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My book says:

Suppose a pump motor is used to deliver water at a certain rate from a given pipe. To get n times the water from same pipe in same time the power must be increased by $n^3$ times.

I cant understand why?Shouldn't the power be increased by n times as $power$=rate of $work $ done and work done is being increased by n times ? Or am I having a conceptual mistake?

1 Answers1

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For turbulent flow, the friction goes up as the square of the velocity. So the force (pressure) goes as $n^2$. And you are moving $n$ times more liquid. The velocity (or volume flow) increases by $n$.

The two factors combine to give the cube law since power = force times velocity, or pressure times flow rate.

Floris
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