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I drink from a glass of water with a vertical straw. What's the longest straw I can use and still drink water if the ambient pressure is 1 atm?

Details and assumptions

  • 1 atm is 101,325 Pa.
  • The acceleration of gravity is -9.8m/s^2 .
  • The density of water is 1g/cm^3.

I am relatively new to physics, so I have no idea how to start. I greatly appreciate everyone's assistance. Thanks in advance.

Brandon Enright
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Sean Gee
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1 Answers1

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I think it is a question how hard you can suck the water in. The force $F$ you need to accelerate the water column depends on the mass of water:

$$F=mg.$$

And the mass depends on the density $\rho$ and the volume $V=hA$ with the length $h$ and the surface area inside the straw $A$. So, the force you need to accelerate the water column is proportional to the height of the water column:

$$F=\rho A h g.$$

If you create a complete vaccum the maximum force $F_{max}$ acting on the surface is $p A$. Then following applies:

$$pA=\rho A h g \\ \Leftrightarrow h = \frac{p}{\rho g} $$

Holger
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    of course it is about the length of the straw. your equation proves it. it solves for the maximum height of the water channel beyond which relative pressure (between ambient and your mouth) can no longer overcome the pressure due to the weight of all that water. whether you can develop the required underpressure is, though relevant to the answer, wasnt the question – gregsan Dec 02 '13 at 09:46
  • You're right. I contradicted myself. I changed my first scentence. Hope it's less mistakeble now. – Holger Dec 02 '13 at 09:49
  • Be sure to change that density to $1000 \text{ kg/m}^3$. Otherwise you might find yourself using a $10 \text{ km}$ straw – DJohnM Dec 03 '13 at 06:43