Max Diam Tube Filled w/ Viscous Liquid: Deriving Formula

[etherist]

Formula for the maximum diameter of vertical tube(open on top and bottom) filled with viscous liquid (such as oil) as a function of viscosity and length so that the liquid remains inside. How the formula is derived? Thanks a lot.

 

[jbriggs444]

Formula for the maximum diameter of vertical tube(open on top and bottom) filled with viscous liquid (such as oil) as a function of viscosity and length so that the liquid remains inside. How the formula is derived? Thanks a lot.

It should not be a function of viscosity but rather a function of surface tension.

Surface tension has units of force per unit length. You would be trying to equate the total surface tension from the fluid skin at the circumference of the tube with the force of gravity on the fluid in the tube. [This ignores the contribution from surface tension on the top surface that could be positive or negative depending on whether the tube material is wettable.

Can you write down a formula for the down force in terms of the density of the fluid, the acceleration of gravity, the diameter of the tube and the height of the tube?

Can you write down a formula for the up force from surface tension in terms of the diameter of the tube and the surface tension of the fluid?

If you equate these, can you solve for diameter in terms of the other parameters?

 

[etherist]

Oh jbriggs444 thanks, it must be surface tension. I had solve the equation, i thought it was different in capillary tube formula since the bottom is open but as you explain it appears that it is the same. I thought the lifting force in this set-up depends on area, since the liquid is sticking on the inside surface but i realize it is wrong. Thanks a lot.