Question

1. A centrifugal pump delivers 50 Kg of water per second. The inlet and outlet pressures are 1 bar and 4.2 bar respectively. The suction is 2.2 m below the centre of the pump and delivery is 8.5m above the centre of the pump. The Suction and delivery pipe diameter are 20 cm and 10 cm respectively. Determine the capacity of the electric motor to run the pump.

Answer 1

amount of water pumped= 50 kg/s
inlet pressure= P1= 1 bar or 1 x 10⁵
outlet pressure= P2= 4.2 bar = 4.2 x 10⁵
suction under the pump= 2.2m
suction above the pump= 8.5 m
diameter of upper suction= D1= 0.2 m
diameter of lower suction = D2 = 0.1 m

Capacity = ?

energy flow= m (u1 + p1v1+ C1²/2 + Z1g) + Q = m (u2 + p2v2 + C2²/2 + Z2g) + W

Datum at suction 1= Z1= 0; Z2= 8.5 +2.2 = 10.7 m
u2 - u1 = 0
Q= 0

new equation will be 
W= m [(p1v1- p2v2) + (Z1 - Z2) g- (C1² - C2²/2) ]

As water can not be compressed so, 
v2 = v1 = v = 1/p = 1/1000

mass flow in the inlet 

m= λ/4 x d1² x C1 x p = λ/4 x d2² x C2 x p
50 = λ/4 x 0.2² x C1 x 1000
C1= 50 x 4/ λ x 0.2² x 1000
= 1.59 m/s
C2= 6.37 m/s

substitute the value in the start equation the answer will be
W= 50 [-320-104.96 - 19.02]
= 22199 J/s
or 22.2 kW

Answer 2

Explanation:

centrifugal pump delivers 50 Kg of water per second. The inlet and outlet pressures are 1 bar and 4.2 bar respectively. The suction is 2.2 m below the centre of the pump and delivery is 8.5m above the centre of the pump. The Suction and delivery pipe diameter are 20 cm and 10 cm respectively. Determine the capacity of the electric motor to run the pump.