1. Underground water is to be pumped by a 70% efficient 3-kW submerged pump to a

ID: 2995368 • Letter: 1

Question

1. Underground water is to be pumped by a 70% efficient 3-kW submerged pump to a pool

whose free surface is 30 m above the underground water level. The diameter of the pipe is 5

cm on the intake side and 7 cm on the supply (pool) side. Determine a) the maximum

volumetric flow rate of the water and b) the pressure difference across the pump. Assume

the elevation difference between the pump inlet and the pump outlet to be negligible.

2. You are in charge of designing an electrical power generating system. You know that your

turbine/generator system has an efficiency of 80% and you need 7 MW of electrical power

from you system. Water that you can harness has a natural drop of 30 m and the velocity at

the exit of the dam has to be 2 m/s. Your boss, a U of A alum, recommends an exit duct with

a diameter of 4 m, find the head loss and determine if this is possible.

P = m.Q.h

here P = power = 0.7 x 3 = 2.1 Kw

h = 30 m

m = mass flow rate

so, 2.1 x 10^3 = m x 9.81 x 30

a) so, m = 7.13 kg/s

b) velocity at intake = m/(? x A)

where ? = density = 1000 kg/m^3 and A = area = pi/4 x d^2

so, v1 = 7.13 / (1000 x pi/4 x 0.07^2) = 1.85 m/s

and V2 = 7.13/ (1000 x pi/4 x 0.05^2) = 3.64 m/s

By bernouli:

P1/? + V1^2/2 = P2/? + V2^2/2 + z.g

so, P1- p2 = ? x ( V2^2 - V1^2)/2 + ? x z x g

= 1000 x [ (3.64^2 - 1.85^2)/2 + 30 x 9.81]

= 299.2 Kpa

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