1

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
  • 12,030
Sean Gee
  • 23

1 Answers1

0

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
  • 197