Question

Power required to drive a centrifugal pump is directly proportional to the ________of its impeller.
A.Cube of diameter
B.Fourth power of diameter
C.Square of diameter
D.Diameter

Answer 1

To answer this question, use the Affinity laws. Affinity laws are for pumps and fans which are used in hydraulics or hydronic to give the relationship between variables involved in the pump or fan performance such as volumetric flow rate, shaft speed and power. These laws can be applied to both centrifugal and axial flows. There are two sets of affinity laws. Use the affinity law for specific centrifugal pumps to find the relationship between power and diameter of the impeller.

Complete answer:
According to the Affinity laws, the relationship between power and diameter of impeller is given by,
$P \propto {D}^{3}$
Where, P is the shaft power in Watt or horsepower
D is the diameter of the impeller in mm or inches
Hence, the power required to drive a centrifugal pump is directly proportional to the cube of diameter of its impeller.

So, the correct answer is option A i.e. cube of diameter.

Note:
The power required to drive a centrifugal pump is directly proportional to the cube of diameter of its impeller, only when shaft speed is held constant and for small variations in impeller diameter. Whereas the power is directly proportional to the fifth power of the diameter of the impeller when we consider only the shaft speed to be constant. If we increase the speed of the pump by 10% then the power of the pump increases by 33%. Students must remember that the affinity laws for fans are not identical with those of pumps.