ANS:C - as cube of

The power requirement of fans, which have a constant wheel diameter, varies as the cube of fan speed.

Explanation:

1. Power Requirement of Fans:
   • The power PPP required by a fan to move air is influenced by the fan's speed NNN.
   • Generally, for fans with a constant wheel diameter (impeller size), the power requirement PPP is proportional to N3N^3N3.
2. Relationship with Fan Speed:
   • Cube of Fan Speed: The power requirement increases significantly with increasing fan speed because the power required to overcome air resistance and to move air increases as the cube of the fan speed.
   • This relationship arises because the power required to drive a fan is related to the kinetic energy imparted to the air by the rotating blades, which depends on the square of the velocity (proportional to fan speed) and also the air density.
3. Options Analysis:
   • As square of fan speed: This would not correctly represent the power requirement of a fan with constant wheel diameter; instead, it generally applies to situations where velocity effects dominate.
   • Directly as fan speed: This does not accurately describe the relationship for fans; power typically increases more than linearly with fan speed.
   • As cube of fan speed: This correctly reflects the power requirement for fans with constant wheel diameter due to the kinetic energy relationship involved in moving air efficiently.

Conclusion:

Therefore, the power requirement of fans with constant wheel diameter varies as the cube of fan speed. This relationship is important in fan design and operation considerations, as higher speeds significantly increase the power consumption and may affect efficiency and operational costs.