Straw sucking height calculation

In summary, the conversation discusses the limitations and factors in determining the maximum height one can suck water up a straw. It also mentions the potential energy and work involved in lifting this column of water, as well as the constraints of human lungs and the viscosity of water. The conversation suggests conducting an experiment to determine the actual maximum height.
  • #1
paulfr
193
3
How high can one suck water up a straw ?
Is this analysis and calculation correct ?
================
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 ?

Thanks for your comments
 
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  • #2
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
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
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
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.
 

1. How is the straw sucking height calculated?

The straw sucking height is calculated by measuring the atmospheric pressure, the density of the liquid being sucked, and the diameter and length of the straw. These factors are used in the equation P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the liquid column.

2. What is the purpose of calculating straw sucking height?

The purpose of calculating straw sucking height is to determine the maximum height at which a straw can effectively draw up a liquid. This information can be useful in designing and testing straw-based drinking devices or understanding the limitations of straw-based water filtration systems.

3. How does air pressure affect the straw sucking height?

Air pressure plays a crucial role in determining the straw sucking height. The higher the atmospheric pressure, the greater the force pushing down on the liquid, making it easier for the straw to draw it up. Conversely, lower atmospheric pressure will result in a lower straw sucking height.

4. Can the diameter of the straw affect the sucking height?

Yes, the diameter of the straw can affect the sucking height. A wider straw will have a larger cross-sectional area, allowing more liquid to be drawn up at once. This can result in a higher sucking height compared to a narrower straw with a smaller cross-sectional area.

5. Are there any other factors that can affect straw sucking height?

Apart from atmospheric pressure, liquid density, and straw dimensions, other factors that can affect straw sucking height include the strength of the person sucking, the angle at which the straw is held, and the presence of any obstacles or bends in the straw.

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