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