Column of water, vacuum pressure and a one-way valve problem

[Anton Zhyzhyn]

A conceptual problem related to a design I'm working on:

If I use a pump to suck air out of the top of a vertical pipe, with the bottom of the pipe in water, I can only make the water rise around 10 metres inside the pipe, if I produce a perfect vacuum.

Now let's say the pipe was 100m long and around 90m was under water, such that my pump was just able to suck the water up to the top of the pipe (and thus remove all air from inside the pipe).

Now let's say the top of the pipe has a perfect one-way valve which prevents the water column from falling once I switch off the pump. Once the pipe is full of water, I turn off the pump and the column remains standing.

Now, say the surrounding water level outside the bottom of the pipe falls by around 1m, such that the top of the pipe is now 11m above the surrounding water level. The perfect one-way valve at the top remains closed.

What happens inside the pipe? Will my column of water still be standing, reaching to the top of the pipe? What governs this behavior and, if the water column can be more than 10m in this situation, what happens if the water level drops significantly further?

 

[anorlunda]

That is a very good question.

The low pressure will cause the water to boil even at room temperature, so steam instead of air will fill the top part of the pipe.

To prevent that from happening, you need a liquid other than water that won't boil or evaporate.

 

[russ_watters]

If we assume the water doesn't boil, the limiting factor is atmospheric pressure. You're making a really tall barometer. The height of the column of water above the surrounding water is fixed to atmospheric pressure and there is a vacuum above (all vacuums are the same, regardless of their volume).

 

[billy_joule]

What happens inside the pipe? Will my column of water still be standing, reaching to the top of the pipe? What governs this behavior and, if the water column can be more than 10m in this situation, what happens if the water level drops significantly further?

You can watch an analogous experiment at 7:45 in this video:

 

[Baluncore]

Now let's say the top of the pipe has a perfect one-way valve which prevents the water column from falling once I switch off the pump. Once the pipe is full of water, I turn off the pump and the column remains standing.

I understand that your one way valve is at the top. If you place another one way valve at the bottom you will not have to support the column with atmospheric pressure, since it cannot escape from the column after atmospheric pressure has pushed it in.

 

[Baluncore]

To prevent that from happening, you need a liquid other than water that won't boil or evaporate.

I beg to differ.
If the vapour pressure of the liquid is significantly less than atmospheric pressure, which is normally the case, then the height of the supported column will have little to do with the vapour pressure above the liquid and much more to do with the density of the liquid.
In a barometer, atmospheric pressure is supporting the liquid column by pushing it up, while the vapour pressure above is pushing it down. The difference pressure is available to support the column. That column will have a height that is inversely proportional to the density of the liquid.

Crudely expressed, at sea level; Column height = 10.3 metre / density relative to water.
For water that works out at 10.3 metres, while for Hg with a density of 13.534 g/cm³ we get 760 mm.

Remember that both the density of a liquid and the vapour pressure are temperature dependent.