I have a doubt about the way in which I could calculate the power requiered to pump water with a hand water pump like the next one:

I´ve seen that many people use the equation below:


where p is the fluid density, h the pump height, g the gravity and Q the water flow.

My doubt exist because I was looking to find the force required to be exerted by a human and I get confused about what height should I consider because I suposse it is the one that represents the piston displacement and what I think logically that is related with what the person in charge is lifting up. I understand that the rest of the force to change water's potential energy is coneccted with the work done created by the difference of pressure. I´m actually not sure about if that is correct.

Thank you and sorry for my english.

  • $\begingroup$ The equation you reference is not shown $\endgroup$
    – Bob D
    Aug 9, 2023 at 14:09
  • $\begingroup$ You will need to calculate the moment of inertia of the pivot of the pump handle. This will give the force required to lift the piston vertically. $\endgroup$ Aug 9, 2023 at 20:06
  • $\begingroup$ I recommend you post this question to the engineering SE. This is an engineering statics/dynamics problem $\endgroup$ Aug 9, 2023 at 20:09

1 Answer 1


The pump in your diagram delivers water when the handle is pushed down not when it’s lifted up. See the animation of your pump here. https://en.m.wikipedia.org/wiki/Hand_pump

The height $h$ of the column of water pumped out per stroke is the vertical distance from the lowest position of the piston valve (wherever that occurs) to the position where the cylinder diameter begins to widen and the bottom of the piston is no longer in contact with the cylinder walls.

Hope this helps


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