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How do we define the power of a pump?

I read a formula from a book which defines the power of the pump as follows:

Power of the pump = Maximum back pressure * maximum flow rate / 2

Can anyone explain why the right hand side equals the left hand side?

I don't understand why the LHS is divided by a factor of 2.

And, is the power of a pump always the same value, no matter at any flow rate/back pressure?

It seems to be that at maximum back pressure, the flow rate is zero and the pump power is zero then?

Please help.

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# Pump power and efficiency

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