Hydrostatic behaviour - water in tube

[ralphamale]

To moderator - I had mistakenly posted this to the "General Physics" forum and later noticed the note about not posting there - sorry! I hope this is the correct location for posting the following question.

I am a novice on this site and am trying to find an answer to a question which is: I filled a tube 48" x 1.5" with water, sealing one end and then inverted it - I expected the water to remain due to the vacuum but it did not. Is there a certain ratio of ht. to dia. required to keep the water in the tube? I would appreciate any imput, guidance or direction on this...Thank you!

 

[kuruman]

Is there a certain ratio of ht. to dia. required to keep the water in the tube?

Yes. For the water not to spill, the pressure on the water-air interface due to the weight of the column must be less than atmospheric pressure. The diameter has nothing to do with it. The condition is $\rho_{water}gh<p_{atm}$. Solving for the height of the column, we get $~h<\dfrac{p_{atm}}{\rho_{water}g}.$ With $\rho_{water}=1000 ~\mathrm{kg/m^3}$, $p_{atm}=100,000~\mathrm{N/m^2}$ and $g=10~\mathrm{m/s^2}$, $h<10~\mathrm{m}$. This is much less that 48"=1.2 m. It didn't work probably because of faulty procedure. The way to do it is to fill the column to the brim, put a card over the lip and, using your hand to hold the card in place, very quickly invert the column being careful not to spill any liquid. Once the column is upside down, remove your hand holding the card. If the card stays in place, remove it very carefully. I've done this with a 10" cylinder, but never with a 48" cylinder.