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## Homework Statement

A motor of power P 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 P1. The ratio of P1 to P is?

## The Attempt at a Solution

Let the velocity of flow of the water be 'v'.

The power required by the motor P = ρAv

^{2}*v, where A is the area of cross section of the pipe. Rate of flow of water, R = Av

P=ρRv

^{2}=ρR

^{3}/A

^{2}

It can be seen that P1=n

^{3}P.

The answer given is n:1

What's wrong?