A pump draws water through a 150 mm diameter pipe from a reservoir whose surface
ID: 1895044 • Letter: A
Question
A pump draws water through a 150 mm diameter pipe from a reservoir whose surface level is at datum level and discharges it through a 100 mm diameter pipe to another reservoir whose surface level is 72 m above datum level.The pump is situated 6 m below datum.The loss of head in the 150 mm suction pipe is three times the velocity head in the 150 mm pipe and the loss of head in the 100 mm delivery pipe is 20 times the velocity head in the 100 mm pipe.Calculate the power output of the pump and the pressure heads at the inlet and outlet of the pump when discharge isa)0.91 m3/min
B)2.73 m3/min
Explanation / Answer
The method of solution is to add up all the energy terms to get the theoretical power required then divide by 0.75, the efficiency, to get the electric power required. Express all terms in watts = N m/s.
The mass flow of water is density x velocity x area = 13.3 kg/s.
Pipe Area is /4 * diameter2 = 0.0044 m2
Kg =1 N s2 / m, Watt = 1 N m /s
The biggest term will be (Discharge Pressure x Volume flow) with volume being pipe area times velocity.
P * A * V = 2253 N m /s
Next will be lifting the mass of water (density x volume) up the 2 m from the reservoir to the pump.
m * g * h = 258 N m/s
A smaller term will be the due to the velocity of the exiting water.
m * V2/2 = 59.4 N m/s
Total = 2253 Watts
Electric input = 2253 /0.75 = 3423 W or reasonably rounded to 3.42 KW
There will also be a friction loss in the 150 mm suction pipe, but with a length of 4 m and a diameter twice the inlet the velocity will be so slow that this term will be much smaller than the above.
Keep track of units to be sure your equations are dimensionally consistent as you combine terms.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.