water supply lines in this system. Bear in mind that the owner would like to maintain flexibility to expand the system in the future to its maximum capabilities. Further Information: In practice, the lengths of the hot water supply piping that connect directly to the heaters are small in comparison to that of the main supply header. Possible Solution: Definition Size the piping and specify the pumping requirements for a partially designed hot water piping system. Preliminary Specifications and Constraints i. The cold feedwater connections for the heaters have been pre-installed. ii. The water pressure available from the City is 40 psia. iii. 8 gpm of hot water is required by the client.

21 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Detailed Design Objective To size the pipes in the system and to size and select an appropriate pump. Piping accessories such as valves will also be specified. Data Given or Known i. 5 tankless water heaters will be installed. ii. A total of 8 gpm of hot water is required. iii. Each heater provides a maximum of 4.6 gpm of hot water. iv. The hot water will be supplied at 60 o F. v. The City provides cold water at 40 psia. vi. The client needs hot water at 80 psia to guarantee complete distribution throughout the building. Assumptions/Limitations/Constraints i. Let the piping material be Type L copper. The owner will probably be using the hot water in heat transfer applications. Copper has high thermal conductivity, which will result in lower resistance to heat transfer. ii. Let the flow velocity be about 5 fps. This velocity is within the range allowed for general building service (4 to 0 fps) and is lower than the erosion limit of water in copper tubes (6 fps). iii. Limit pipe frictional losses (major losses) to 3 ft of water per 00 ft of pipe. This limit is an industry standard. iv. Pipe changes should be gradual to reduce losses. v. All bends will be 90 o threaded (screwed) regular bends. For smaller pipes (order of 4 in. diameters or less), threaded bends are typically used. vi. Branch and line flow tees are threaded. vii. There is negligible elevation head. Assume that all components are on the same level. viii. Ball valves will be used to isolate the heaters. ix. The lengths of the pipe that connect directly to the heaters will be ignored when determining head loss and pump head. In practice, the lengths of the hot water supply piping that connect directly to the heaters are small in comparison to that of the main supply line.

22 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. x. The properties of water will be taken at 60 o F. Sketch The pipe sections are labeled and shown on the partial layout that was provided. Analysis Bear the following points in mind for this design problem: i. Pipe sizing for this system can be done quickly by using the appropriate friction loss charts for Type L copper tubes. However, if the required sizes, flow rates, velocities, etc. are not included on the published charts or if the design is based on a specialized pipe material, then the designer should use Colebrook s equation (or other correlation equation) to find the friction factor (f) and iterate to find the pipe diameters. ii. Assign larger head losses per 00 ft of pipe to shorter pipe sections. The designer should attempt to have a constant velocity throughout the system (approximately). iii. The client would like to maintain flexibility to expand the system in the future to its maximum capabilities. Therefore, the hot water supply piping system will be sized based on the maximum flow capacity of each heater (4.6 gpm). Sizes of the pipe sections The pipe sections in this design are: Sections -6, -6, 3-7, 4-8, 5-9, 6-7, 7-8, 8-9, 9-0 (See sketch). Sections -6, -6, 3-7, 4-8, 5-9 will be of the same size since the flow rate will be 4.6 gpm in these sections. Figure A.3 for the friction loss in copper tubing will be consulted to determine the size, water

23 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. velocity, and friction loss of each section. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Therefore, Nominal pipe size: ¾ in. Water velocity: 3.4 fps Lost head: 7.3 ft per 00 ft of pipe. The water velocity is lower than the design constraint of 5 fps. However, the friction loss is higher than the design target of 3 ft. per 00 ft. of pipe. This will not be problematic because the lengths of these pipe sections are very small. Thus, the major head loss in these sections will also be very small compared to the rest of the supply pipeline. Another viable alternative would have been to select the in. nominal diameter pipe. In that case, the flow velocity would be fps and the friction loss would be ft. per 00 ft. of pipe. The total flow rate through section 6-7 is 9. gpm. Thus, the size, water velocity, and friction loss is Nominal pipe size: in. Water velocity: 3.7 fps Lost head: 6 ft per 00 ft of pipe. The total flow rate through section 7-8 is 3.8 gpm. Thus, the size, water velocity, and friction loss is Nominal pipe size: ¼ in. Water velocity: 3.6 fps Lost head: 4. ft per 00 ft of pipe. The total flow rate through section 8-9 is 8.4 gpm. Thus, the size, water velocity, and friction loss is Nominal pipe size: ½ in. Water velocity: 3.4 fps Lost head: 3. ft per 00 ft of pipe. The total flow rate through section 9-0 (main supply line) is 3 gpm. Thus, the size, water velocity, and friction loss is

24 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Nominal pipe size: in. Water velocity:.6 fps Lost head:.4 ft per 00 ft of pipe. It should be noted that as one proceeds downstream of each heater, the friction loss in the pipe decreases. In this case, this is desirable since the hot water should flow easily towards the main supply line with as limited a flow resistance as possible. Note also that the pipe velocities in the sections are close. Minor Losses Now that the pipe diameters are known, the minor losses for each section can be estimated. The loss coefficients for the bends, fittings, valves, and area changes are given in the table below (see Table A.4). Ball valves will be installed on the hot water supply line to isolate the heaters and the pump. A check valve will also be installed to prevent backflow of water into and flooding of the heaters. The check valve will be installed in section 9-0. The total minor loss is also presented in the table below. The minor loss is determined from lm ave. H K L g Pipe Section No. Check alve, K L Ball alves, K L MINOR LOSSES 90 o Bend, K L Tees- Branch, K L Tees-Line, K L Gradual Expansion, K L Total Minor Loss, ft (two) 0.0 (two) (two) 0.3 Note that for pipe expansions, the following data was used:

25 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Pipe expansion: K expansion = 0.30 for d/d = 0. K expansion = 0.5 for d/d = 0.4 K expansion = 0.5 for d/d = 0.6 K expansion = 0.0 for d/d = 0.8. Details of the pipe data for each section are shown below. Pipe Section No. Flow Rate, gpm PIPE DATA Lost Head, ft/00 ft Fluid elocity, ft/s Nominal Size, in. Total Head Loss, Ft ¾ ¾ ¾ ¾ ¾ ¼ ½ Pump sizing The head loss and the pressure required by the owner will be used to find the pump head (h pump ). Let point be the inlet to the hot water piping system at HTR 5 and let point be immediately after the check valve in section 9-0. Note that this will give the longest run of pipe. If the pump is able to move water through this long run of pipe, it will be able to move water through all the other shorter branches. So, further, only the head loss in this longest run of pipe will be considered. So, the pump head is given by: h pump p g g z p g g z H lt. Since the elevation differences are negligible, h pump p p g g g H g lt

26 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. h pump p p g g H -6 H 6-7 H 7-8 H 8-9 H 9-0. Then, h pump lbf/in lb/ft 3. ft/s 3. lb-ft/s x lbf in x ft.6 ft/s 3.4 ft/s 3. ft/s.405 ft h pump 95.7 ft 96 ft For this system and to meet the requirements of the building owner, a pump that is rated to produce 3 gpm at 96 ft of head is required. Use manufacturer s charts to select an appropriate pump. The pump head is large. So, a base-mounted pump could be a good choice. The performance of a small in-line pump may not be sufficient for this application. A review of the various Taco pumps ( shows that a CI series based-mounted pump is suitable. The pump performance plot is shown below. The model 5 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is:.5 in. x.5 in. x.0 in. casing 9.75 in. impeller diameter 3 hp motor 760 rpm speed Note that to-the-point design was avoided, and a slightly larger size and power were chosen. As expected, the efficiency of this pump is less than 30% since the total flow rate is low.

27 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

28 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

29 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Drawings The final pipe sizes and accessories are presented in the drawing below. Conclusions The piping system has been designed. The pipe data and pump schedule are shown below. It should be noted that in some sections of the piping system, the major head loss exceeded 3 ft per 00 ft of pipe. However, moving downstream from the heaters, the friction loss decreased, which will facilitate flow into the main supply line. It should be noted that ½ in. x in. and ½ in. x in. fittings will be required on the pump suction and discharge, respectively for installation of the pump. The pump suction velocity should not be much larger than 5 fps. In this case, the velocity will be about 3 fps (see section 9-0). It should be noted that for tankless water heaters, the pump may be installed upstream of the heaters in the col feedwater line. This will ensure that biological matter that proliferates at higher temperatures will not accumulate in and block the pump. For some tankless water heaters, the recommended inlet water pressure is 30 to 80 psia (maximum 50 psia). Installation of the pump upstream of the heaters will boost the water pressure at the inlet of the heater.

30 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Pipe Section No. Flow Rate, gpm PIPE DATA Lost Head, ft/00 ft Fluid elocity, ft/s Nominal Size, in. Total Head Loss, Ft ¾ ¾ ¾ ¾ ¾ ¼ ½ TAG P- MANUFACTURER AND MODEL NUMBER TACO, FI/CI SERIES 5, OR EQUAL TYPE CENTRIFUGAL, BASED- MOUNTED PUMP SCHEDULE CONSTRUCTION CAST IRON.5 X.5 X.0 CASING, 9.75 FLOW RATE (GPM) FLUID WORKING FLUID HEAD LOSS (FT) MOTOR SIZE (HP) ELECTRICAL MOTOR OLT/PH SPEED /HZ (RPM) 3 WATER /3/60

31 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.6 A heating coil is a heat exchanger that can be used to transfer energy from hot 50% ethylene glycol solution to air for the purposes of space heating. A proposal has been submitted that will focus on the development of a heating coil that contains one row with 6 loops of coils. Each loop will be 4 in. long and they will be connected to each other by way of 80 o smooth return bends. The 50% ethylene glycol solution will be supplied at 00 o F and 5 gpm to the heating coil component. A dedicated pump will be required for this component. Design the piping system in the heating coil and specify any major accessories that will be required. Possible Solution: Definition Size the piping and specify the pumping requirements of a one-row, six-loop heating coil. Preliminary Specifications and Constraints i. 50% ethylene glycol is the working fluid in the pipe. ii. The loops will be connected to each other by way of 80 o smooth return bends. Detailed Design Objective To size the pipe and to size and select an appropriate pump. Piping accessories such as valves will also be specified. Data Given or Known i. The heating coil contains row with 6 loops of coils. ii. Each loop is 4 inches long. iii. 80 o smooth return bends will be used to connect the loops. iv. The ethylene glycol solution will be at 00 o F. v. The flow rate of the ethylene glycol solution is 5 gpm. Assumptions/Limitations/Constraints

32 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. i. Let the piping material be Type L copper. Copper has high thermal conductivity, which will result in lower resistance to heat transfer and possibly, increased performance of the heating coil. ii. Let the flow velocity be about 5 fps. This velocity is lower than the erosion limit of ethylene glycol solution in copper tubes. At 00 o F, the erosion limit of ethylene glycol solution in copper tubes is lb/ft 6 fps 6. fps 3 6.4lb/ft. iii. Limit pipe frictional losses (major losses) to 3 ft of water per 00 ft of pipe. This limit is an industry standard. iv. All bends will be 80 o threaded (screwed) smooth bends. For smaller pipes (order of 4 in. diameters or less), threaded bends are typically used. v. The 80 o threaded smooth bends have negligible length in comparison to the total length of piping in the heating coil. vi. There is negligible elevation head. Assume that all components are on the same level. vii. Ball valves will be used to isolate the heating coil. viii. The properties of water will be taken at 00 o F. Sketch The piping in the heating coil is shown below. Analysis Size of the pipe Figure A.3 for copper tubing friction loss will be consulted to determine the size, water velocity, and friction loss of/in the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. The flow rate is 5 gpm. Therefore,

33 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Nominal pipe size: ¾ in. Water velocity: 3.4 fps Lost head: 7.3 ft per 00 ft of pipe. The water velocity is lower than the design constraint of 5 fps. However, the friction loss is higher than the design target of 3 ft. per 00 ft. of pipe. The impact of the larger friction loss will be on the pump size. If the size is too large, then a in. nominal diameter pipe will be selected. In that case, the flow velocity would be fps and the friction loss would be ft. per 00 ft. of pipe. However, it should be noted that the larger pipe size may increase the cost and weight of the heating coil box beyond a level that is desirable for a client. Major and Minor Losses The major loss in this constant area pipe is 7.3ft ft H l x 64 in x ft. 00 ft in With the pipe diameter known, the minor losses can be determined. There will be five 80 o return bends, ball valves to isolate the heating coil, and a check valve on the discharge line to prevent backflow of water into and flooding of the coil. The loss coefficients are given below: Ball valve: K ball = 0.05, Check valve: K check = 5., 80 o return bend: K 80-bend =.0. The total minor loss is determined from lm ave. H K L g Thus, H lm H lm =.73 ft. 3.4 ft/s ft/s

34 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The total head loss is H lt = H l + H lm = ft +.73 ft = 3.7 ft. Pump sizing The energy equation will be used to determine the pump head. h pump p g g z p g g z H lt Let point be the inlet to the coil and let point be the outlet. Since the elevation differences are negligible, z = z. The pipe diameter is constant. So, to satisfy the law of mass conservation, =. The problem did not require any increase in pressure at the outlet of the coil. So, the inlet and outlet pressures should be equal. Thus, the pump head becomes: hpump H lt h 3.7 ft 4 ft. pump For this case, a pump that is rated to produce 5 gpm at 4 ft of head is required. Use manufacturer s charts to select an appropriate pump. Since the pump head and capacity are small, a small in-line mounted pump will be sufficient. A review of the various Taco pumps ( shows that a 0 Series In-line circulator will be suitable. The pump performance plot is shown below. The model 0 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is: ¾ in. x ¾ in. x 6.35 in. casing / hp motor 75 rpm speed A Taco representative will need to be contacted to purchase a 08 /60 Hz/3 phase motor. Currently, the motor supplied is 5 /60 Hz/ phase.

35 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

36 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

37 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

38 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Drawings The final pipe sizes and accessories are presented in the drawing below. Conclusions The piping system has been sized and a pump has been selected. The pipe size is known, and the piping material has been selected. The pump schedule is shown below. It should be noted that even though the major head loss exceeded 3 ft per 00 ft of pipe, the pump size is very small. Though the final option may depend on the client, the pump will probably be installed on the discharge side of the heating coil, where the water is cooler. The pump suction velocity should not be much larger than 5 fps. In this case, the velocity will be about 3.4 fps. TAG P- MANUFACTURER AND MODEL NUMBER TACO, 0 SERIES 0, OR EQUAL TYPE CENTRIFUGAL, IN-LINE MOUNTED PUMP SCHEDULE CONSTRUCTION CAST IRON ¾ X ¾ X 6.35 CASING FLOW RATE (GPM) 5 FLUID WORKING FLUID 50% ETHYLENE GLYCOL HEAD LOSS (FT) MOTOR SIZE (HP) ELECTRICAL MOTOR OLT/PH SPEED /HZ (RPM) 4 / 75 08/3/60

39 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.7 A plant manager has hired a recent graduate of a mechanical engineering program to consider the design of a piping system to supply kerosene to 3 burners that will be located outdoors. Burner A will require 0 gpm of fuel, burner B, 0 gpm, and burner C, 5 gpm. For convenience, the manager will purchase a vented outdoor fuel oil storage tank to supply enough kerosene for 8 hours of operation. They wish to install the discharge pipe connection at the base of the tank to take advantage of the fuel static pressure head and to facilitate pipe installation. It is understood that codes will need to be verified. The fuel oil storage tank and piping should be supplied with sufficient heat tracing to maintain the kerosene temperature at about 68 o F. Given that the fuel will be atomized and combusted completely in the burner, there will be no need for return piping from the burners to the storage tank. Design the burner kerosene supply piping system that will meet the requirements of the manager. Further Information: Consultation with NFPA 3 may provide guidance to justify some design decisions. Possible Solution: Definition Size the piping and specify the pumping requirements for a kerosene oil piping system. Preliminary Specifications and Constraints i. The fluid is kerosene. ii. 3 burners will be attached to the piping system. iii. An outdoor fuel oil storage tank should be used. iv. Temperature of kerosene should be 68 o F. Detailed Design Objective To size the pipes in the system and to size and select an appropriate pump. Piping accessories such as valves will also be specified. Data Given or Known i. 3 burners will be installed.

40 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. ii. Burner A requires 0 gpm, burner B requires 0 gpm, and burner C requires 5 gpm of kerosene. iii. An outdoor storage tank with an 8-hour supply of fuel will be installed. iv. The kerosene temperature will be 68 o F. Assumptions/Limitations/Constraints i. Let the piping material be Schedule 40 steel. Steel is an acceptable material for oil supply lines as per NFPA 3, section 8... ii. Let the flow velocity be about 5 fps. This velocity is lower than the erosion limit of kerosene in Schedule 40 steel pipes. At 68 o F, the erosion limit of kerosene in Schedule 40 steel pipes is 3 5. lb/ft 0 fps. fps lb/ft. iii. Limit pipe frictional losses (major losses) to 3 ft of water per 00 ft of pipe. This limit is an industry standard. iv. Pipe changes should be gradual to reduce losses. v. All bends will be 90 o threaded (screwed) regular bends. For smaller pipes (order of 4 in. diameters or less), threaded bends are typically used. vi. Branch and line flow tees are threaded. vii. The pipe entrance from the storage tank is sharp-edged. viii. Assume that the vapor pressure of kerosene at 68 o F is.90 torr = psia. This was obtained from the California Air Resources Board. Sketch The pipe sections are labeled and shown on a partial layout that represents the problem.

41 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Analysis This is an open-loop system due to the presence of a vented storage tank. Bear the following points in mind for this design problem: i. Pipe sizing for this system can be done quickly by using the appropriate friction loss charts for Schedule 40 steel piping. However, if the required sizes, flow rates, velocities, etc. are not included on the published charts or if the design is based on a specialized pipe material, then the designer should use Colebrook s equation (or other correlation equation) to find the friction factor (f) and iterate to find the pipe diameters. ii. Assign larger head losses per 00 ft of pipe to shorter pipe sections. The designer should attempt to have a constant velocity throughout the system (approximately). iii. Given that this is an open-loop piping system, it will be necessary to check the NPSH and the possibility of cavitation. Sizes of the pipe sections The pipe sections in this design are: Sections -, -3, -4, 4-5, 4-6 (See sketch). The flow rate in Section - (main supply line) will be ( ) gpm = 55 gpm. Figure A.4 for Schedule 40 pipe friction loss for open pipe systems will be consulted to determine the size, kerosene velocity, and friction loss of this section. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Therefore, Nominal pipe size: ½ in. Kerosene velocity: 3.6 fps Lost head: 3.0 ft per 00 ft of pipe. The kerosene velocity is lower than the design constraint of 5 fps. The friction loss does not exceed the design constraint of 3 ft. per 00 ft. of pipe. The total flow rate through section -3 is 0 gpm. Thus, the size, kerosene velocity, and friction loss is: Nominal pipe size: ½ in. Kerosene velocity:.8 fps

42 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Lost head:.45 ft per 00 ft of pipe. The total flow rate through section -4 is 45 gpm. Thus, the size, kerosene velocity, and friction loss is: Nominal pipe size: ½ in. Kerosene velocity:.9 fps Lost head:.0 ft per 00 ft of pipe. The total flow rate through section 4-5 is 0 gpm. Thus, the size, kerosene velocity, and friction loss is: Nominal pipe size: in. Kerosene velocity:. fps Lost head:.5 ft per 00 ft of pipe. The total flow rate through section 4-6 is 5 gpm. Thus, the size, kerosene velocity, and friction loss is: Nominal pipe size: in. Kerosene velocity:.6 fps Lost head:. ft per 00 ft of pipe. The lengths of sections -3, 4-5, and 4-6 (pipes connected to burners) will need to be selected such that the total head loss in these sections are balanced. Or, balancing valves can be installed. Major and Minor Losses The lengths of the pipes will be needed in order to determine the major losses in each section of the system. For section - (main supply pipe from storage tank), NFPA 3, section 8.7. require that the vent of a supply tank be at least 5 ft. away from any air inlet or any flue gas outlet of any appliance. In this case, the burner A will be taken as an appliance. Let the pipe length of section - be 8 ft. For section -, the major head loss is: H l 3.0 ft. x 8 ft 0.4 ft. 00 ft The minimum 5 ft separation between the storage tank and the burner is to ensure that kerosene vapors do not become entrained in the air intake or flue gas exhaust of the burners, which could cause an

43 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. explosion. Hence, the same minimum distance will be applied between the burners. Let the distance between the burners be 5 ft. This will also ensure that there is sufficient space between the burners for maintenance. Thus, the length of section -4 is 5 ft. For section -4, the major head loss is: H l.0 ft. x 5 ft 0.0 ft. 00 ft Let the lengths of sections -3 and 4-5 be 3 ft. For a uniform layout, the total length of section 4-6 will be (5 + 3) ft = 8 ft. For section -3, the major head loss is: H l.45 ft. x 3ft ft. 00 ft For section 4-5, the major head loss is: H l.5 ft. x 3 ft ft. 00 ft For section 4-6, the major head loss is: H l. ft. x 8 ft 0.76 ft. 00 ft With the pipe diameters known, the minor losses for each section can be estimated. The loss coefficients for the bends, fittings, valves, and area changes are given in the table below (see Table A.4). Ball valves will be installed on the supply line sections that connect directly to the burners. A strainer will be installed in section -, immediately upstream of the pump. The total minor loss is also presented in the table below. The minor loss is determined from lm ave. H K L g

44 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Pipe Section No. Entrance, K L Strainer, K L Ball alves, K L MINOR LOSSES 90 o Bend, K L Tees- Branch, K L Tees- Line, K L Gradual Contraction, K L Total Minor Loss, ft (three) Note that the following data was used for minor loss calculations: For the pipe entrance: K entrance = 0.5 (sharp-edged entrance) For the strainer: K strainer =.5 Pipe contraction: K contraction = 0.07 for a contraction angle of 60 o Details of the pipe data for each section are shown below. Pipe Section No. Flow Rate, gpm Lost Head, ft/00 ft Fluid elocity, ft/s PIPE DATA Pipe Length, ft Nominal Size, in. Major Loss, ft Minor Loss, ft Total Head Loss, ft ½ ½ ½ Pump sizing The pump head is required to determine the pump size required. The pump head is h pump p g g z p g g z H lt.

45 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Let point be the inlet to the pipe and let point be the exit at burner C. Note that this will give the longest run of pipe. If the pump is able to move kerosene through this long run of pipe, it will be able to move fluid through all the other shorter branches. Therefore, only the head loss in sections -, -4, and 4-6 will be considered. Therefore, the pump head is: h pump p g g z p g g z H - H -4 H 4-6. The pipe will be routed in the tank so that the inlet to the piping system will be at the bottom of the tank to take advantage of any static pressure head. Thus, the elevation differences between points and will be negligible and z = z. Hence, h pump p g p g g H g - H -4 H 4-6. To ensure that the pump will operate under all circumstances, it will be sized for the case where the kerosene level in the tank is low. Thus, p is approximately atmospheric pressure. Within the burner, the fluid will exit out to approximately atmospheric pressure. So, p = p = p atm. Then, h h pump pump g H - H.6 ft/s 3.6 ft/s 3. ft/s -4 H ft 0.7 ft 0.8ft h.7 ft ft. pump For this system and to meet the requirements of moving the kerosene to the burners, a pump that is rated to produce 55 gpm at ft of head is required. Use manufacturer s charts to select an appropriate pump. Since the pump head and capacity are small, a small in-line mounted pump will be sufficient. A review of the various Taco pumps ( shows that a 0 Series In-line circulator will be suitable. The pump performance plot is shown below.

46 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The model 0 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is: in. x in. x in. casing /6 hp motor 75 rpm speed A Taco representative will need to be contacted to purchase a 08 /60 Hz/3 phase motor. Currently, the motor supplied is 5 /60 Hz/ phase. For small pumps, the NPSHR is usually not presented. From studying the performance plots of a variety of pumps, the NPSHR is usually small at low flow rates, on the order of to 0 ft. To avoid cavitation, the NPSHA must be greater than the NPSHR. The NPSHA is p P s s vapor NPSHA. g g g pump,inlet The energy equation will be used to find the pump inlet pressure, p s. p g g z ps g s s g z s H lt,suction Point is the inlet to the pipe in the tank. As stated earlier, p = p atm. Since the pipe diameter is constant in section - of the system, s. So, p atm g z ps z g s H lt,suction The elevation differences between point and the suction point of the pump will be negligible. So, z = z s. Then, p atm g p g s H lt,suction

47 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. p s g p atm H lt,suction. g Then, NPSHA p atm g s g H lt,suction P g vapor p NPSHA atm P g vapor s H g lt,suction. Note that H lt,suction is the total head loss in the suction line of the pipe, only. To generate a more conservative value of the NPSHA, assume that the suction line has a length of 8 ft (i.e., length of section -) since the location of the pump in section - has not been determined. Therefore, NPSHA lbf/in 3 5. lb/ft 3. ft/s NPSHA = 4. ft. of kerosene. in x ft 3. lb-ft/s x lbf 3.6 ft/s 3. ft/s 3.0 ft 00 ft x 8 ft In terms of water, NPSHA 4. ft.of kerosene x SG NPSHA = 33.8 ft. of water. kerosene 5. lb/ft 4.ft.of kerosene x 6.4 lb/ft 3 3 The NPSHA for this case is large, and probably much larger than the NPSHR for this small pump. The possibility of cavitation is very low.

48 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

49 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

50 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Drawings The final pipe sizes and accessories are presented in the drawing below. Conclusions The piping system has been designed. All the pipe sizes are known, and the piping material has been selected, in compliance with code. A pump has been specified and selected. The pipe data and pump schedule are shown below. The following additional points are made:. Every effort was made to size sections -3, -4, 4-5, and 4-6 so that the head losses would be approximately equal. In this design, a balancing valve will be needed in section 4-5 to increase the friction loss and balance the system.. All the pipes that were directly connected to the burners have outer diameters larger than ⅜ in. as required by NFPA 3, section The manager will not be allowed to attach a discharge pipe connection at the base of the tank. According to NFPA 3, section 8.6., any tank that exceeds 330 gallons shall have supply piping that services oil-burning appliances connected to the top of the tank. In this problem, the size of the 60 min tank is 55 gal/min x x 8 hr 6, 400 gallons. This additional piping was not considered in hr the sizing of the pump. However, since to-the-point design was avoided, any adverse impact on the pump will be avoided. It should be noted that the Model 0 Taco in-line circulator that was chosen is capable of producing 5 ft of head at 55 gpm, which should be sufficient to cover any unexpected losses.

51 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 4. No information was provided on the losses that will occur as the kerosene exits the atomizers of the burners. While the Model 0 pump is probably sufficient to handle the additional head, the client would be advised to provide this information once the burners have been purchased so that a recalculation of the pump head can be conducted or supply an independent pump for the burners. 5. A in. x ½ in. fitting will be required on the pump suction and discharge for installation of the pump. 6. The pump suction velocity should not be much larger than 5 fps. In this case, the velocity will be about 4 fps (see section -). Pipe Section No. Flow Rate, gpm Lost Head, ft/00 ft Fluid elocity, ft/s PIPE DATA Pipe Length, ft Nominal Size, in. Major Loss, ft Minor Loss, ft Total Head Loss, ft ½ ½ ½ TAG P- MANUFACTURER AND MODEL NUMBER TACO, 0 SERIES, MODEL 0, OR EQUAL TYPE CENTRIFUGAL, IN-LINE MOUNTED PUMP SCHEDULE CONSTRUCTION CAST IRON X X CASING FLOW RATE (GPM) FLUID WORKING FLUID HEAD LOSS (FT) MOTOR SIZE (HP) ELECTRICAL MOTOR OLT/PH SPEED /HZ (RPM) 55 KEROSENE / /3/60

52 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.8 A pipe-pump assembly is being considered by a farmer for use in irrigating a field during summer. There is an underground water well that is 50 ft deep. The well is an open-hole type in which the free surface of water is about 8 ft below grade. To ensure that one of the pumps will operate for only a few hours per day, the farmer will fill a,500-gallon tank in 4 hours, which will provide enough water for days of farm operation. The tank cannot be more than 0 ft long and should come complete with valved piping connections whose locations will be specified by the farmer. The tank can be located anywhere in the line that the farmer deems fit. Due to location of the field and well, a pump must be located no more than 600 ft from the well. The pipe will be connected to an existing irrigation system that is 750 ft from the well and is 0 ft long. The farmer s land is flat, from the well to the field. Design the main piping system to meet the water requirements of the farmer. Specify the maximum depth of the pipe inlet in the well for the purposes of installation by the farmer. Further Information: The design engineer may consider the use of a foot valve (a type of check valve), complete with a strainer at the inlet to the piping system. This will ensure that the pumps are properly primed, that is, completely filled with water before the start of pumping. Possible Solution: Definition Size the main piping and specify the pumping requirements for a water piping system. Preliminary Specifications and Constraints i. The fluid is water from a well. ii. The maximum depth of the well is 50 ft. iii. A -day storage supply of water is required by the farmer. iv. The length of the tank is restricted to 0 ft. v. The pump must be located no more than 600 ft from the well. Detailed Design Objective

53 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. To size the main pipes in the system and to size and select an appropriate pump. Piping accessories such as valves will also be specified. Dimensions of the tank will also be specified. Data Given or Known i. The maximum depth of the well is 50 ft. ii. The free surface of the water in the well is 8 ft below grade. iii. A 500-gallon tank will need to be filled in 4 hours. iv. The tank should contain a -day reserve of water. v. The tank length will be no more than 0 ft. vi. A pump can be located up to 600 ft from the well. vii. The distance between the well and existing irrigation system is 750 ft. viii. The irrigation system is 0 ft long. Assumptions/Limitations/Constraints i. Let the piping material be Schedule 40 steel. This material was chosen to increase durability of the piping system, given that the pipes will be installed outdoors. ii. Let the flow velocity be about 7 fps. This velocity is lower than the erosion limit of water in Schedule 40 steel pipes (0 fps). iii. Limit pipe frictional losses (major losses) to 3 ft of water per 00 ft of pipe. This limit is an industry standard. It will be used as a guide in this design problem. iv. Pipe changes should be gradual to reduce losses. This may be needed at the suction and discharge of the pumps. v. All bends will be 90 o threaded (screwed) regular bends. For smaller pipes (order of 4 in. diameters or less), threaded bends are typically used. vi. The pipe entrance from the storage tank is sharp-edged. vii. The storage tank will come complete with a vent. viii. The season is summer. Let the ambient temperature be 70 o F. Sketch

54 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The pipe sections are labeled and shown on a partial layout that represents the problem. Given that information on the existing irrigation system was not provided, the most conservative design scenario would be with the total length of the irrigation piping system forming a part of the longest run of pipe. Analysis This is an open-loop system due to the presence of the open well, the vented storage tank, and the open irrigation system. Bear the following points in mind for this design problem: i. Pipe sizing for this system can be done quickly by using the appropriate friction loss charts for Schedule 40 steel piping. However, if the required sizes, flow rates, velocities, etc. are not included on the published charts or if the design is based on a specialized pipe material, then the designer should use Colebrook s equation (or other correlation equation) to find the friction factor (f) and iterate to find the pipe diameters. ii. Given that this is an open-loop piping system, it will be necessary to check the NPSH and the possibility of cavitation. Dimensions of the water storage tank The minimum dimensions of the storage tank will be based on the maximum volume of stored water that is required. Since the length of the tank is constrained to 0 ft, the diameter of a cylindrical tank would be easy to determine. Thus, from

55 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. cylinder D D L, 4 4 cylinder L gal ft D x 6.5 ft. 0 ft 64.7 gal 3 The minimum dimensions of the cylindrical water storage tank are 6½ ft diameter and 0 ft length. Size of the pipe The pipe size is constant throughout the system. The total volume flow rate will be needed to determine the pipe size. Thus, 500 gal hour x 0.4 gpm. 4 hours 60 min Figure A.4 for Schedule 40 pipe friction loss for open piping systems will be consulted to determine the size, water velocity, and friction loss of the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Therefore, Nominal pipe size: ½ in. Water velocity:. fps Lost head:.0 ft per 00 ft of pipe. The water velocity is lower than the design constraint of 7 fps. The friction loss is also lower than the design constraint of 3 ft. per 00 ft. of pipe. Major and Minor Losses The total length of the pipe will be needed in order to determine the major loss. Though this will need to be verified through a consideration of NPSH and cavitation, assume that the length of pipe into the well is 0 ft. In this case, the pipe inlet will be below the water surface, but far from the bottom of the well where the water may be muddy. Below are the lengths of each section of pipe and the total length for use in sizing pump, P.

56 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. L well = 0 ft L well-p = 300 ft L P-tank = 0 ft L tank-vertical = 6.5 ft L total-p = ft Below are the lengths of each section of pipe and the total length for use in sizing pump, P. L tank-irrigation = 0 ft L irrigation = 0 ft L total-p = 30 ft. It should be noted that the supply line from the well to the tank was connected to the top of the tank to eliminate losses at the pipe exit and to avoid water static head that would increase the size of pump, P. The tank discharge line to the irrigation system will be connected at the base of the tank to take advantage of the water static head. For pump, P, the major head loss will be H l-p.0 ft. x ft.93 ft. 00 ft For pump, P, the major head loss will be H l-p.0 ft. x 30 ft 4.6 ft. 00 ft With the pipe diameter known (½ in.), the minor losses can be estimated. The loss coefficients for the bends, fittings, and valves are given below (see Table A.4). Ball valves will be installed to isolate equipment. A strainer will be installed close to the well. For the pipe entrance: K entrance = 0.5 (sharp-edged entrance)

57 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For the pipe entrance: K reentrant = 0.8 (reentrant entrance) For the strainer: K strainer =.5 For 90 o bends: K 90-bend =.5 For ball valves: K ball = 0.05 For check valve: K check =.9 The minor loss is determined from lm ave. H K L g Thus, for pump, P, H lm K reentrant K check 3K 90 K strainer 3K ball. ft/s ave g H lm ft. 3. ft/s For pump, P, H lm K entrance K 90 3K ball ave g. ft/s H lm 0.6 ft. 3. ft/s The total head losses are H lt,p =.93 ft ft = 3.67 ft H lt,p = 4.6 ft ft = 4.76 ft. Pump sizing The pump head is required to determine the pump size required. The pump head is h pump p g g z p g g z H lt.

58 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For pump, P, let point be the inlet to the pipe in the well and let point be in the jet that exits into the tank. For the vented tank, p = p atm. If the diameter of the jet is equal to the diameter of the pipe, =. Hence, the pump head is: h P p atm g z p g z H lt,p. The pressure at the inlet to the pipe is p patm ghwater. However, this will result in the selection of a smaller pump. To ensure that the pump will be able to operate under all conditions, let h water = 0 (i.e., no static pressure head). So, with the top of the well as the datum point (z = 0), h h P P z z 6.5 ft h P = 4 ft. H lt,p 0 ft3.67 ft For pump, P, let point 3 be the inlet to the pipe attached at the base of the tank and let point 4 be in the jet that exits from the irrigation system. Thus, h P p4 g 4 g z 4 p 3 g 3 g z 3 H lt,p. For a conservative design, assume that the tank is empty, and p 3 = p atm. The fluid will exit the irrigation system into the atmosphere. So, p 4 = p atm. If the diameter of the jet is equal to the diameter of the pipe, 4 = 3. Thus, the pump head is: h P z z H. 4 3 lt,p In this case, the inlet of the pipe at the tank and the exit at the irrigation system are at the same elevation. Hence, z 4 = z 3. Then, hp H lt,p

59 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. h P = 4.76 ft 5 ft. For this system and to meet the requirements of moving the water to the irrigation system, pump, P must produce gpm at 4 ft of head and pump, P must produce gpm at 5 ft of head. Use manufacturer s charts to select an appropriate pump. For pump, P, a base-mounted pump will be chosen since the pump head is large. Since the pump head and capacity are small for pump, P, a small in-line mounted pump will be sufficient. A review of the various Taco pumps ( shows that a CI/FI Series base-mounted pump will be suitable for pump, P and a 0 Series In-line circulator will be suitable for pump, P. The pump performance plots are shown below. For pump, P, a model 06 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is: in. x ¼ in. x 6.0 in. casing 6.5 in. impeller diameter 3 hp motor 3500 rpm speed For pump, P, the model 0 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is: ½ in. x ½ in. x 6.35 in. casing / hp motor 75 rpm speed A Taco representative will need to be contacted to purchase a 08 /60 Hz/3 phase motor for pump, P. Currently, the motor supplied is 5 /60 Hz/ phase.

60 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

61 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

62 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

63 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. NPSH Cavitation may be a problem that could affect pump, P. The NPSHA and NPSHR will be compared to show that the choice of pipe at a depth of 0 ft does not exceed the maximum depth allowed before which cavitation occurs. For pump, P operating at gpm at 4 ft of head, the NPSHR is approximately 8 ft (see pump performance plot for FI/CI series model 06 pump). The maximum depth of the pipe will occur when NPSHA = NPSHR. Therefore, p P s s vapor NPSHA. g g g pump,inlet The energy equation will be used to find the pump inlet pressure, p s. P g g z ps g s s g z s H lt,suction Point is at the inlet of the pipe. For ease, let the datum point be at point. Thus, z = 0. Let the centerline of the pump be level with the top of the well. Thus, z s z = z s will represent the maximum depth of the pipe in the well. Therefore, P g g ps g s s g z s H lt,suction. Assuming that the free surface of the water is 8 ft below grade (as per the problem preamble), P Patm atm s gh P g z 8. Since the pipe is a constant diameter pipe, s. Therefore, P atm g zs 8 g ps g z s H lt,suction P atm g p 8 ft s H g lt,suction.

64 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Hence, p s g P atm 8 ft H lt,suction. g Then, NPSHA P atm g 8 ft H lt,suction s g P g vapor NPSHA P atm P g vapor 8 ft H lt,suction s g Note that H lt,suction is the total head loss in the suction line of the pipe, only. The head loss in the suction line of the pipe is H lt Hl,suction KL g. The total length of suction piping is (z s + 300) ft. Therefore, H lt.0 ft.wg. 00 ft x H 0.0z 6.45 ft. lt s. ft/s z 300 ft s 3. ft/s Then, NPSHA P atm P g vapor 8 ft 0.0z s s 6.45 ft. g z s is the maximum depth of the pipe in the well when NPSHA = NPSHR. Therefore,

65 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. z s 0.0 P NPSHR atm P g vapor At 70 o F, P vapor = psia for water. P atm = 4.7 psia. s 8 ft 6.45 ft. g Hence, z s ft lbf/in lb/ft 3. ft/s 3. lb-ft/s x lbf in x ft. ft/s 3. ft/s 4.45 ft z s = 538 ft. The maximum depth of the pipe must be 538 ft to avoid cavitation in pump, P, if the free surface of the water in the well is 8 ft below grade. Therefore, the pipe inlet set at 0 ft below grade is acceptable. Though this is acceptable, it should be strongly noted that as the free surface of the water falls further below grade, less static pressure head will be available and cavitation may occur as water is removed from the well. For example, the following calculation shows that cavitation will occur when the water free surface reaches 6.4 ft below grade if the pipe inlet is set to 0 ft: z s 0.0 P NPSHR atm P g vapor s g h water 6.45 ft ft 8 ft lb/ft 3. ft/s lbf/in 0 water h water = 6.4 ft. 3. lb-ft/s x lbf in x ft. ft/s 3. ft/s h 6.45 ft This might be acceptable if the well is large with a large cross-sectional area to give the volume that is required by the farmer, or they are willing to wait until the well refills before removing water. If this is not the case, the designer would need to shorten the length of pipe installed in the well, and check the depth at which cavitation would occur. Another alternative could be to move the pump closer to the well or use a submersible pump that can be placed in the water and well.

66 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For small pumps, the NPSHR is usually not presented. From studying the performance plots of a variety of pumps, the NPSHR is usually small at low flow rates, on the order of to 0 ft. To avoid cavitation, the NPSHA must be greater than the NPSHR. With regards to pump, P, the NPSHA is p P s s vapor NPSHA. g g g pump,inlet The energy equation will be used to find the pump inlet pressure, p s. P 3 g 3 3 g z 3 ps g s s g z s H lt,suction Point 3 is the inlet to the pipe at the tank. As stated earlier and for a conservative design, P 3 = P atm. Since the pipe diameter is constant, 3 s. So, P atm g z 3 ps z g s H lt,suction The elevation differences between point 3 and the suction point of the pump will be negligible. So, z 3 = z s. Then, P atm g p s g p g P s H lt,suction atm H lt,suction. g Then, NPSHA P atm g s g H lt,suction P g vapor NPSHA P atm P g vapor s g H lt,suction. Note that H lt,suction is the total head loss in the suction line of the pipe, only. To generate a more conservative value of the NPSHA, assume that the suction line has a length of 0 ft (i.e., length of the section).

67 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Thus, NPSHA NPSHA = 8.8 ft lb/ft 3. ft/s lbf/in 3. lb-ft/s x lbf in x ft. ft/s 3. ft/s.0 ft 00 ft x 0 ft The NPSHA for this case is large, and probably much larger than the NPSHR for this small pump (P). The possibility of cavitation is very low. Drawings The final pipe sizes and accessories are presented in the drawing below. Conclusions The piping system has been designed. The pipe size is known, and the piping material has been selected. Pumps have been specified and selected. The following additional points are made:. The farmer was wise to have requested the pump, P not run continuously. It is a large 3 hp basemounted pump.. A calculation based on the volume of water required from the well showed that a minimum 7 ft diameter well would be needed if 8.4 ft of water will be drawn from the well before cavitation

68 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. occurred. The farmer would need to consider digging the well, and possibly covering it after installation of the pipe to avoid losing land space. 3. Additional details would be required for the existing irrigation system. In this design problem, it was assumed that the water is ejected from the irrigation system as a single jet. In practice, a sprinkler system may be used, which will have an associated minor loss that needs to be considered. 4. The pipe between the pumps may need support anchors. These anchors would probably be mounted on concrete pads on the ground. 5. For pump, P, in. x ½ in. and ½ in. x ¼ in. reducing fittings will be required on the pump suction and discharge, respectively, for installation of the pump. 6. The pump suction velocities should not be much larger than 5 fps. In this case, the velocities will be about fps. 7. Though an inexpensive choice, a foot valve (complete with a strainer) could have been used in lieu of the check valve and strainer. However, foot valves (especially those with poppet disks) tend to add high frictional loss to the piping system. They may also leak, requiring priming of the pump. 8. If corrosion of the pipe is a concern, plastic piping could have been selected instead of Schedule 40 pipe. TAG P- P- MANUFACTURER AND MODEL NUMBER TACO, FI/CI SERIES, MODEL 06, OR EQUAL TACO, 0 SERIES, MODEL 0, OR EQUAL TYPE CENTRIFUGAL, BASE- MOUNTED CENTRIFUGAL, IN-LINE MOUNTED PUMP SCHEDULE CONSTRUCTION CAST IRON X ¼ X 6.0 CASING, 6.5 CAST IRON ½ X ½ X 6.35 CASING FLOW RATE (GPM) FLUID WORKING FLUID HEAD LOSS (FT) MOTOR SIZE (HP) ELECTRICAL MOTOR OLT/PH SPEED /HZ (RPM) WATER /3/60 WATER 5 / 75 08/3/60

69 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.9 An engineer has presented a piping system layout that includes a pump, condenser, and cooling tower for a building cooling application. Size the piping and specify the pump required if the total volume flow rate of water is 450 gpm, the pressure drop in the condenser is 5 ft of water gage, the vertical distance from the pump centerline to the top of the cooling tower is 45 ft, the horizontal distance from the condenser to the tower is 70 ft, and the pump is 5 ft below the tower basin. All the necessary accessories are shown in the sketch provided by the engineer. Possible Solution: Definition Size the main piping and specify the pump required for a cooling tower water piping system. Preliminary Specifications and Constraints i. The fluid is water. ii. The dimensions, layout, and accessories are all constrained as shown in the engineer s drawing. Detailed Design Objective To size the main pipe in the system and to size and select an appropriate pump. Data Given or Known

70 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. i. The total volume flow rate of water is 450 gpm. ii. The pressure drop in the condenser is 5 ft water gage. iii. The vertical distance from the pump centerline to the top of the cooling tower is 45 ft. iv. The horizontal distance from the condenser to the tower is 70 ft. v. The pump is 5 ft below the tower basin. Assumptions/Limitations/Constraints i. Let the piping material be Schedule 40 steel. This material was chosen to increase durability of the piping system, given that some sections of the piping system will be installed outdoors. ii. Let the flow velocity be about 5 fps. This velocity is lower than the erosion limit of water in Schedule 40 steel pipes (0 fps). iii. Limit pipe frictional losses (major losses) to 3 ft of water per 00 ft of pipe. This limit is an industry standard. It will be used as a guide in this design problem. iv. Pipe changes should be gradual to reduce losses. This may be needed at the suction and discharge of the pumps. v. All bends will be 90 o flanged regular bends. The high volume flow rate required suggests that larger pipe sizes may be possible, which will require more rigidly connected fittings. vi. The pipe entrance from the cooling tower basin is sharp-edged. vii. The pump is located 35 ft from the cooling tower. This is half the distance between the condenser and the cooling tower. Sketch No sketch is required. It was provided by the engineer. Analysis This is an open-loop system due to the cooling tower. Bear the following points in mind for this problem: i. Pipe sizing for this system can be done quickly by using the appropriate friction loss charts for Schedule 40 steel piping. However, if the required sizes, flow rates, velocities, etc. are not included on the published charts or if the design is based on a specialized pipe material, then the designer should use Colebrook s equation (or other correlation equation) to find the friction factor (f) and iterate to find the pipe diameters.

71 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. ii. Given that this is an open-loop piping system, it will be necessary to check the NPSH and the possibility of cavitation. Size of the pipe The pipe size is constant throughout the system. The total volume flow rate will be needed to determine the pipe size. It is given as 450 gpm. Figure A.4 for Schedule 40 pipe friction loss for open piping systems will be consulted to determine the size, water velocity, and friction loss of the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Thus, Nominal pipe size: 6 in. Water velocity: 5.0 fps Lost head:.3 ft per 00 ft of pipe. The water velocity does not exceed the design constraint of 7 fps. The friction loss is also lower than the design constraint of 3 ft. per 00 ft. of pipe. Major and Minor Losses The total length of the pipe is provided to determine the major loss. The major head loss will be H l.3 ft. x 00 ft ft 4.6 ft. With the pipe diameter known (6 in.), the minor losses can be estimated. The loss coefficients for the bends, fittings, and valves are given below (see Table A.4). For the pipe entrance: K entrance = 0.5 (sharp-edged entrance) For the strainer: K strainer =.5 For 90 o bends: K 90-bend = 0.30 For ball valves: K ball = 0.05

72 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The minor loss is determined from lm ave. H K L g Therefore, H lm K entrance 5K 90 K strainer 4K ball ave g 5.0 ft/s H lm.44 ft. 3. ft/s The total losses are H lt H l H lm H condenser H 4.6 ft.44 ft 5 ft ft. lt Pump sizing The pump head is required to determine the pump size required. The pump head is: h pump p g g z p g g z H lt. Let point be the inlet to the pipe at the cooling tower basin and let point be in the jet that exits into the top of the cooling tower. For a more conservative sizing of the pump, let the basin be nearly empty. Thus, p = p atm. p = p atm at the top of the cooling tower. If the diameter of the jet is equal to the diameter of the pipe, =. Hence, the pump head is: h pump z z H lt Let the datum point where z = 0 be at the pump centerline. Thus, h pump 45 ft 5 ft ft h pump 5ft.

73 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For this system and to meet the requirements of moving the water to the cooling tower, the pump must produce 450 gpm at 5 ft of head. Use manufacturer s charts to select an appropriate pump. A basemounted pump will be chosen since the pump capacity and head is large. A review of the various Taco pumps ( shows that a CI/FI Series base-mounted pump will be suitable. The pump performance plots are shown below. A model 503 pump is selected, and the performance plot is analyzed. From the performance plot for this family of pumps, the final choice is: 6 in. x 5 in. x 3.0 in. casing ⅛ in. impeller diameter 0 hp motor 60 rpm speed

74 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Taco, Inc. (Reprinted with permission)

75 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. NPSH Cavitation may be a problem that could affect the pump in this open-loop system. The NPSHA and NPSHR will need to be compared. For the selected pump operating at 450 gpm, the NPSHR is approximately 4 ft (see pump performance plot for FI/CI series model 503 pump). The NPSHA is, p P s s vapor NPSHA. g g g pump,inlet The energy equation will be used to find the pump inlet pressure, p s. p g g z ps g s s g z s H lt,suction Point is the inlet to the pipe at the cooling tower basin. For a conservative analysis, p = p atm. For the constant area pipe, = s. Thus, p atm g z ps z g s H lt,suction. The datum point was chosen at the pump centerline. Thus, z s = 0. Then, p atm g z p g s H lt,suction. Therefore, p s g p atm z H lt,suction. g The NPSHA becomes, NPSHA p atm g z H lt,suction s g P g vapor NPSHA p atm P g vapor s g z H lt,suction.

76 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. It should be noted that H lt,suction is the total head loss in the suction line of the pipe, only. The head loss in the suction line of the pipe is: H lt Hl,suction KL g. The total length of suction piping is (35 + 5) ft = 50 ft. Therefore, H lt.3 ft.wg. 00 ft x 50 ft 5.0 ft/s ft/s. ft. Then, at 70 o F, P vapor = psia for water and P atm = 4.7 psia, NPSHA lb/ft 3. ft/s lbf/in 3. lb-ft/s x lbf in x ft 5.0 ft/s 3. ft/s 5 ft. ft NPSHA = 46 ft. Since NPSHA > NPSHR, no cavitation will occur, even if the cooling tower basin is nearly empty. Drawings The final pipe size is shown on the engineer s original drawing.

77 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Conclusions The pipe has been sized and the pumps has been specified and selected. The following additional point is made:. A 6 in. x 5 in. reducing fitting will be required on the pump discharge for installation of the pump.. The pump suction velocity should not be much larger than 5 fps. In this case, the velocity will be about 5 fps. TAG P- MANUFACTURER AND MODEL NUMBER TACO, FI/CI SERIES, MODEL 503, OR EQUAL TYPE CENTRIFUGAL, BASE- MOUNTED PUMP SCHEDULE CONSTRUCTION CAST IRON 6 X 5 X 3.0 CASING,.5 FLOW RATE (GPM) FLUID WORKING FLUID HEAD LOSS (FT) MOTOR SIZE (HP) ELECTRICAL MOTOR OLT/PH SPEED /HZ (RPM) 450 WATER /3/60

78 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 3.0 Independent Living Developments Inc. has recently awarded a project for the first phase of the detailed design of a system to deliver potable water from a bore-well to a -floor, -apartment residence to a mechanical engineering consulting firm. In this first phase of the project, the client has requested that the design be restricted to include elements associated with the extraction of water from a bore-well in sufficient quantity to meet the needs of their proposed residential complex and to deliver it at a pressure of 00 psia at the inlet to each floor riser. This phase of the project is not to include any aspects of the design of the bore-well or the layout of the internal plumbing systems of the building. Detailed drawings of items such as connections and penetrations are not required at this time. The proposed construction site is a rectangular plot of land with an area of ½-acre that has road access on one side and land on the other three sides. The footprint of the -apartment complex is planned to be 60 ft by 0 ft. Any existing building structures on the plot of land have been slated for demolition. The complex will be located in an area where the average outdoor temperature in winter is -4 o F, and in the summer, 80 o F. The apartment complex will have a basement, which will serve as a storage area and mechanical room and will have a foundation that is 6 ft below grade and a clear height of 8 ft to meet the requirements of the International Building Code. The first floor has eight -bedroom apartments (floor area ft each and height 0 ft) and the second floor has four 3-bedroom apartments (floor area ft each each and height 0 ft). There is an existing bore-well located 50 ft from the proposed building. Standard draw-down and recovery tests that were conducted at the well depth of 00 ft showed that the well could support continuous extraction of water at 0 gpm. Through consultation with the local utility company, it was found that each person uses approximately 60 gallons of water per day. In order to guarantee the availability of sufficient amounts of water, the client has requested the use of a water storage tank. With reference and adherence to the International Building Code and the International Plumbing Code (or Uniform Plumbing Code), design the piping system required to deliver water from the well to the floors of the complex (up to and including the floor risers). The designer should ensure that necessary components such as pumps, pipes, valves, piping accessories, the tank and its size, to name a few, are clearly specified. Further Information: The design engineer may consider the use of a foot valve (a type of check valve), complete with a strainer at the inlet to the piping system. This will ensure that the pumps

79 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. are properly primed, that is, completely filled with water before the start of pumping. Other alternatives may include a submersible pump complete with a foot valve. Possible Solution: Definition Design a system to supply sufficient water at 00 psia to each floor of a -storey apartment complex. Preliminary Specifications and Constraints i. The fluid is water from a bore well. ii. The complex has floors, with a total of apartments. iii. The st floor of the complex has eight -bedroom apartments and the nd floor has four 3-bedroom apartments. iv. The apartment sizes range from ft with heights of 0 ft. v. The building footprint is 60 ft by 0 ft.

80 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. vi. The basement foundation is 6 ft below grade and the clear height of the ceiling is 8 ft. vii. The minimum pressure at the main line to each floor should be 00 psia. viii. The bore well is located 50 ft from the building. ix. The bore well depth is 00 ft and can support 0 gpm of continuous water flow. x. The average winter outdoor temperature is -4 o F. The average summer outdoor temperature is 80 o F. xi. Each person uses 60 gallons of water per day. Detailed Design Objective To size the main pipes in the system and to size and select appropriate pumps. Piping accessories will also be specified. Dimensions and schedules of any necessary equipment will also be specified. Data Given or Known i. There are apartments in the complex. ii. There are 8 bedrooms in the complex. iii. The minimum pressure at the main line to each floor should be 00 psia. iv. The complex will be located on a ½-acre section of flat land. v. The bore well is located 50 ft from the building. vi. The bore well depth is 00 ft and can support 0 gpm of continuous water flow. vii. The average winter outdoor temperature is -4 o F. The average summer outdoor temperature is 80 o F. viii. Each person uses 60 gallons of water per day. Assumptions/Limitations/Constraints i. Let the piping material be Schedule 40 PC plastic piping. This material was chosen for its durability and strength. Portions of piping system may also be routed underground. The corrosion resistance of PC will be useful if the soil is corrosive. Section 604. of the Uniform Plumbing Code permits the use of PC to supply cold water in building supply distribution systems outside the building. ii. Let the flow velocity be about 6 fps. This velocity is lower than the erosion limit of water in most pipe materials (except copper). This velocity is also lower than the maximum value allowed for potable water in building service (6.9 fps).

81 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. iii. Limit pipe frictional losses (major losses) to about 3 ft of water per 00 ft of pipe. This limit is an industry standard. It will be used as a guide in this design project. iv. The friction loss charts of Schedule 40 steel will be used to size the Schedule 40 PC pipes. This will yield a more conservative sizing since the PC piping is smoother than steel piping. v. Pipe changes should be gradual. Section of the International Plumbing Code requires the use of increasers and reducers for the connection of pipes of different sizes, where necessary. vi. All fittings will be threaded (screwed). In practice, PC piping sections and fittings will usually be glued. Therefore, the losses due to the fittings will be lower than those of threaded fittings. vii. The pipe entrance from any storage tank will be sharp-edged. viii. The storage tank will come complete with a vent. ix. Let the ground temperature be 50 o F. (See Practical Note 5-3) x. Assume that the -bedroom apartments have shower and the 3-bedroom apartments have showers. Therefore, there are 6 showers in the complex. xi. Assume that the -bedroom apartments house 3 persons and the 3-bedroom apartments house 4 persons. Therefore, there are 40 persons living in the complex. xii. Assume that the soil is wet or containing water. This will probably be the case during the winter. Property data for wet soil is usually presented in most text on fluid mechanics and heat transfer. Sketch A tentative sketch of the system is provided.

82 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Analysis This is an open-loop system due to the presence of the open well and a possible vented storage tank. Bear the following points in mind for this design project: i. Pipe sizing for this system can be done quickly by using the appropriate friction loss charts for Schedule 40 steel piping. However, if the required sizes, flow rates, velocities, etc. are not included on the published charts or if the design is based on a specialized pipe material, then the designer could use Colebrook s equation (or other correlation equation) to find the friction factor (f) and iterate to find the pipe diameters. ii. Given that this is an open-loop piping system, it will be necessary to check the NPSH and the possibility of cavitation. iii. Given that the system will be located in a cold climate area, freezing of the water may occur. It may be necessary to route the section of piping that is outdoor underground. Therefore, a portion of the analysis will be dedicated to the determination of the burial depth required. All plumbing codes require that allocations for freezing be considered in the design of water distribution systems that are routed outdoor.

83 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. iv. The installation of the water storage tank will help to avoid continuous operation of the large pump(s) that would be required to lift water from the well. The water tank may need to be an underground tank to avoid freezing of the water. There may not be sufficient space in the basement of the building complex to house the tank. Water flow rate required Showers will typically impose the greatest demand on the water distribution system, especially at the peak morning hour. In this complex, it was assumed that there will be 6 shower heads. Section of the International Plumbing Code requires that shower head piping provide 3 gpm of water flow. The total volume flow rate is 3gpm x 6 showers 48 gpm 50 gpm. shower Dimensions of the water storage tank An underground water storage tank will be installed to help to avoid continuous operation of the large pump(s) that will be required to lift water from the well. 60 gal per person per day of water is typically used. It was assumed that there are 40 persons living in the complex. A 5-day storage capacity will be selected. Check the volume required, and tank availability from suitable manufacturers. 60 gal x 5 daysx 40 persons,000 gal. person-day A smaller tank could have been chosen to give a smaller number of storage days. The final decision of a tank size may depend on the cost of the tanks, which is not being considered in this project. The size of the,000-gallon tank will provide sufficient water to allow for filling the tank with water from the well. Further, it would require 4 hours of continuous showering at all the shower heads in the complex (at 50 gpm) to empty the tank completely. This is not possible. Therefore, this tank size will provide a reasonable reserve of water for the complex. A survey of the websites of several manufacturers who fabricate underground water storage tanks has led to the Darco, Inc. polyethylene OCTANK. The,000-gallon tank will be chosen, which has a length of 5 ft and a height of 90 in. Though not shown, the specification sheets recommend that the

84 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. tank be fully buried about 0 ft below grade so that the manway cover is about ft above grade. Approximately 3 ft of the manway will be buried (see final drawing). Minimum burial depth of the pipe The system will be located in a cold climate area, where ambient air temperatures will be well below the freezing point of water. Therefore, the pipes will be buried to avoid freezing the water during winter. To determine the burial depth of the pipe, it will be assumed that the exposed top surface of the ground in contact with the winter air is -4 o F. This will be the temperature for 3 months of the year. The ground will be modeled as a semi-infinite medium, where far from the top surface of the ground, the ground temperature is 50 o F. This temperature will also be the initial temperature in the problem. From fundamental transient heat conduction in semi-infinite media, the temperature distribution is T T T surface initial T initial x erfc. 4t For this problem, the depth, L is required at which T = T freezing for water. So, T T freezing surface T T initial initial L erfc. 4t Find L: o o 3 F 50 F erfc o o 4 F 50 F L 4t The argument of the complimentary error function that gives 0.33 is approximately Thus, L t The thermal diffusivity of wet soil is approximately k.6 Btu/h-ft-R ft /h. c p lb/ft 0.55 Btu/lb-R The burial depth is L t weeks 7 days 4 hours /h 3 months ft month week day

85 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. L 8.3ft. The minimum burial depth of the pipes is 8 ft below grade. A check of frost depth data provided by the government, shows that pipes should be buried 8 to 9 ft below grade to avoid freezing the water in areas where the outdoor temperature are as low as -4 o F. However, Section of the International Plumbing Code requires that outdoor water supply piping be buried at least 6 inches below the frost depth. Therefore, the burial depth of the pipes will be 9 ft below grade. Since the depth of the basement foundation is 6 ft below grade, the pipe will enter the basement at 6 ft below grade. Sizes of the pipes At this point in the design, a rough sketch of the system that builds upon the tentative sketch provided would be useful to facilitate sizing the pipe sections.

86 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. From the sketch, there are 4 pipe sections to be sized. Section - This section of pipe will supply water from the well to the storage tank. The total volume flow rate will be needed to determine the pipe size. A,000-gallon tank would be filled with a 5-day supply of water. The completely empty tank should be filled in a 4-hour period (maximum) by using a submersible pump in the well. Thus, the volume flow rate required to fill the tank would be,000 gal hour t x 8.3 gpm. 4 hours 60 min Typically, the tank will probably never be completely empty after the initial fill because the triggering of low-level switches in the tank would initiate P to start filling the tank. Figure A.4 for Schedule 40 pipe friction loss for open piping systems will be consulted to determine the size, water velocity, and friction loss of the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Therefore, Nominal pipe size: ¼ in. Water velocity:.3 fps Lost head:.8 ft per 00 ft of pipe. The water velocity is lower than the design constraint of 6 fps. The friction loss is also lower than the design constraint of 3 ft. per 00 ft. of pipe. Section 3-4 This is the main supply line from the storage tank to the building. The total volume flow rate required is 50 gpm. Figure A.4 for Schedule 40 pipe friction loss for open piping systems will be consulted to determine the size, water velocity, and friction loss of the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide.

87 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Therefore, Nominal pipe size: ½ in. Water velocity: 3. fps Lost head:.5 ft per 00 ft of pipe. The water velocity is lower than the design constraint of 6 fps. The friction loss is also lower than the design constraint of 3 ft. per 00 ft. of pipe. Section 4-5 This is the branch supply line to the first floor. Only a fraction of the total volume flow rate will be needed to service this floor. Based on the assumptions, there will be 8 showers on this floor. Therefore, the total volume flow rate required by this floor will be 5 gpm. Figure A.4 for Schedule 40 pipe friction loss for open piping systems will be consulted to determine the size, water velocity, and friction loss of the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Therefore, Nominal pipe size: in. Water velocity:.7 fps Lost head:. ft per 00 ft of pipe. The water velocity is lower than the design constraint of 6 fps. The friction loss is also lower than the design constraint of 3 ft. per 00 ft. of pipe. Section 4-6 This is the branch supply line to the second floor. Only a fraction of the total volume flow rate will be needed to service this floor. Based on the assumptions, there will be 8 showers on this floor. Therefore, the total volume flow rate required by this floor will be 5 gpm. Figure A.4 for Schedule 40 pipe friction loss for open piping systems will be consulted to determine the size, water velocity, and friction loss of the pipe. A friction loss of 3 ft. per 00 ft. of pipe will be used as a guide. Therefore, Nominal pipe size: in.

88 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Water velocity:.7 fps Lost head:. ft per 00 ft of pipe. The water velocity is lower than the design constraint of 6 fps. The friction loss is also lower than the design constraint of 3 ft. per 00 ft. of pipe. Major Losses The total length of the pipe sections will be needed in order to determine the major loss. In this case, appropriate codes will be used to provide some guidance when deciding the length of the pipes. Consider each section. Length of Section - Assume that the length of pipe into the well is 70 ft. In this case, the pipe inlet will be about 79 ft below grade. This will ensure that a limited amount of solid material will enter the pipeline. The total length of the tank is 5 ft. So, roughly 35 ft of outdoor piping will be required. Let the tank be 0 ft from the well and 5 ft from the building. The total length of the section - piping is ( ) ft = 96 ft. Note that to avoid additional head on pump P, the pipe of section - will terminate close to the top of the tank. Further to this point, the Darco OCTANK has its supply piping at the top of the tank. Length of Section 3-4 In order to take advantage of the static pressure head of the water in the tank, the pipe at point 3 will be attached to the bottom of the tank. Given that the pipe will be sloped from the bottom discharge of the tank to enter the basement, 6 ft of pipe will be needed (Pythagoras theorem was used to approximate the pipe length). The pipe may enter the basement of the building and run parallel to either the 60 ft or the 0 ft length of the building. For a conservative approach, it will be assumed that the piping runs along the 0 ft length of the building. The height of the tank is 90 inches. The pipe will be elevated from the basement floor to the first floor over a height of 8 ft.

89 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The total length of the section 3-4 piping is ( ) ft = 44 ft 50 ft. Length of Section 4-5 The design problem requires that the pressure at the inlet of section 4-5 be 00 psia. For the purposes of this design project and sizing the pump, the length of this section that supplies the individual plumbing of the floor is not needed. Length of Section 4-6 The floor height is 0 ft. The total length of the section 4-6 piping is 0 ft. The same point mentioned above for the section 4-5 pipe will apply here. The following sketch shows the lengths of the straight runs of piping.

90 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For pump, P, the major head loss will be H l-p.8 ft. x 96 ft.69 ft. 00 ft For pump, P, the major head loss will be H l-p.5 ft. x L 00 ft 3-4. ft. x L 00 ft 46.5 ft.. ft. x 50 ft x 0 ft 3.97 ft. 00 ft 00 ft Minor Losses With the pipe diameters known, the minor losses can be estimated. It should be noted that the plumbing code has several specific requirements for piping accessories and fittings that may be required. The section or group of sections serviced by a given pump will be considered. Section - for pump, P In this section of the piping system, a hinged disk foot valve, complete with a strainer, will be installed at the entrance of the suction line. As per the specification sheets of the,000-gallon tank obtained from Darco, a filter will be installed at the exit of section -. The loss coefficient of a strainer will be used. Unions will be needed to connect the pipe lengths. For 5-ft or 0-ft lengths of pipe, approximately 6 unions will be required in this section. The loss coefficients of all the fittings are shown below (see Table A.4). Note that the pipe nominal diameter is ¼ in. For the pipe entrance: K entrance = 0.8 (reentrant entrance) For the foot valve: K foot =.5 For the strainer: K strainer =.5 For 90 o bends: K 90-bend =.5 (regular)

91 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For unions: K union = 0.8 (screwed) The minor loss is determined from lm ave. H K L g So, for pump, P, H lm-p K entrance K foot 4K 90 K strainer 6K union.3 ft/s ave g H lm-p.84 ft. 3. ft/s Section 3-6 for pump, P The longest run of piping will be considered to determine the losses that need to be overcome by pump P. For protection of the pump, a strainer will be installed in the suction piping section in the basement. A check valve will be installed upstream of the pump to ensure that the suction line will be filled with water to prime the pump. Another check valve will be installed on the pump discharge line to mitigate backflow into the pump and flooding. Section 606. of the International Plumbing Code requires that water service pipes be provided with accessible shut-off valves close to where the pipe enters the building. The same section of the code also requires that for buildings with multiple floors, every riser (line that services the floor) will require a shut-off valve located at the source of the supply, that is, close to the main line. For this design project, all the shut-off valves will be gate valves. The isolation valves around the pump P will also be gate valves. Section of the International Plumbing Code requires that, in the case where the pressure to the fixtures on the floor may exceed 80 psia, pressure-reducing valves (PR) should be installed. Section 608. of the Uniform Plumbing Code imposes the same requirement. Thus, pressure-reducing valves will be installed in section 4-5 (riser to st floor) and the riser to the nd floor. The loss coefficients of globe valves will be used to represent those of the pressure-reducing valves.

92 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. 5 unions will be specified for 5-ft and/or 0-ft sections of pipe. Most local codes (e.g., Section.6.. of the 005 National Plumbing Code of Canada) require that a water distribution system be installed so that it can be drained or blown out with air. To meet this requirement, blow-off strainers will be installed on the line located in the basement and on the st and nd floor risers. The loss coefficients of all the fittings are shown below (see Table A.4). For the pipe entrance: K entrance = 0.8 (reentrant entrance) For the strainer: K strainer =.5 For 90 o bends: K 90-bend = 0.95 (regular) For check valves: K check =. For gate valves: K gate = 0.6 For gradual contraction: K contraction = 0.07 For line flow tee: K tee-line = 0.90 For pressure-reducing valves (PR): K PR = 6.9 For unions: K union = 0.8 (screwed) For the blow-off strainer: K b-o_strainer =.5 Therefore, for pump, P, H H lm-p lm-p K K entrance check K K strainer 4K 4K 3K K K K 90 union gate 90 union 3-4 gate 4-6 K tee-line Kcontraction g Kb-o_strainer K PR g b-o_strainer H lm-p = 3.89 ft +.7 ft = 5.06 ft 3. ft/s 3. ft/s ft/s ft/s Total head loss For pump P, H lt-p =.69 ft +.84 ft = 4.53 ft. For pump P, H lt-p = 3.97 ft ft = 9.03 ft.

93 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. The following sketch below shows the system complete with all the piping specialties for which the minor losses have accounted. Pump sizing The pump head is required to determine the pump sizes. The pump head is: h pump p g g z p g g z H lt. For pump P, let point be the inlet to the pipe in the well and let point be in the jet that exits into the tank. The exit of the pipe enters only a small distance into the tank. For the vented tank, p = p atm. If the diameter of the jet is equal to the diameter of the pipe, =. Thus, the pump head is:

94 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. lt,p atm P H z g p z g p h. The pressure at the inlet to the pipe is water atm gh p p. However, this will result in the selection of a smaller pump. To ensure that the pump will be able to operate under all conditions, let h water = 0 (i.e., no static pressure head). So, with the inlet of the pipe as the datum point (z = 0), lt-p P H z h 4.53 ft 75 ft P h h P = 80 ft. For pump P, let point 3 be the inlet to the pipe inserted 7 ft into the tank and let point 6 be immediately upstream of the pressure-reducing valve on the nd floor riser. Thus, lt,p P H z g g p z g g p h. For a conservative design, assume that the tank is empty, and that p 3 = p atm. The pressure at point 6 will be p 6 = 00 psia, as is required by the client. The velocity in the pipe at point 3 will be 3 = 3. fps and at point 6, it will be 6 =.7 fps. Let the datum point be located at the pipe inlet (z 3 = 0). Hence, z 6 = (90 in + 8 ft + 0 ft + ft) = 8 ft. Therefore, the pump head is: lt,p 3 atm P H g g p z g g p h lt,p atm 6 P H z g g p p h. Then, 9.03 ft 8 ft 3. ft/s 3. ft/s.7 ft/s lbf 3. lbm-ft/s ft in 3. ft/s 6 lbm/ft 4.7 lbf/in 00 lbf/in 3 P h h P = 98. ft ft + 8 ft ft.

95 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. For this system and to meet the requirements of moving the water from the well to the underground storage tank, pump P must produce 8 gpm at 80 ft of head and pump, P must produce 50 gpm at 35 ft of head. Use manufacturer s charts to select an appropriate pump. For pump, P, a submersible pump will be chosen. Since the pump head is large for pump P, a base-mounted pump will be chosen. A review of the various ITT Goulds submersible pumps ( shows that a Bruiser Model 7SB will be suitable for pump P. Cut-sheets are presented. Taco pumps ( will be consulted for an appropriate base-mounted pump that will be suitable for pump P. A CI/FI Series Model 509 pump will be selected. The pump performance plot is shown. For pump P, the final choice is: ¼ in. discharge connection ¾ hp motor 3450 rpm speed. For pump P, the final choice is: ½ in. x ½ in. x 9 in. casing 8.00 in. impeller diameter 0 hp motor 3500 rpm speed. It should be noted that for pump P a ½ in.-½ in. fitting will be required on the pump discharge for installation of the pump. Excerpts from the manufacturer s catalog sheets are shown below.

96 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

97 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd.

98 03 André G. McDonald and Hugh L. Magande. Published 03 by John Wiley & Sons, Ltd. Source: Goulds Pumps (Reprinted with permission) Source: Taco, Inc. (Reprinted with permission) Cavitation and NPSH Pump P is a submersible pump that has a little or no suction line. Therefore, cavitation will not be an issue for this pump. Cavitation may be a problem that could affect pump P. The NPSHA and NPSHR will be compared. In order to make a conservative comparison, the underground storage tank will be assumed to be nearly empty. Thus, no static pressure head will be induced at the entrance of the suction line of pump P (point 3). For pump P operating at 50 gpm at 35 ft of head, the NPSHR is approximately 0 ft (see pump performance plot for FI/CI series model 509 pump above). Therefore,