water vacuum pipe

alibaba2

hi to everyone,
i have the following question, see attached image.
a vertical pipe containing water is exactly 28ft tall. at the top (A) the pipe is tight shut. at the bottom (B)the pipe is open and ends in a bowl of water.
since no air can enter the pipe, the water remains within the pipe and does not flow out of the bowl.
up to what height can this setup work? i.e. at what height will the pressure inside the pipe overcome the outside pressure and will flow out.and is there a connection between the amount of water in the bowl and height of the water column inside the pipe.

thank you

Doc Al

Quote by alibaba2

up to what height can this setup work? i.e. at what height will the pressure inside the pipe overcome the outside pressure and will flow out.

What do you think? How can you find the hydrostatic pressure at the bottom of that column of water? How does that compare to atmospheric pressure?

alibaba2

i guess that at 33ft (1 atm) the water column pressure will equalize with the outside pressure . At 34 ft height, the additional 1ft height will flow out leaving 33ft of water.
what about the relation between the volume of water in the bowl and the height of the column (volume in the column)?

thanks

haruspex

Quote by alibaba2

what about the relation between the volume of water in the bowl and the height of the column (volume in the column)?

Volumes don't matter. All that matters is the height difference between the top of the water in the pipe and the top of the water in the bowl. That determines the pressure difference, and if it's less than atmospheric then the column of water in the pipe can stay put.

mrspeedybob

Equilibrium height won't simply be the height needed to equal atmospheric pressure though. The top of the pipe will not be a vacuum, it will be water vapor. The height of the column in equilibrium will be proportional to the difference between atmospheric pressure and water vapor pressure. How is the water vapor pressure calculated?

JustinRyan

@ 20 deg C water boils at 2kPa.

Vapour pressure will depend on the temperature and the diameter of the pipe.

alibaba2

so what would be the maximum diameter of the pipe to achieve 30ft of height?

jbriggs444

Quote by alibaba2

so what would be the maximum diameter of the pipe to achieve 30ft of height?

On the surface of the Earth? It depends on how you measure. 25,000 miles would seem to be an upper bound.

The cap on the pipe would look more like a sphere with a hole as you approach that limit.

jetwaterluffy

If it starts water-filled, it should work to an infinite extent, there was a video in YouTube about this not long ago. Not a reliable source, I know, but how else do you explain why trees are over 10m?

Although if there is any air bubbles in the water, the whole thing will be wrecked.

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alibaba2	i guess that at 33ft (1 atm) the water column pressure will equalize with the outside pressure . At 34 ft height, the additional 1ft height will flow out leaving 33ft of water. what about the relation between the volume of water in the bowl and the height of the column (volume in the column)? thanks

mrspeedybob	Equilibrium height won't simply be the height needed to equal atmospheric pressure though. The top of the pipe will not be a vacuum, it will be water vapor. The height of the column in equilibrium will be proportional to the difference between atmospheric pressure and water vapor pressure. How is the water vapor pressure calculated?

JustinRyan	@ 20 deg C water boils at 2kPa. Vapour pressure will depend on the temperature and the diameter of the pipe.

jetwaterluffy	If it starts water-filled, it should work to an infinite extent, there was a video in YouTube about this not long ago. Not a reliable source, I know, but how else do you explain why trees are over 10m? Although if there is any air bubbles in the water, the whole thing will be wrecked.