# Maximum height at which a siphon can drain an open water tower

## Homework Statement

If you have a water tower (basically a cup) open to the atmosphere, with a siphon (basically a straw) inside it as shown below: (sorry assume the height h extends to the bottom of the cup instead of only part way - would that change anything though?)

Then what is the maximum height at which you could have "y" to still drain the cup?

p = po + pgh

## The Attempt at a Solution

So my understanding here is that you have the pressure exerted by the atmosphere and the pressure exerted by the water here, which depends on depth. Since the water pressure only depends on height, even though the straw is outside of the water tower, at a depth H, there will still be a pressure pgH pushing down on the water.

The trouble is then, how to push the water up the height Y. That's entirely dependent on the atmospheric pressure right? Thas the only other force / pressure source i can see acting here. So since atmospheric pressure is equivalent to 10m of water, the max Y could be would be 10m i believe. Am i on the right track here?

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CWatters
Homework Helper
Gold Member
Am i on the right track here?
Yes. What happens at the top of the syphon if you make Y too high?

Yes. What happens at the top of the syphon if you make Y too high?
Would there be a vacuum?

Also if water is coming out of the open end of the siphon this couldn't really last right? Because as water comes out, the height Y that atmospheric pressure must be able to push water up the tube gets larger.

BvU
Homework Helper
2019 Award
How interesting. So if I cover up the left half of the figure, I see a column of water with height y+h and P0 pressure at the bottom. If y is 9 m and h is 9 m too, then what about the pressure in the top 8 m of the tube ?

Perhaps have a look at how an old mercury barometer works. They use mercury instead of water so that they don't have to be >10m tall.