Vacuum Well Pump: Understanding Pressure & Density

[Idea04]

Homework Statement

When you look at the manual hand pump, you would push down on a lever and a piston would rise creating a vacuum in the chamber. which would bring the water upward because of atmospheric pressure push the water upward.
Now I have two questions about this.
My first question is if the water supply is at a level of 32 feet downward and the water was brought up to the vacuum chamber, and with one push upward on the piston inside the pump. Would that create enough vacuum force to pull the water upward, or would the weight of the water create too much pressure that the atmospheric pressure can't push it upward? keeping in mind that the pump creates a low vacuum and atmospheric pressure is 14.7 psi and the water pressure downward is around 13psi.
My second question is what actually happens in the water that is in the pipe going up to the pump? Does the water decrease in density when there is a drop in pressure in the pump.

Homework Equations

The Attempt at a Solution

 

[berkeman]

Well, with my own personal hand-operated vacuum pump, you only get movement of the liquid up the pull-up tube equal to the piston displacement for each hand-pull. Since the ID of the tubing and the OD of the pump piston are about equal, that makes sense, right?

So since my hand pump pison only moves a few cm per hand pull, it would take a lot of pulls to pull a liquid up an in-tube 32' tall.

On your second question, what would make the incompressible liquid water change density?

 

[Idea04]

yes that does make sence, So if the water was brought up the pipe the water at the top of the pipe near the pump would have less pressure than at the bottom of the pipe. And there for would be easier to move into the pump under low vacuum. This action would create lower pressure in the pipe and would start to bring more water up. am I on the right track.

 

[andrevdh]

The water in the underground source is still subject to atmospheric pressure on top of it surface in most cases. Drilling from above and inserting a pipe into it therefore makes no difference to the pressure conditions. Removing the pressure on top of it by raising a piston inside of the pipe will cause the atmosperic pressure on top of the water outside of the pipe to push the water up into the pipe. As the water rises up in the pipe the pressure at the bottom of the column rises due to the weight of the column of water in the pipe. Equilibrium will be reached (water will not rise anymore) if the pressure on top of the water in the pipe and the pressure at the bottom due to its weight equals atmospheric pressure. If the depth of the pipe is such that the pressure due to the weight of the column is less than this equilibrium depth the water will exit at the top. It follows that if the pump can create a perfect vacuum at the top equilibrium will be reached again at some maximum attainable depth of the pipe - which is around 10.3 meters or 33.8 feet at sea level.

The density of water will stay the same if it stays in the same phase (liquid). The density is governed mostly by intermolecular forces and the temperature of the liquid.

 

[Idea04]

Thank you very much. But If I'm to understand this right let's say for example if you had a pipe running 12 feet vertically and the water was in the pipe up to 11 1/2 feet, If you create a low vacuum on top of the water the water will rise to equalize the pressure.

 

[andrevdh]

The high pressure at the bottom (atmospheric) pushes the water upwards against the reduced pressure on top of the water in the pipe. But as the water rises up in the pipe it builds up it own backpressure (at the entry point at the bottom) due to the weight of the water in the pipe. The water will keep on rising as long as the pressure on top of the water in the pipe and the pressure created by its own weight (at the entrance of the pipe underground) is lower than the atmospheric pressure. So basically the upwards motion of the water is driven by a pressure difference at its top and bottom. This is similar to the functioning of a barometer.

The atmospheric pressure in underground water can also propagate from a point where the underground water is open to the atmosphere into the rest of the underground water as explained by Pascal's principle. So the atmosphere need not be in direct contact with the surface of the water at the point where it enters the pipe.

The construction of such hand pumps is also such that the diameter of the piston is much larger than the diameter of the pipe thereby creating a much more effective vacuum at the top.