# 32 foot limit

I can vaguely recall from a hydrodynamics class I took many years ago that water can be pumped straight up only 32 feet (a bit more or less, depending on atmospheric pressure). I was having a conversation recently with a friend and mentioned the 32’ limit. I got called on it for an explanation as to why this is so. I was unable to recall all of the technical details and to make any simple explanation for my friend.
I was wondering if someone here could give me a simple breakdown of the 32’ limit.

Thnx,
Anga

You can only suck water up 32’. You can pump it to any arbitrary height.

A column of water 32’ high generates a pressure at the bottom of about 1 atmosphere. If the column is higher than that, the water pressure at the bottom will be greater than the atmospheric pressure holding it in.

The reason is that when you suck water up a tube, you’re not actually pulling it up at all, you’re reducing the pressure unside the tube and allowing the pressure outside to push it up.
Since the pressure (on Earth, at sea level etc) is fairly constant, it can only push the water up the tube so far.

Try it on Jupiter and you’ll get better results, try it on Mars and it will be less impressive.

No, the reason you can’t suck water up higher than 32’ is that a 32’ foot column of water is very heavy. To suck it up that high requires extremely low pressure at the top of the column (where the pump is presumably). The low pressure causes the water to boil (become a gas) and the pump can no longer function. This all depends heavily on temperature. The term is cavitation and would happen to a column lower than 32’ if the temperature was increased.

YAAAAAY my degree did something for me.

emacknight, you are basically saying the same thing as the other replies. You’re all right. And yes, the limit does not apply to pumping water, only to sucking it. Otherwise, pumped-storage hydroelectric power stations wouldn’t be much use.

Ha, that`s funny. Then none of our taller buildings would have toilets on any floor above thirty-two feet.

No, it seems your degree did not do enough. boiling, cavitation etc are irrelevant. The fact is that atmospheric pressure can only raise water so far, regardless of whether the liquid boils or not (BTW, it does not boil). In the case of any fluid the column held by atmospheric pressure is equal to the pressure exerted by the fluid. If it is more dense then the column is shorter. What is the height of a column of mercury?

Oh, and if you want a bit of maths to prove it, I’ll have a go at working it out from first principles:

If a column of air 1-inch square extending all the way to the “top” of the atmosphere could be weighed, this column of air would weigh approximately 14.7 pounds at sea level. Thus, atmospheric pressure at sea level is approximately 14.7 psi. (Cite)

The density of water is 1 g cm[sup]-3[/sup], which is (1 x 2.54[sup]3[/sup] = 16.4 g per cubic inch or 16.4/(28.35 x 16) = 0.0361 pounds per cubic inch. (Because there are 2.54 cm in an inch, 28.35 grams in an ounce and 16 ounces in a pound.)

So imagine a column of water with cross-section 1 square inch. How high does it have to be for the mass of the water to equal 14.7 lb?

Answer = 14.7/0.0361 = 407 inches, or 33.9ft.

I assume that the small discrepancy is because you can never achieve a true vacuum with a pump in the real world, so there will always be a bit of pressure keeping the water from reaching its full potential height.

Isn’t this what is used to measure atmospheric pressure? The height of a column of mercury in a vacuum? Normal atmospheric pressure will raise around 29.2 inches of mercury, I believe. Or was your question rhetorical?

Oh, and incidentally, I’ve just found this site which backs up my 33.9 ft figure

To be fair to emacknight, he’s a bit right.

At 25 [sup]o[/sup]C, water boils at a pressure of about 0.5 psi.

The limiting factor is the difference between atmospheric pressure and that boiling point. So you should really have used a slightly lower figure in your calcs, r_k, and arrived at an answer of 32.8’.

But you can’t get less than zero pressure; regardless of whether the liquid boils or not.

Consider this apparatus; the column of water is replaced with a column of solid material(that cannot boil) of equal density, zero friction between the solid column and the sides of the tube is assumed.
When the pressure in the tube is evacuated, the air pressure outside of the tube (pressing down on the water surface) will force the solid column up the tube thus, but to a height (I believe) of no more than 32 feet because that is the limit of what the force outside air pressure can achieve.

Or have I made some terrible error?

Yes. See my previous post.

Eh?

It’s not solely dependant on the density of the column, the boiling point is also a real factor.

Fair enough, but we’re still saying that there is a definite limit to how high the extrnal pressure will push the column into the evacuated space?

Sure.

Why wouldn’t it boil? The pressure is very close to zero, and temperature is presumably close to room temperature.

Unless I’m mistaken, Jupiter and Mars don’t have any appreciable atmosphere? And if they don’t have much of an atmosphere, then there wouldn’t be much atmospheric pressure… Wouldn’t the column of water be smaller on both planets? I think Mangetout was just referring to the planetary mass or gravity.

I don’t feel like converting it to inches, but 29.2 inches seems right or close enough… it’s 760 mm of mercury.

And another vote for it would boil. As long as the vapor pressure of the water is equal to the pressure inside the tube, you’ll have some boiling. I’ve made ice water boil before by using a vacuum.

Mars has very little atmosphere, so there is next to no pressure to push anything up the tube. Jupiter is nearly all atmosphere (at least that’s one way to look at it), so the pressure at the surface should be incredibly high.

The Galileo Probe measured 21 atmospheres on its descent to Jupiter before it died.