A motor is used to deliver water through a pipe. Let the motor have a power P initially. To double the rate of flow of water through the pipe, the power is increased to P’. What is the value of P’/P?

8

Power = Force x Velocity

 = (Mass/Time) x Velocity²

 = Rate of flow x Velocity²

Rate of flow = Area x Velocity

Doubling the rate of flow will double the velocity.

P = Rate of flow x Velocity²

P’ = (2 x Rate of flow) x (2 x Velocity)²

    = 8P

P/P’ = 8.