If two pumps from the family are operated at the same value

If two pumps from the family are operated at the same value of flow coefficient where the subscripts I and 2 refer to any two pumps from the family of geometrically similar pumps. When the shaft horsepower supplied to a certain centrifugal pump is 25 hp, the pump discharges 700 gpm of water while operating at 1800 rpm with a head rise of 90 ft. If the pump speed is reduced to 1200 rpm, determine the new head rise, h_a new shaftpower, W_shafi

Solution

>> As given that,

W1 =Shaft Horsepower = 25 hp

Q1 = Flow rate = 700 gpm

N1 = Speed of pump = 100 rpm

H1 = Head Rise = 90 ft

N2 = 1200 rpm

>> Using Equality of head coefficients,

gh/(w²D²)₁ = gh/(w²D²)₂

As, D1 = D2

and, w = 2*pi*N/60

So, solving, h2 = 40 ft

>> Now using Equality of Power Coefficient,

W/(p*w³D⁵)₁ = W/(p*w³D⁵)₂

Solving, W2 = 7.41 hp ......ANSWER...