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Illustration 14.4: Pumping Water up from a Well

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Why can't you pump water up out of a well deeper than 10.3 m? You may not have even known of this limitation! We can answer this question by considering the change in pressure in a liquid as a function of depth (position is given in meters). Restart.

First, what is the pressure at the top of the water in the well (the dark blue line)? It is just atmospheric pressure. Measure the pressure of the water in the tube at the pump by dragging the pressure gauge there. Change the well depth by dragging down the dark blue line and see what happens. Varying this level increases the height to which the pump must pump the water. When the well is deeper than 10.3 m (i.e., when the height of the water column up to the pump is greater than 10.3 m), what is the problem? Can the pump pressure ever be less than zero? No. The best a pump could do is to create a vacuum, which would be P = 0 Pa. In reality, the pump could never reach P = 0 Pa since there would be vapor pressure in the top of the tube.

Note that this animation is exactly how you use a straw to get liquid out of a glass. You reduce the pressure in your mouth (from atmospheric pressure) and the liquid goes up the straw and into your mouth.

What would happen if you tried to pump out a less dense material (like oil)? (Remember that P = P0+ρgy). Could you have a deeper well or would it require a shallower well? Try it.

Illustration authored by Anne J. Cox.

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