Practice Problems on Pumps. Answer(s): Q 2 = 1850 gpm H 2 = 41.7 ft W = 24.1 hp. C. Wassgren, Purdue University Page 1 of 16 Last Updated: 2010 Oct 29

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1 _02 A centrifugal with a 12 in. diameter impeller requires a power input of 60 hp when the flowrate is 3200 gpm against a 60 ft head. The impeller is changed to one with a 10 in. diameter. Determine the expected flowrate, head, and input power if the speed remains the same. Q 2 = 1850 gpm H 2 = 41.7 ft W = 24.1 hp 2 C. Wassgren, Purdue University Page 1 of 16 Last Updated: 2010 Oct 29

2 _05 Data measured during tests of a centrifugal at 3500 rpm are given in the table below: Parameter Inlet Section Outlet Section gage pressure, p [kpa] elevation above datum, z [m] avg speed of flow, V [m/s] The working fluid is water. The flow rate is 11.5 m 3 /hr and the torque applied to the shaft is 3.68 N m. Evaluate the total heads at the inlet and outlet, the hydraulic power input to the fluid, and the efficiency. If the electric motor efficiency is 85%, calculate the electric power requirement. H inlet = 21.6 m H outlet = 55.7 m W fluid = 1.07 kw = 79.4% W required = 1.59 kw for motor C. Wassgren, Purdue University Page 2 of 16 Last Updated: 2010 Oct 29

3 _06 A small centrifugal, when tested at 2875 rpm with water, delivered a flowrate of 252 gpm and a head of 138 ft at its best efficiency point (efficiency is 76%). Determine the specific speed of the at this test condition. Sketch the impeller shape you expect. Compute the required power input to the. N sd = 1130 rpm gpm 1/2 /ft 3/4 N s = W shaft = 11.6 hp C. Wassgren, Purdue University Page 3 of 16 Last Updated: 2010 Oct 29

4 _07 Water is to be ed from one large open tank to a second large open tank. The pipe diameter throughout is 6 in. and the total length of the pipe between the pipe entrance and exit is 200 ft. Minor loss coefficients for the entrance, exit, and the elbow are shown on the figure and the friction factor can be assumed constant and equal to A certain centrifugal having the performance characteristics shown is suggested as a good for this flow system. a. With this, what would be the flow rate between the tanks? b. Do you think this would be a good choice? 10 ft K elbow = 1.5 pipe diameter = 6 in total pipe length = 200 ft K exit = 1.0 K entrance = 0.5 Q 1600 gpm The operating efficiency is close to the optimal efficiency of 86% so this is a good to use. C. Wassgren, Purdue University Page 4 of 16 Last Updated: 2010 Oct 29

5 _08 Data measured during tests of a centrifugal at 3500 rpm are given in the table below: Parameter Inlet Section Outlet Section gage pressure, p [kpa] elevation above datum, z [m] avg speed of flow, V [m/s] The flow rate is 11.5 m 3 /hr and the torque applied to the shaft is 3.68 N m. Evaluate the total dynamic heads at the inlet and outlet, the hydraulic power input to the fluid, and the efficiency. Specify the electric motor size needed to drive the. If the electric motor efficiency is 85%, calculate the electric power requirement. H inlet = 10.2 m H outlet = 45.4 m W 1100 W fluid = 80% W 1.8 hp W motor 2.1 hp C. Wassgren, Purdue University Page 5 of 16 Last Updated: 2010 Oct 29

6 _10 The pipe system used for a yard sprinkler system is shown below. two 90 regular threaded elbows sudden contraction discharge to the atmosphere 1 m 1 m 1 m pond 5 m gate valve ( 1 / 2 closed) 10 m Upstream of the contraction: 2.5 cm inner diam. galvanized iron pipe Downstream of the contraction: 1.9 cm inner diam. galvanized iron pipe Properties of water at given conditions: = 1000 kg/m 3, = 1*10-6 m 2 /s, vapor pressure = 2.34 kpa (abs) The performance specifications are given below H head, NPSH [m] efficiency 5 0 NPSHR flow rate [L/s] Curve fits to the data in the plot (where [Q] = L/s): H [m] = ( m s 2 /L 2 ) Q 2 ( m s/l) Q m = ( s 2 /L 2 ) Q 2 + ( s/l) Q NPSHR [m] = (0.3 m s 2 /L 2 ) Q m Determine: a. Determine the system head curve (i.e. the head the must supply in order to have a given flow rate). b. Determine the operating point for the given conditions. c. Is this a good to use for the given conditions? Justify your answer. d. Will this cavitate for the given conditions? not available at this time C. Wassgren, Purdue University Page 6 of 16 Last Updated: 2010 Oct 29

7 _11 Consider the pipe/ system shown below. water 10 m well-rounded inlet cast iron pipe diameter = 0.10 m water density = 1000 kg/m 3 water kinematic viscosity = 1.0*10-6 m 2 /s 50 m 50 m head, H [m] E E E E E-02 flow rate, Q [m 3 /s] The performance head curve is approximated as: H = (3.23*10 1 m) + (1.65*10 2 s/m 2 )Q - (4.82*10 3 s 2 /m 5 )Q 2 where [H] = m and [Q] = m 3 /s. a. Determine the system head curve for the pipe system. b. Determine the operating point for the system. c. How will the flow rate within the pipe change over time if the pipe carries hard water and lime deposits form on the interior pipe walls? Explain your answer. You should assume that the deposits do not significantly affect the pipe diameter. d. If we wanted to add a valve to control the flow rate in the pipe, would it be better to put the valve upstream or downstream of the? Explain your answer. H S = -10 m + (2.07*10 4 s 2 /m 5 )Q 2 Q = 4.41*10-2 m 3 /s flow rate will decrease over time due to increased roughness put valve downstream of so that it won t affect NPSHA C. Wassgren, Purdue University Page 7 of 16 Last Updated: 2010 Oct 29

8 _12 Consider the pipe/ system shown in the figure below. h = 0.5 m H = 2 m 90 rounded pipe bend D = 0.2 m (equivalent length of 30 pipe diameters) L 1 = 10 m L 2 = 20 m P The pipe is made of concrete L 1 L 2 with a roughness of 3 mm. h D H water with density of 1000 kg/m 3, kinematic viscosity of 1.0*10-6 m 2 /s, and vapor pressure of 2.34 kpa head, H [m] E E E E E-02 flow rate, Q [m 3 /s] The performance head curve is approximated as: H = (3.23*10 1 m) + (1.65*10 2 s/m 2 )Q - (4.82*10 3 s 2 /m 5 )Q 2 where [H] = m and [Q] = m 3 /s. a. Determine the system head curve for the pipe system. b. Determine the operating point for the system. c. How will the flow rate within the pipe change over time if the pipe carries hard water and lime deposits form on the interior pipe walls? Explain your answer. You should assume that the deposits do not significantly affect the pipe diameter. d. Calculate the net positive suction head available at the inlet. e. If we wanted to add a valve to control the flow rate in the pipe, would it be better to put the valve upstream or downstream of the? Explain your answer. H S = 2 m + (5.01*10 2 s 2 /m 5 )Q 2 Q = 9.26*10-2 m 3 /s flow rate will decrease due to increased roughness NPSHA = 6.93 m move the valve downstream of the to avoid decreasing NPSHA C. Wassgren, Purdue University Page 8 of 16 Last Updated: 2010 Oct 29

9 _13 Consider the pipe system shown in the figure below. The fluid to be ed is water with a density of 1.0E3 kg/m 3, a kinematic viscosity of 1.0E-6 m 2 /s, and a vapor pressure of 2.3E3 Pa. 7.0 m 1.0 m sharp-edged inlet 90 threaded elbow all pipes are comprised of 0.20 m inner diameter commercial steel pipe 10. m 10. m The used in this system has the performance plot shown below. head [m] % 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% efficiency flow rate [m 3 /s] Curve fits to the performance data are given below: H [m] = (-3.25E1 s 2 /m 5 ) Q 2 + (1.23E0 s/m 2 ) Q + (2.78E1 m) P = (-3.74E0 s 2 /m 6 ) Q 2 + (3.60E0 s/m 3 ) Q a. Determine the operating volumetric flow rate of the system. b. Is the given a good choice for this system? Explain your answer. c. Determine the NPSHA to the for the flow rate determined in part (a). d. Give one specific modification to the pipe system that could be employed to decrease the likelihood that cavitation will occur in the. 3 Q 2.85E-1 m /s ; this is not a good for this system NPSHA = 6.01E0 m; decrease the elevation, decrease pipe length, use a rounded inlet C. Wassgren, Purdue University Page 9 of 16 Last Updated: 2010 Oct 29

10 _14 Consider the pipe/ system shown below in which water (with a density of 1.0E3 kg/m 3 and dynamic viscosity of 1.3E-3 Pa s) is ed from tank A to tank B. p B = 200 kpa (gage) 15 cm diameter pipe with a total length of 40 m and roughness of 0.9 mm 90 regular threaded elbow gravity 10. m 8.0 m B flow gate valve ( 1 / 2 open) 90 regular threaded elbow p A = 0 (gage) A 0.5 m re-entrant inlet 5.0 m The to be used in the system has the following performance curve. head [m] 7.0E E E E E E E E+00 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0.0E E E E-01 flow rate [m 3 /s] efficiency Curve fits to the performance data are given below: H [m] = (-1.5E3 s 2 /m 5 ) Q 2 + (2.8E1 s/m 2 ) Q + (6.3E1 m) P = (-5.6E1 s 2 /m 6 ) Q 2 + (1.2E1 s/m 3 ) Q + (2.1E-1) a. Determine the operating point for the system. b. Is the given efficient for this application? Explain your answer. c. Do you anticipate that cavitation in the will be an issue? Explain your answer. 3 Q 1.0E-1 m /s ; this is an efficient for this application; cavitation in the will most likely not be an issue C. Wassgren, Purdue University Page 10 of 16 Last Updated: 2010 Oct 29

11 _15 Data from tests of a Peerless end suction Type 1440 operated at 1750 rpm with a 14.0 in. diameter impeller are: flowrate [gpm] total head [ft] power input [hp] Plot the performance curves for this ; include a curve of efficiency versus volume flow rate. Locate the best efficiency point and specify the rating at this point. Q BEP = 820 gpm = 83% H BEP = 185 ft C. Wassgren, Purdue University Page 11 of 16 Last Updated: 2010 Oct 29

12 _16 Typical performance curves for a centrifugal, tested with three different impeller diameters in a single casing, are shown in the figure below. Specify the flow rate and head produced by the at its best efficiency point with a 12 in. diameter impeller. Scale these data to predict the performance of this when tested with 11 in. and 13 in. impellers. Comment on the accuracy of the scaling procedure. Q 12 in.,bep = 2200 gpm H 12 in.,bep = 130 ft Using D 2 = 11 in. and D 1 = 12 in., Q 1 = 2200 gpm, Q 11 in. = 1690 gpm. Using D 2 = 13 in. and D 1 = 12 in., Q 1 = 2200 gpm, Q 13 in. = 2800 gpm. From the performance diagram, Q 11 in gpm. From the performance diagram, Q 13 in gpm. Using D 2 = 11 in. and D 1 = 12 in., H 1 = 130 ft, H 11 in. = 109 ft. Using D 2 = 13 in. and D 1 = 12 in., H 1 = 130 ft, H 13 in. = 153 ft. From the performance diagram, H 11 in. 110 ft. From the performance diagram, H 13 in. 150 ft. C. Wassgren, Purdue University Page 12 of 16 Last Updated: 2010 Oct 29

13 _17 A Peerless Model 16A 18B is proposed as the supply unit for the Purdue Engineering Mall fountain. The following requirements have been provided by the architectural firm: The outlet is to be located 3 feet below ground level. The water flow is to reach a peak height of 30 feet above ground level. The discharge from the is 6 inches in diameter. The characteristics are given in the following plot. a. What head must be supplied by the? Report your answer in ft. b. What flow rate must be supplied by the? Report your answer in gal/min (gpm). c. What impeller diameter should be used? (either 15.00, 16.00, 17.00, or inch diameter) d. What is the efficiency? Report your answer in terms of a percentage. e. What power is required to drive the? Report your answer in horsepower (hp). f. What range of NPSH is acceptable at the inlet? Report your answer in ft. H S = 33 ft Q = 9.05 ft 3 /s = 4060 gpm inch ~80% W 42.4 hp input into > ~9 ft C. Wassgren, Purdue University Page 13 of 16 Last Updated: 2010 Oct 29

14 _18 A station is used to fill a tank on a hill using water from a lake. The flow rate is 10.5 L/s and atmospheric pressure is 101 kpa (abs). The is located 4 m above the lake, and the tank surface level is 115 m above the. The suction and discharge lines are 10.2 cm diameter commercial steel pipe. The equivalent length of the inlet line between the lake and the is 100 m. The total equivalent length between the lake and the tank is 2300 m, including all fittings, bends, screens, and valves. The overall efficiency of the and motor set is 70%. lake 4 m 115 m tank water density = 1000 kg/m 3 water dynamic viscosity = 1*10-3 Pa.s water vapor pressure = 1820 Pa (abs) What is the net positive suction head available for this? NPSHA = 4.4 m C. Wassgren, Purdue University Page 14 of 16 Last Updated: 2010 Oct 29

15 _19 Brine, with a specific gravity of 1.2, passes through an 85% efficient at a flow rate of 125 L/s. The centerlines of the s 300 mm diameter inlet and 200 mm diameter outlet are at the same elevation. The inlet suction gage pressure is 150 mm of mercury (specific gravity of 13.6) below atmospheric pressure. The discharge pressure is measured 1.2 m above the centerline of the s outlet and indicates 138 kpa (gage). Neglecting losses in the pipes, what is the input power to the? inlet diameter = 300 mm inlet pressure = -150 mmhg (gage) 1.2 m outlet pressure = 138 kpa (gage) outlet diameter = 200 mm W into 26.4 kw C. Wassgren, Purdue University Page 15 of 16 Last Updated: 2010 Oct 29

16 C. Wassgren, Purdue University Page 16 of 16 Last Updated: 2010 Oct 29

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