Question

A motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is increased to $P_1$. The ratio of $P_1$ to $P_0$ is

• A. $n:1$
• B. $n^2:1$
• C. $n^3:1$
• D. $n^4:1$

Answer 1

The correct option is C $n^3:1$

Let the flow rate, density and velocity of flowing water be $Q,\rho ,v$ respectively.

Force exerted by flowing water =$\rho Qv$

Power generated by flowing water=$F.v=\rho Q{v}^2$

But we know thta $Q=A.v$. Where A is area of pipe

$\Rightarrow Power=\frac{\rho Q^3}{A^2}$

$\Rightarrow Power$ $\alpha$ $Q^3$

$\Rightarrow P_1:P_0=n^3:1$

Hence,correct answer is optiin $C$