Rate of flow of water through a pipe

[zorro]

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 = ρAv²*v, where A is the area of cross section of the pipe. Rate of flow of water, R = Av
P=ρRv²=ρR³/A²

It can be seen that P1=n³P.
The answer given is n:1
What's wrong?

 

[hikaru1221]

I think there is nothing wrong with your solution :)

 

[zorro]

Thanks!