Question

A motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n$ times the water through the same pipe in the same time the power of the motor must be increased as follows.

• A. $n$-times
• B. $n^2$ - times
• C. $n^3$ - times
• D. $n^4$ - times

Answer 1

The correct option is C $n^3$ - times

Case I:
Power $=\frac{\Delta K.E}{t}$
$=\frac{\frac{1}{2}m{v}^2}{t}=\frac{1}{2}dA.v^3$

where $d$ is density $A$ is area and $v$ is velocity of water

Case II:
$P=\frac{1}{2}\times dA.v^3$
When water delivered is n- times velocity will become n times i.e. $P$ will become $n^3$ times