Exploring the Physics of Siphon Height Calculations

[syang9]

Hi there. Came upon another tricky question in my mcat prep book.. this one makes no sense to me.

https://dl-web.getdropbox.com/get/siphon.PNG?w=389b1d3a

"A siphon is used to draw water from a water tower. What is the approximate maximum height d at which the siphon will be capable of draining the water tower nearly completely?"

A. 1m
B. 10m
C. 100m
D. There is no maximum height.

The answer is B--here is the explanation given, which, again, makes absolutely no sense to me.
"B is correct. Atmospheric pressure pushes the water up through the siphon, thus P_atmos = rho*g*y, where y is the height from the surface of the liquid to the top of the siphon. At a greater height than h, the absolute pressure would be lower than zero; an impossibility. (Remember: 10m of water creates 1 atm of pressure)"

Here are the things that don't make sense to me:

OK, atmospheric pressure is pushing on the fluid. Fine; what about the pressure from the rest of the fluid? Isn't that also pushing water into the siphon, which is at atmospheric pressure? Isn't the whole reason the siphon even works the pressure due to the rest of the fluid? Isn't one end of the siphon at atmospheric pressure, and the other end at a higher pressure due to the weight of the fluid surrounding it? And this pressure difference allows fluid to flow? Why is atmospheric pressure the only responsible party?

What is it talking about when it says 'at a greater height than h'? Why would absolute pressure be lower than zero? What does this have anything to do with the height of the siphon?

I would really appreciate it if someone could walk me through their own thought process. Personally, I didn't even understand how a definite numerical height could be calculated since no numbers were even given in the initial problem.

 

[LowlyPion]

Consider the water barometer.

An atmosphere will only support 33 feet of water to a vacuum.

That's the maximum hydrostatic pressure that the tube can create and hence cannot draw water any higher than 10 m from the level of the water in the tank.

33 feet ∼ 10 m

 

[Delphi51]

Thanks for the interesting problem!

If you had a steel chain in the hose instead of water, it would work at any height as long as the weight of the chain in the down part was greater than the weight in the up part. But liquids don't stick together like steel links. The water going down just reduces the pressure at the top so water from the up leg can be sucked up - or more correctly, pushed up by the atmospheric pressure on the water in the tank. The greatest suction that can be provided is a total vacuum so that the full strength of atmospheric pressure can act on that hose full of water going up to height y above the water level in the tank. The volume of this water is Ay, where A is the cross sectional area of the hose. The force of gravity on it is
F = mg = pVg = pAyg where p is the density (can't make a rho here!). The pressure must provide this force. The force due to a pressure on area A is F = PA. So we have
PA = pAyg
P = pgy after cancelling the A's.

If the y is such that a P greater than 1 atmosphere is required, then there is no flow.

The same thing comes up in water wells. If the well is too deep, no pump located at the top of the well can bring the water up. A pump located down in the bottom of the well CAN provide a pressure greater than an atmosphere to accomplish the job.

 

[syang9]

okay, i think i get it. so you're saying that, in order for the siphon to work, water has to make it past the up leg of the siphon. the weight of that water is pV = pAy, and the only thing that can provide the necessary force to support this weight is the 1atm of pressure that comes from the atmosphere. 1 atmosphere supports 10m of water (is this the same as saying 10m of water generates 1 atmosphere of pressure? why?) so 10m is the maximum distance that atmospheric pressure can propel water

 

[syang9]

have i got it?

 

[LowlyPion]

have i got it?

Seems so.

Good Luck.