Practice Problems: Pumps And Turbines

Question 1:
A mechanical engineer is designing a centrifugal pump system for a municipal water treatment plant. The pump must deliver 2500 gpm of water against a total head of 180 ft. The pump operates at 1750 rpm and has an efficiency of 78%. The motor driving the pump has an efficiency of 92%. What is the required motor power input?
(a) 115 hp
(b) 125 hp
(c) 135 hp
(d) 145 hp

Question 2:
A power plant engineer is evaluating a Pelton wheel turbine installation. The turbine operates under a net head of 850 m with a water flow rate of 4.5 m³/s. The turbine efficiency is 89% and the generator efficiency is 96%. The nozzle coefficient of velocity is 0.98. What is the electrical power output delivered to the grid?
(a) 33.5 MW
(b) 35.8 MW
(c) 37.2 MW
(d) 39.1 MW

Question 3:
A facilities engineer operates a pump system with a specific speed of 2200 (US units) at 1450 rpm, delivering 1200 gpm against a head of 95 ft. The engineer plans to increase the pump speed to 1750 rpm. Using pump affinity laws, what will be the new discharge?
(a) 1380 gpm
(b) 1448 gpm
(c) 1520 gpm
(d) 1595 gpm

Question 4:
A process engineer designs a pump installation to lift water from a sump to an elevated storage tank. The vertical lift is 65 ft, and the total pipe length is 280 ft with an 8-inch diameter schedule 40 pipe. The friction factor is 0.022, and the flow rate is 1000 gpm. Minor losses total 12 ft. What is the total dynamic head?
(a) 88 ft
(b) 95 ft
(c) 102 ft
(d) 109 ft

Question 5:
A hydroelectric plant engineer operates a Francis turbine with a runner diameter of 3.2 m, rotating at 200 rpm under a head of 75 m. The turbine produces 18 MW with a flow rate of 28 m³/s. What is the turbine efficiency?
(a) 87.5%
(b) 89.2%
(c) 91.4%
(d) 93.8%

Question 6:
A consulting engineer evaluates a pumping system where two identical centrifugal pumps are connected in parallel. Each pump delivers 800 gpm at 120 ft head when operating alone. The system curve is H = 40 + 0.08Q² (H in ft, Q in gpm). What is the approximate total flow when both pumps operate together?
(a) 1245 gpm
(b) 1380 gpm
(c) 1520 gpm
(d) 1600 gpm

Question 7:
A marine engineer selects a pump with a required NPSH of 18 ft. The pump draws water from a reservoir where the surface is 8 ft below the pump centerline. Atmospheric pressure is 14.2 psia, water temperature is 100°F (vapor pressure 0.95 psia), and friction losses in the suction line are 3.5 ft. What is the available NPSH?
(a) 17.2 ft
(b) 18.8 ft
(c) 20.5 ft
(d) 22.3 ft

Question 8:
A project engineer specifies a multistage centrifugal pump with 5 identical stages. Each stage develops 45 ft of head at a flow rate of 600 gpm. The overall pump efficiency is 72%. What is the brake horsepower required?
(a) 42.5 hp
(b) 47.8 hp
(c) 52.3 hp
(d) 56.9 hp

Question 9:
A power generation engineer analyzes a Kaplan turbine operating at 150 rpm with a flow rate of 125 m³/s under a net head of 22 m. The turbine efficiency is 92% and it drives a generator with 97% efficiency. What is the specific speed of the turbine in metric units?
(a) 625
(b) 720
(c) 815
(d) 890

Question 10:
A municipal engineer operates a booster pump station with a pump curve described by H = 250 - 0.0015Q² (H in ft, Q in gpm). The system curve is H = 80 + 0.0008Q². At what flow rate does the pump operate?
(a) 725 gpm
(b) 865 gpm
(c) 975 gpm
(d) 1085 gpm

Question 11:
A chemical plant engineer designs a pumping system to transport fluid with specific gravity of 1.15 and dynamic viscosity of 25 cP at 350 gpm through a 4-inch schedule 40 pipe at 1750 rpm. The Reynolds number indicates turbulent flow. What correction factor should be applied to the water performance curve for head?
(a) 0.82
(b) 0.88
(c) 0.94
(d) 1.00

Question 12:
A hydropower engineer evaluates a Pelton wheel with a jet diameter of 180 mm, nozzle velocity coefficient of 0.97, operating under a gross head of 625 m. The penstock friction losses are 35 m. What is the jet velocity?
(a) 102 m/s
(b) 105 m/s
(c) 108 m/s
(d) 112 m/s

Question 13:
A plant engineer operates a centrifugal pump at 1170 rpm delivering 1500 gpm at 85 ft head with 75% efficiency. Due to process changes, the pump speed is increased to 1750 rpm. What is the new brake horsepower required?
(a) 82 hp
(b) 105 hp
(c) 128 hp
(d) 145 hp

Question 14:
A facilities engineer evaluates cavitation potential in a pump installation. The pump is located 12 ft above the water source, with a suction line friction loss of 4.2 ft. Water temperature is 85°F (vapor pressure 0.60 psia), atmospheric pressure is 14.5 psia, and required NPSH is 15 ft. Is cavitation likely to occur?
(a) Yes, NPSH_A = 12.8 ft
(b) Yes, NPSH_A = 14.2 ft
(c) No, NPSH_A = 17.5 ft
(d) No, NPSH_A = 19.8 ft

Question 15:
A water resource engineer designs a Francis turbine installation with a runner diameter of 2.8 m rotating at 250 rpm under a net head of 58 m. The flow rate is 35 m³/s and the turbine develops 18 MW. What is the specific speed in metric units?
(a) 145
(b) 185
(c) 225
(d) 265

Question 16:
A consulting engineer sizes a pump for a cooling water system. The system requires 3200 gpm against a total head of 145 ft. Three pumps are available: Pump A (3500 gpm at 140 ft, 82% eff), Pump B (3000 gpm at 155 ft, 80% eff), and Pump C (3400 gpm at 148 ft, 84% eff). Which pump is most energy efficient for this duty?
(a) Pump A: 154 hp
(b) Pump B: 168 hp
(c) Pump C: 147 hp
(d) All equally efficient

Question 17:
A power plant engineer operates an impulse turbine with bucket velocity of 55 m/s and jet velocity of 115 m/s. The deflection angle of the buckets is 165°. The velocity coefficient for the buckets is 0.88. What is the theoretical blade efficiency?
(a) 88.2%
(b) 90.5%
(c) 92.8%
(d) 94.3%

Question 18:
A municipal engineer operates two identical pumps in series, each capable of delivering 950 gpm at 75 ft head when operating alone. The system resistance curve is H = 25 + 0.00012Q² (H in ft, Q in gpm). What is the operating flow rate with both pumps running?
(a) 875 gpm
(b) 950 gpm
(c) 1025 gpm
(d) 1100 gpm

Question 19:
A process engineer evaluates a pump with an impeller diameter of 12 inches operating at 1750 rpm, delivering 1200 gpm at 120 ft head. The impeller is trimmed to 10.5 inches. Using affinity laws, what is the new head developed?
(a) 87 ft
(b) 92 ft
(c) 97 ft
(d) 102 ft

Question 20:
A hydroelectric engineer designs a reaction turbine with a runner diameter of 4.2 m, operating at 180 rpm under a head of 95 m with a flow rate of 58 m³/s. The turbine produces 48 MW with an efficiency of 91%. What is the peripheral velocity of the runner?
(a) 35.8 m/s
(b) 39.6 m/s
(c) 42.3 m/s
(d) 45.1 m/s