Question

A pump draws water from a reservoir through a 150 mm diameter suction pipe and delivers it to a 75 mm diameter discharge pipe.

a. The end of the pipe is 2 m below the free surface of the reservoir.
b. The pressure gage on the discharge pipe (located 2 m above the reservoir surface) reads 170 kPa.
c. The average velocity in the discharge pipe is 3 m/s.
Assume no head loss in the suction or discharge pipe. Determine the power added to the fluid by the pump.

Answer 1

3.42 kW

Step-by-step explanation:

calculate the mass flow rate of the water = density * velocity * area

= 13.3 kg/s

where Area of pipe = π/4 * d^2 = π/4 * 0.075^2 m = 0.0044 m^2

given that : 1 Kg = 1 N s^2 / m, 1 Watt = 1 N m /s

calculate : power produced by discharge pipe

Discharge Pressure x Volume flow =

Pressure * Area * velocity

P * 0.0044 * 3 = 2253 N m /s

calculate: power due the mass of water

mass of water * 2 = 258 N m/s

where: mass of water = density * volume

Calculate power produced due the velocity of exiting water

= m * V2/2 = 59.4 N m/s

hence The power added to fluid = 2253 watts

power added to the fluid by pump = 2253 / 0.75 = 3.42 kW