A pump motor is used to deliver water at a certain rate from a given pipe. To obtain, twice as much water from the same pipe, in the same time, the power of motor has to be increased to:

If the motor pumps water (density = $\mathrm{\rho }$) continuously through a pipe of area of cross section A with velocity v, then mass flowing out per second, m = Av$\mathrm{\rho }$ Rate of increase of kinetic energy = power of pump:

P = $\frac{1}{2}{\mathrm{mv}}^2 = \frac{1}{2}\left(\mathrm{Av\rho }\right){\mathrm{v}}^2 = \frac{1}{2}{\mathrm{A\rho v}}^3$

To get double amount of water, velocity should be doubled. Hence power becomes 8 times.