The problem I have is this:

A capillary tube is immersed vertically in water. Knowing that water starts to evaporate below 2kPa, determine the maximum capillary rise and tube diameter. Assume the contact angle is 6 degrees and surface tension is 1 N/m.

The only equation I know of to use for this would be:

$h = \frac{2\sigma_s cos(\theta)}{ \rho gR}$

where h is the capillary rise, $\sigma_s$ is the surface tension, $\rho$ is the density of water, g is 9.8 m/s ^2 and R is the radius. However I have 2 unknowns and only 1 equation and this relationship does not include pressure.

My question is what other equation can I use in solving this problem, or is there a different equation that I should be using to solve this problem.

The correct answer to this problem should be h=10.2 m, and R = 20 micro m.

  • $\begingroup$ How would you include the pressure? $\endgroup$
    – Bernhard
    Commented May 16, 2014 at 22:06
  • $\begingroup$ The question gives the pressure, I am not sure how or if it is used. $\endgroup$
    – ez4nick
    Commented May 16, 2014 at 22:08

1 Answer 1


Think of a barometer.

The hydrostatic pressure can not exceed the difference between the atmospheric pressure and vapor pressure.

$101325Pa -2000Pa = \rho gh$

Then use $h$ in your equation to find $R$.


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