Question

Power required to drive a centrifugal pump is directly proportional to …………………….. of its impeller.
(a) Cube of a diameter
(b) Fourth power of diameter
(c) Square of diameter
(d) Diameter

Answer 1

- Hint – In this question use the concept that the power required to drive a centrifugal pump is directly proportional to the impeller diameter, but we have to figure out which power of diameter makes the actual significance while calculating the power of the centrifugal pump.

Complete step-by-step solution -

Power consumed by a Centrifugal pump is dependent on the quantity of water pumped and the rate of pumping.
So the quantity of water pumped is dependent on the diameter and how big the diameter greater will be the water pumped.
And the power (P) required to drive a centrifugal pump is directly proportional to fourth power of the diameter (d) of its impeller.
$\Rightarrow p{\text{ }}\alpha {\text{ }}{d^4}$.................. (1)
Let’s take an example: consider two pumps, pump 1 and pump 2 with similar make, only difference being in their impeller diameter.
Consider pump 1 diameter = ${d_1}$ and pump 2 diameter = ${d_2}$
Let’s consider that ${d_2} > {d_1}$
So according to equation (1) the power required by the second pump is greater than power required by the first pump as power is directly proportional to the fourth power the diameter.
$\Rightarrow \dfrac{{{p_2}}}{{{p_1}}} = {\left( {\dfrac{{{d_2}}}{{{d_1}}}} \right)^4}$
$\Rightarrow {p_2} = {p_1}{\left( {\dfrac{{{d_2}}}{{{d_1}}}} \right)^4}$
So this is the required answer.
Hence option (B) is correct.

Note – The work performed by the pump is equal to the weight of liquid pumped in unit time multiplied by total head in meters. However the pump capacity in ${m^3}/hr$ and liquid specific gravity are used rather than the weight of liquid pumped for work done by the pump. In a centrifugal pump the fluid enters the rapidly rotating impeller along its axis and is cast out by centrifugal force along its circumference through the impeller’s vane tips.