With a constant diameter impeller of a centrifugal pump

ANS:B - head varies as the square of speed.

With a constant diameter impeller of a centrifugal pump:

• Capacity (Q) varies directly as the square of speed: This statement is generally true. The capacity or flow rate (Q) of a centrifugal pump is directly proportional to the impeller speed (N) squared, assuming the pump operates under similar conditions and the impeller diameter remains constant. Mathematically, Q∝N2Q \propto N^2Q∝N2.
• Head (H) varies as the square of speed: This statement is not accurate. The head developed by a centrifugal pump is primarily dependent on the impeller speed (N) and is proportional to the square of the speed (N²). This relationship arises because the kinetic energy imparted to the fluid by the impeller varies with the square of its rotational speed.
• Horsepower input varies as the square of speed: This statement is also generally true. The power input (P) required to drive a centrifugal pump increases with the cube of the impeller speed (N³), assuming constant efficiency. Therefore, if efficiency is constant, power input varies directly with speed squared, not speed itself.

Therefore, among the options provided, the correct statement regarding a centrifugal pump with a constant diameter impeller is: Capacity varies directly as the square of speed. This means that the flow rate or capacity of the pump increases proportionally with the square of the impeller speed when the diameter of the impeller remains constant.