## Problems Pumps

J. The pressure developed by a centrifugal pump for Newtonian liquids that are not highly viscous depends upon the liquid density, the impeller diameter, the rotational speed, and the volumetric flow rate.

(a) Determine a suitable set of dimensionless groups that should be adequate to relate all of these variables.

You want to know what pressure a pump will develop with a liquid having an SG of 1.4 at a flow rate of 300 gpm using an impeller with a diameter of 12 in. driven by a motor running at 1100 rpm. You have a similar test pump in the lab with a 6 in. impeller driven by an 1800 rpm motor. You want to run a test with the lab pump under conditions that will allow you to determine the pressure developed by the larger pump.

(b) Should you use the same liquid in the lab as in the larger pump, or can you use a different liquid? Why?

(c) If you use the same liquid, at what flow rate will the operation of the lab pump simulate that of the larger pump?

(d) If the lab pump develops a pressure of 150 psi at the proper flow rate, what pressure will the field pump develop at 300 gpm?

(e) What pressure will the field pump develop with water at 300 gpm?

2. The propeller of a speed boat is 1 ft in diameter and is 1 ft below the surface of the water. At what speed (rpm) will cavitation occur at the propeller? Water density = 64lbm/ft3, Pv of water = 18.65mm Hg.

3. You must specify a pump to be used to transport water at a rate of 5000 gpm through 10 mi of 18 in. sch 40 pipe. The friction loss in valves and fittings is equivalent to 10% of the pipe length, and the pump is 70% efficient. If a 1200 rpm motor is used to drive the pump, determine:

(a) The required horsepower and torque rating of the motor.

(b) The diameter of the impeller that should be used in the pump.

4. You must select a centrifugal pump that will develop a pressure of 40 psi when pumping a liquid with an SG of 0.88 at a rate of 300 gpm. From all the pump characteristic curves in Appendix H, select the best pump for this job. Specify pump head, impeller diameter, motor speed, efficiency, and motor horsepower.

5. An oil with a 32.6° API gravity at 60°F is to be transferred from a storage tank to a process unit that is 10 ft above the tank, at a rate of 200 gpm. The piping system contains 200 ft of 3 in. sch 40 pipe, 25 90° screwed elbows, six stub-in tees used as elbows, two lift check valves, and four standard globe valves. From the pump performance curves in Appendix H, select the best pump to do this job. Specify the pump size, motor speed, impeller diameter, operating head and efficiency and the horsepower of the motor required to drive the pump.

6. You must purchase a centrifugal pump to circulate cooling water that will deliver 5000 gpm at a pressure of 150 psi. If the pump is driven by an 1800 rpm motor, what should the horsepower and torque rating of the motor be, and how large (diameter) should the pump impeller be, assuming an efficiency of 60%?

7. In order to pump a fluid of SG = 0.9 at a rate of 1000 gpm through a piping system, a hydraulic power of 60 hp is required. Determine the required pump head, the torque of the driving motor, and the estimated impeller diameter, if an 1800 rpm motor is used.

8. From your prior analysis of pumping requirements for a water circulating system, you have determined that a pump capable of delivering 500 gpm at a pressure of 60psi is required. If a motor operating at 1800 rpm is chosen to drive the pump, which is 70% efficient, determine:

(a) The required horsepower rating of the motor.

(b) The required torque rating of the motor.

(c) The diameter of the impeller that should be used in the pump.

(d) What color the pump should be painted.

9. You want to pump water at 70°F from an open well, 200 ft deep, at a rate of 30 gpm through a 1 in. sch 40 pipe, using a centrifugal pump having an NPSH of 8 ft. What is the maximum distance above the water level in the well that the pump can be located without cavitating? (Vapor pressure of water at 60°F = 18.7 mmHg.)

10. Steam condensate at 1 atm and 95°C (Pv = 526 mmHg) is returned to a boiler from the condenser by a centrifugal boiler feed pump. The flow rate is 100 gpm through a 2.5 in. sch 40 pipe. If the equivalent length of the pipe between the condenser and the pump is 50 ft, and the pump has an NPSH of 6 ft, what is the maximum height above the condenser that the pump can be located?

11. Water at 160°F is to be pumped at a rate of 100gpm through a 2in. sch 80 steel pipe from one tank to another located 100 ft directly above the first. The pressure in the lower tank is 1 atm. If the pump to be used has a required NPSH of 6 ft of head, what is the maximum distance above the lower tank that the pump may be located?

12. A pump with a 1 in. diameter suction line is used to pump water from an open hot water well at a rate of 15 gpm. The water temperature is 90°C, with a vapor pressure of 526 mmHg and density of 60 lbm/ft3. If the pump NPSH is 4 ft, what is the maximum distance above the level of the water in the well that the pump can be located and still operate properly?

13. Hot water is to be pumped out of an underground geothermally heated aquifer located 500 ft below ground level. The temperature and pressure in the aquifer are 325°F and 150psig. The water is to be pumped out at a rate of 100 gpm through 2.5 in. pipe using a pump that has a required NPSH of 6 ft. The suction line to the pump contains four 90° elbows and one gate valve. How far below ground level must the pump be located in order to operate properly?

14. You must install a centrifugal pump to transfer a volatile liquid from a remote tank to a point in the plant 500 ft from the tank. To minimize the distance that the power line to the pump must be strung, it is desirable to locate the pump as close to the plant as possible. If the liquid has a vapor pressure of 20 psia, the pressure in the tank is 30 psia, the level in the tank is 30 ft above the pump inlet, and the required pump NPSH is 15 ft, what is the closest that the pump can be located to the plant without the possibility of cavitation? The line is 2 in. sch 40, the flow rate is 100 gpm and the fluid properties are p = 45 lbm/ft3 and p = 5cP.

15. It is necessary to pump water at 70°F (Pv = 0.35 psia) from a well that is 150 ft deep, at a flow rate of 25 gpm. You do not have a submersible pump, but you do have a centrifugal pump with the required capacity that cannot be submerged. If a 1 in. sch 40 pipe is used, and the NPSH of the pump is 15 ft, how close to the surface of the water must the pump be lowered for it to operate properly?

16. You must select a pump to transfer an organic liquid with a viscosity of 5cP and SG of 0.87 at a rate of 1000 gpm through a piping system that contains 1000 ft of 8 in. sch 40 pipe, four globe valves, 16 gate valves, and 43 standard 90° elbows. The discharge end of the piping system is 30 ft above the entrance, and the pressure at both ends is 10 psia.

(a) What pump head is required?

(b) What is the hydraulic horsepower to be delivered to the fluid?

(c) Which combination of pump size, motor speed, and impeller diameter from the pump charts in Appendix H would you choose for this application?

(d) For the pump selected, what size motor would you specify to drive it?

(e) If the vapor pressure of the liquid is 5psia, how far directly above the liquid level in the upstream tank could the pump be located without cavitating?

17. You need a pump that will develop at least 40psi at a flow rate of 300 gpm of water. What combination of pump size, motor speed, and impeller diameter from the pump characteristics in Appendix H would be the best for this application? State your reasons for the choice you make. What are the pump efficiency, motor horsepower and torque requirement, and NPSH for the pump you choose at these operating conditions?

18. A centrifugal pump takes water from a well at 120°F (—v — 87.8 mmHg) and delivers it at a rate of 50 gpm through a piping system to a storage tank. The pressure in the storage tank is 20 psig, and the water level is 40 ft above that in the well. The piping system contains 300 ft of 1.5 in. sch 40 pipe, 10 standard 90° elbows, six gate valves, and an orifice meter with a diameter of 1 in.

(a) What are the specifications required for the pump?

(b) Would any of the pumps represented by the characteristic curves in Appendix H be satisfactory for this application? If more than one of them would work, which would be the best? What would be the pump head, impeller diameter, efficiency, NPSH, and required horsepower for this pump at the operating point?

(c) If the pump you select is driven by an 1800 rpm motor, what impeller diameter should be used?

(d) What should be the minimum torque and horsepower rating of the motor, if the pump is 50% efficient?

(e) If the NPSH rating of the pump is 6 ft at the operating conditions, where should it be located in order to prevent cavitation?

(f) What is the reading of the orifice meter, in psi?

19. Water at 20°C is pumped at a rate of 300 gpm from an open well in which the water level is 100 ft below ground level into a storage tank that is 80 ft above ground. The piping system contains 700 ft of 32 in. sch 40 pipe, eight threaded elbows, two globe valves, and two gate valves. The vapor pressure of the water is 17.5 mmHg.

(a) What pump head and hydraulic horsepower are required?

(b) Would a pump whose characteristics are similar to those shown in Fig. 8-2 be suitable for this job? If so, what impeller diameter, motor speed, and motor horsepower should be used?

(c) What is the maximum distance above the surface of the water in the well at which the pump can be located and still operate properly?

20. An organic fluid is to be pumped at a rate of 300 gpm, from a distillation column reboiler to a storage tank. The liquid in the reboiler is 3 ft above ground level, the storage tank is 20 ft above ground, and the pump will be at ground level. The piping system contains 14 standard elbows, four gate valves, and 500 ft of 3 in. sch 40 pipe. The liquid has an SG of 0.85, a viscosity of 8 cP, and a vapor pressure of 600 mmHg. If the pump to be used has characteristics similar to those given in Appendix H, and the pressure in the reboiler is 5 psig, determine

(a) The motor speed to be used.

(b) The impeller diameter.

(c) The motor horsepower and required torque.

(d) Where the pump must be located to prevent cavitation.

21. A liquid with a viscosity of 5 cP, density of 45 lbm/ft3, and vapor pressure of 20 psia is transported from a storage tank in which the pressure is 30 psia to an open tank 500 ft downstream, at a rate of 100 gpm. The liquid level in the storage tank is 30 ft above the pump, and the pipeline is 2 in. sch 40 commercial steel. If the transfer pump has a required NPSH of 15 ft, how far downstream from the storage tank can the pump be located without danger of cavitation?

22. You must determine the specifications for a pump to transport water at 60°C from one tank to another at a rate of 200 gpm. The pressure in the upstream tank is 1 atm, and the water level in this tank is 2 ft above the level of the pump. The pressure in the downstream tank is 10 psig, and the water level in this tank is 32 ft above the pump. The pipeline contains 250 ft of 2 in. sch 40 pipe, with 10 standard 90° flanged elbows and six gate valves.

(a) Determine the pump head required for this job.

(b) Assuming your pump has the same characteristics as the one shown in Fig. 8-2, what size impeller should be used, and what power would be required to drive the pump with this impeller at the specified flow rate?

(c) If the water temperature is raised, the vapor pressure will increase accordingly. Determine the maximum water temperature that can be tolerated before the pump will start to cavitate, assuming that it is installed as close to the upstream tank as possible.

23. A piping system for transporting a liquid (p = 50 cP, p = 0.85 g/cm3) from vessel A to vessel B consists of 650 ft of 3 in. sch 40 commercial steel pipe containing four globe valves and 10 elbows. The pressure is atmospheric in A and 5 psig in B, and the liquid level in B is 10 ft higher than that in A. You want to transfer the liquid at a rate of 250 gpm at 80°F using a pump with the characteristics shown in Fig. 8-2. Determine

(a) The diameter of the impeller that you would use with this pump.

(b) The head developed by the pump and the power (in horsepower) required to pump the liquid.

(c) The power of the motor required to drive the pump

(d) The torque that the motor must develop.

(e) The NPSH of the pump at the operating conditions.

24. You must chose a centrifugal pump to pump a coal slurry. You have determined that the pump must deliver 200 gpm at a pressure of at least 35 psi. Given the pump characteristic curves in Appendix H, tell which pump you would specify (give pump size, speed, and impeller diameter) and why? What is the efficiency of this pump at its operating point, what horsepower motor would be required to drive the pump, and what is the required NPSH of the pump? The specific gravity of the slurry is 1.35.

25. You must specify a pump to take an organic stream from a distillation reboiler to a storage tank. The liquid has a viscosity of 5 cP, an SG of 0.78, and a vapor pressure of 150mmHg. The pressure in the storage tank is 35psig, and the inlet to the tank is located 75 ft above the reboiler, which is at a pressure of 25 psig. The pipeline in which the pump is to be located is 22 in. sch 40, 175 ft long, and there will be two flanged elbows and a globe valve in each of the pump suction and discharge lines. The pump must deliver a flow rate of 200 gpm. If the pump you use has the same characteristics as that illustrated in Fig. 8-2, determine

(a) The proper impeller diameter to use with this pump.

(b) The required head that the pump must deliver.

(c) The actual head that the pump will develop.

(d) The horsepower rating of the motor required to drive the pump.

(e) The maximum distance above the reboiler that the pump can be located without cavitating.

26. You have to select a pump to transfer benzene from the reboiler of a distillation column to a storage tank at a rate of 250 gpm. The reboiler pressure is 15 psig and the temperature is 60°C. The tank is 5 ft higher than the reboiler and is at a pressure of 25psig. The total length of piping is 140 ft of 2 in. sch 40 pipe. The discharge line from the pump containsthree gate valves and 10 elbows, and the suction line has two gate valves and six elbows. The vapor pressure of benzene at 60°C is 400 mmHg.

(a) Using the pump curves shown in Fig. 8-2, determine the impeller diameter to use in the pump, the head that the pump would develop, the power of the motor required to drive the pump, and the NPSH required for the pump.

(b) If the pump is on the same level as the reboiler, how far from the reboiler could it be located without cavitating?

27. A reboiler at the bottom of a distillation column contains an organic liquid at 1 atm and 320°F, at which its density is 0.7 g/cm3, its viscosity is 0.5 cP, and its vapor pressure is 800 mmHg. The liquid must be pumped to another column at a rate of 200 gpm and discharges at 1 atm at a point 30 ft higher than the reboiler. You must select the best pump from those represented by the curves in Appendix H and determine where the pump is to be installed. The suction line of the pump will include 20 ft of 21 in. sch 40 pipe, eight elbows, four gate valves, and a contraction from the reboiler. Using the curves in Appendix H, determine:

(a) The required pump head, and the best pump for this job.

(b) The best size of impeller to use in this pump, the motor speed, and the motor horsepower.

(c) The efficiency and NPSH required for the pump.

(d) How far above the reboiler the pump can be installed and still function properly.

28. A circulating pump takes hot water at 85°C from a storage tank, circulates it through a piping system at a rate of 150 gpm, and discharges it to the atmosphere. The tank is at atmospheric pressure, and the water level in the tank is 20 ft above the pump. The piping consists of 500 ft of 2 in. sch 40 pipe, with one globe valve upstream of the pump and three globe valves and eight threaded elbows downstream of the pump. If the pump has the characteristics shown in Fig. 8-2, determine

(a) The head that the pump must deliver, the best impeller diameter to use with the pump, the pump efficiency and NPSH at the operating point, and the motor horsepower required to drive the pump.

(b) How far the pump can be located from the tank without cavitating. Properties of water at 85°C: Viscosity 0.334 cP, density 0.970 g/cm3, vapor pressure 433.6 mmHg.

29. A slurry pump operating at 1 atm must be selected to transport a coal slurry from an open storage tank to a rotary drum filter, at a rate of 250 gpm. The slurry is 40% solids by volume and has an SG of 1.2. The level in the filter is 10 ft above that in the tank, and the line contains 400 ft of 3 in. sch 40 pipe, two gate valves, and six 90° elbows. A lab test shows that the slurry can be described as a Bingham plastic with v = 50 cP and r0 = 80dyn/cm2.

(a) What pump head is required?

(b) Using the pump curves in Appendix H, choose the pump that would be the best for this job. Specify the pump size, motor speed, impeller diameter, efficiency, and NPSH. Tell what criteria you used to make your decision.

(c) What horsepower motor would you need to drive the pump?

(d) Assuming the pump you choose has an NPSH of 6 ft at the operating conditions, what is the maximum elevation above the tank that the pump could be located, if the maximum temperature is 80°C? (Pv of water is 0.4736 bar at this temperature.)

30. A red mud slurry residue from a bauxite processing plant is to be pumped from the plant to a disposal pond, at a rate of 1000 gpm, through a 6 in. ID pipeline that is 2500 ft long. The pipeline is horizontal, and the inlet and discharge of the line are both at atmospheric pressure. The mud has properties of a Bingham plastic, with a yield stress of 250dyn/cm2, a limiting viscosity of 50 cP, and a density of 1.4 g/cm3. The vapor pressure of the slurry at the operating temperature is 50 mmHg. You have available several pumps with the characteristics given in Appendix H.

(a) Which pump, impeller diameter, motor speed and motor horsepower would you use for this application?

(b) How close to the disposal pond could the pump be located without cavitat-ing?

(c) It is likely that none of these pumps would be adequate to pump this slurry. Explain why, and explain what type of pump might be better.

31. A pipeline is installed to transport a red mud slurry from an open tank in an alumina plant to a disposal pond. The line is 5 in. sch 80 commercial steel, 12,000 ft long, and is designed to transport the slurry at a rate of 300 gpm. The slurry properties can be described by the Bingham plastic model, with a yield stress of 15dyn/cm2, a limiting viscosity of 20cP, and an SG of 1.3. You may neglect any fittings in this pipeline.

(a) What delivered pump head and hydraulic horsepower would be required to pump this mud?

(b) What would be the required pump head and horsepower to pump water at the same rate through the same pipeline?

(c) If 100 ppm of fresh Separan AP-30 polyacrylamide polymer were added to the water in case (b), above, what would the required pump head and horsepower be?

(d) If a pump with the same characteristics as those illustrated in Fig. 8-2 could be used to pump these fluids, what would be the proper size impeller and motor horsepower to use for each of cases (a), (b), and (c), above. Explain your choices.

32. An organic liquid is to be pumped at a rate of 300 gpm from a distillation column reboiler at 5 psig to a storage tank at atmospheric pressure. The liquid in the reboiler is 3 ft above ground level, the storage tank is 20 ft above ground, and the pump will be at ground level. The piping system contains 14 standard elbows, four gate valves, and 500 ft of 3 in. sch 40 pipe. The liquid has an SG of 0.85, a viscosity of 8 cP, and a vapor pressure of 600 mmHg. Select the best pump for this job from those for which the characteristics are given in Appendix H, and determine

(a) The motor speed

(b) The impeller diameter

(c) The motor horsepower and required torque

(d) Where the pump must be located to prevent cavitation.

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