Question

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain n times water from the same pipe in the same time, by what amount should the power of the motor be increased?

• A. $n^2$ times
• B. $n^3$ times
• C. $n$ times
• D. $n^{3/2}$ times

Answer 1

The correct option is B $n^3$ times

Since the rate of the water is following through the pipe is $\frac{dm}{dt}=A{v}_p$

Where A is the area of cross section v is the velocity through which water is following out of the pipe $\rho$ is the density of the material.

$\frac{d{m}^{\prime }}{dt}=\frac{ndm}{dt}\Rightarrow A{v}^{\prime }\rho =nAv\rho \Rightarrow v^{\prime }=nv$

So power $F.v=\frac{p^{\prime }}{p}=\frac{v^{\prime }\frac{d{m}^{\prime }}{dt}{v}^{\prime }}{v\frac{dm}{dt}V}=n^2\times n=n^3$