Understanding the Physics of Deep Well Pumping

[Maxo]

Homework Statement

Homework Equations

P1 = P2 + ρgh

The Attempt at a Solution

I know that only the pump at the bottom works for a very deep well, but I don't understand why the higher pump doesn't. So let's ignore the pump at the bottom and only focus on the one at the top. It works by removing air from the pipe, creating vacuum, which then "sucks" the water from the ground, like a straw. Sure. But why doesn't it work for a very deep well? If there is vacuum in the pipe, why doesn't the water goes towards it? What exactly is it that limits it from functioning for a deep well?

 

[haruspex]

It works by removing air from the pipe, creating vacuum, which then "sucks" the water from the ground, like a straw.

There is no such force as a force of suction. What force does propel the water up the pipe in this case?

 

[verty]

By the way, how deep would the well need to be for the atmospheric pressure to be 3dB lower? I think the answer is, well into the Earth's mantle, so this is a pretty odd question.

 

[Orodruin]

I suggest to ask yourself the question "how does a mercury barometer work?"
The answers are closely related.

 

[Maxo]

There is no such force as a force of suction. What force does propel the water up the pipe in this case?

What I meant was that the air is "sucked" out, analogous to when drinking from a straw. The force is the difference in air pressure. So this force is not called suction. I don't know if there is some special name for this force?

I suggest to ask yourself the question "how does a mercury barometer work?"
The answers are closely related.

Ok. So if we have P2 = pressure at points A/B (water surface) and P1 = pressure inside the pipe. P2 is the atmospheric pressure Patm and P1 is for an ideal pump 0. Then the formula P2 + P1 + ρgh becomes

h = (P2-P1) / (ρ*g) = Patm / (ρ*g)

ρwater = 1000 kg/m^3 so

h = 1.013*10^5 / (1000*9.8) = 10.3 m

In other words, the pump at the ground is only able to maximally pump up water from well that is 10.3 meters deep or less? Did I understand it correctly?

 

[Orodruin]

The exact height will vary with air pressure (just as the reading on the barometer), but yes.

 

[haruspex]

What I meant was that the air is "sucked" out, analogous to when drinking from a straw. The force is the difference in air pressure. So this force is not called suction. I don't know if there is some special name for this force?

You've answered your own question - the force is that of air pressure acting on the surface. There is some air each side, so there is a force each way. The net force is the difference of the two.