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

[Hereformore]

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?

Homework Equations

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?

 

[CWatters]

Am i on the right track here?

Yes. What happens at the top of the syphon if you make Y too high?

 

[Hereformore]

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]

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 ?

 

[CWatters]

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.

http://weather.about.com/od/weatherinstruments/a/barometers.htm

 

[Hereformore]

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.

http://weather.about.com/od/weatherinstruments/a/barometers.htm

Oh I see! So the opening of the siphon feels pgy + pgh. Pgy must equal atmospheric pressure.

So the height y = when pgy = 1atm. If the column is higher then the fluid can't riser higher. On the right side, from the ground, since the opening has atmospheric pressure, the column should spill out until the height of the water left is equal to y right? It shouldn't matter whether the opening is pointing horizontal or vertical since it still feels 1atm.

I may have just confused myself. The pressure of the water LEAVING a horizontal opening should be 1atm. The atmoshperic pressure should be one 1 atm as well going into the tube (just like how a damn feels presure horizontally). Yet the water is still flowing out. So water can still flow even though the presure is equal?

 

[CWatters]

The short answer is that pgy must be less than atmospheric pressure or a vacuum will form at the high point.

http://en.wikipedia.org/wiki/Siphon#Maximum_height

The velocity of a syphon is explained here but I've never had to look at that..

http://en.wikipedia.org/wiki/Siphon#Velocity