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• Ronard Pa–a

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Problem Set 2 in Fluid Machinery 1. A model centrifugal pump has a scale ratio of 1:15. The model when tested at 3600 rpm, delivered 0.10 cu.m/sec of water at a head of 40 m with an efficiency of 80 percent. Assuming the prototype has an efficiency of 88 percent, what will be its speed, capacity, and power requirement at a head of 50 m? N = 268 rpm, Q = 25.1 cu.m/sec, P = 14000 kW 2. A 19.5 in. diameter centrifugal pump impeller discharges 20 cfs at a head of 100 ft when running at 1200 rpm. (a) If its efficiency is 85 percent, what is the brake horsepower, i.e., what is the horsepower input a shaft of the pump? (b) If the same pump were run at 1500 rpm, what would be h, Q, and the brake horsepower for homologous conditions? (a) 267 hp, (b) 156.3 ft, 25 cfs, 521 bhp 3. An axial flow pump delivers 300 L/s at a head of 6.0 m when rotating at 1800 rpm. (a) If its efficiency is 80 percent, how many kilowatts of power must the shaft deliver to the pump? (b) If this same pump were operated at 1500 rpm, what would be h, Q, and the power delivered by the shaft for homologous conditions? (a) 22.1 kW, (b) 360 L/s, 8.64 m, 38.1 kW 4. A centrifugal pump with an 18-in diameter impeller is rated at 25 cfs under a head of 100 ft when running at 1200 rpm. (a) If its efficiency is 85%, what is the brake horsepower? (b) If the same pump is run at 1800 rpm, what would be its rating in terms of h, Q, and the brake horsepower? Assume the efficiency does not change with the change in speed. (a) 333.7 hp, (b) 37.5 cfs, 225 ft, 1126 hp 5. A centrifugal pump with a 300 mm diameter impeller is rated at 40 L/s against a head of 25 m when rotating at 1750 rpm. What would be the rating of a pump of identical geometric shape with a 200 mm diameter impeller? Assume pump efficiencies and pump speeds are identical. 11. 85 L/s, 11.11 m 6. At its optimum point of operation a given centrifugal pump delivers 3.2 cu.m/sec of water against a head of 25 m when rotating at 1450 rpm. (a) If the efficiency is 82%, what is the brake power of the drive shaft? (b) If a homologous pump with an impeller diameter one half as large is rotating at 1200 rpm, what would be the discharge, head, and shaft power at its point of optimum efficiency? Assume both pumps operate at the same efficiency. 0.33 cu.m/s, 4.28 m, 16.9 kW 7. At its BEP, a given pump develops 30 ft of head when operating at 720 rpm. The flow rate is 4.2 cfs. Find the head and flow rate for a homologous pump operating at 600 rpm if its diameter is 90% that of the given pump. 2.55 cfs, 16.88 ft 8. At its best efficiency point (η = 0.82), a mixed-flow pump, with D = 500 mm, delivers Q = 0.75 cu.m/sec of water at H = 39 m when operating at N = 1170 rpm. Calculate the specific speed of this pump. Estimate the required power input. 1.23, 350 kW 9. A pump is to discharge 0.8 cu.m/sec at a head of 40 m when running at 300 rpm. What type of pump will be required? Radial-flow centrifugal pump 10. All dimensions of a model pump are one-third as large as the corresponding dimensions of a prototype pump. The model pump operating at 1800 rpm delivers 3.0 cfs at a head of 35 ft. (a) Find the speed and capacity of the prototype if it is to develop a head of 35 ft. (b) Find the specific speed of the model pump and the prototype. They should be the same. Assume the efficiency of the model and prototype are the same. (a) 600 rpm, 27 cfs, (b) 4590 11. All dimensions of a model pump are one-third as large as the corresponding dimensions of a prototype pump. The model pump operating at 1800 rpm delivers 3.0 cfs at a head of 35 ft. (a) Find the speed and head of the prototype when it delivers 3.0 cfs. (b) Find the specific speed of the model pump and the prototype. They should be the same. Assume the efficiency of the model and prototype are the same. (a) 66.7 rpm, 0.432 ft, (b) 4590 12. A pump is to deliver 2.0 cu.m/sec against a head of 160 m when operating at 300 rpm. What type of pump will be required? Radial-flow pump

** Solve problems from Fluid Mechanics by F.M. White page 755 and Fluid Mechanics Fundamentals and Applications by Y.A. Cengel and J.M. Cimbala page 804.