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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?

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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.

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  • $\begingroup$ I did'nt understand why friction goes up as the square of velocity.Is that a formula or something? $\endgroup$
    – user74370
    Aug 2 '15 at 14:11
  • $\begingroup$ Yes it is. See if you can understand this link - although it states the $v^2$ relationship as a given. Also, this earlier answer talks a bit more about fluid flow profiles - but while it addresses a different aspect, there may be some insights there for you. $\endgroup$
    – Floris
    Aug 2 '15 at 14:19

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