# Straw sucking height calculation

1. Nov 15, 2012

### paulfr

How high can one suck water up a straw ?
Is this analysis and calculation correct ?
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Straw sucking height limit calculation
Sucking up thru a straw from a height ...limit h = ? m

If the pressure P [=F/A] , the work done to lift the water column to h is
W = F dot s = PA x h/2 [average height = h/2]

The potential energy of the column is PE = ρAhg (h/2) [c of m is in the middle].
When the column rises up to its highest, there is no motion,
so all the energy is potential.
Equating work done to potential energy due to energy conservation

PAh/2 = ρAhg (h/2)
P = ρhg
h = P / ρ g
h = 1.0e5 N/m^2 / (1000 kg/m^3) ( 10 m/s^2)
h = 10 meters

Does that look correct ?

Last edited: Nov 15, 2012
2. Nov 15, 2012

### Simon Bridge

What you have answered is what height column of water would balance a given pressure difference.

There are additional constraints if you are thinking of a human sucking on the end ... like the capacity of the lungs. How long would it take for a human to suck up a 10m column of air through a straw? Against the resistance of having to pull up that mass of water?

Then I'd want to ask if the human lungs could do that much work - I suspect that will be the limiting factor. You'll find that the area of the straw matters ... compare sucking through a drinking straw and a hose pipe.

3. Nov 15, 2012

### Staff: Mentor

Well, you can make the straw thin to lower the volume, or do it in several steps. The limited pressure difference of the lungs is more problematic - lungs are not good vacuum pumps.

4. Nov 15, 2012

### Simon Bridge

If you make the straw thin, don't you need to be concerned by the viscosity of the water too? That would add to the work needed to get it along a length h of straw. For very thin straws you may get some help from the capillary effect I guess. iirc there is a minimum area that you can make a straw and still get water up it (well - it has to be bigger than a single molecule...)

The working is good - it's just that the question answered is not the one that was asked.

5. Nov 16, 2012

### Staff: Mentor

How much of a vacuum do you think you can apply with your mouth, relative to atmospheric pressure? Think about the opposite situation. How much pressure do you think you can apply with your mouth, relative to atmospheric pressure? For example, do you think you can inflate an automobile tire by blowing through the inlet valve? To do this, you would have to blow with a pressure of about 30 psi. I'm guessing, you could possibly blow with a pressure of no more than about one or two psi (maybe less). Think about how hard it is to inflate a balloon. I'm also guessing that the vacuum you could create would be less than the blowing pressure you could apply. If you could apply a vacuum of 1 psi, you could suck up a column of water about 2 feet. The easiest way to settle this is to do an experiment. Get a flexible piece of laboratory tubing, stick it in a bowl of water, and see how high you can suck up a column of water.