Finding the Optimal Location for a Water Pump in a Deep Mine

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The optimal location for a water pump in a deep mine is at the bottom of the mine, as suction pumps can only lift water about 10 meters due to atmospheric pressure limitations. A forcing pump is necessary to effectively move water from deeper levels. The discussion emphasizes understanding the physics behind pumping water, particularly the limitations of suction pumps. For additional efficiency, placing the pump slightly above the bottom, around 10 meters up, could be considered. This highlights the importance of proper pump placement in mining engineering to ensure effective water removal.
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Homework Statement



You are required to pump water out of a very deep mine. Where should you put the pump?

Homework Equations



P=P(surface)+rho(g)(h)

The Attempt at a Solution



I am sure that this is a very easy problem but I can't see mathematically how to solve it. I know that if the resevoir of water at the bottom was under atmosperic pressure a suction pump could only raise the water about 10 meters and therefore not be useful. So, you would use a forcing pump below the column of water but how do I work out where exactly it goes?
 
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What level is this question (are you in mining engineering college?)
I suspect it just wants you to know that you can't 'suck' water more than 10m - which you have done, and so you would have to pu tit at the bottom.

I suppose for extra credit you could put it 10m up from the bottom!
 

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