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

Answer: (C)

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 $\alpha Q^{3}$
$\Rightarrow P_{1}: P_{0}=n^{3}: 1$