- #1

guv

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- Homework Statement
- As in the figure, when water wets on the outside of the glass cylinder, it follows a shape as shown. Is it possible to derive or estimate how ##H## depends on ##g##, water density ##\rho##, radius of the glass tube ##r_0##, surface tension ##\sigma##, wetting angle ##\theta## at the top?

- Relevant Equations
- ##F_{surface \; tension} = \int_0^H \pi (r(y)^2 - r_0^2) \rho g dy##

There are two difficulties, first ##r(y)## is not known, the surface tension force ##F_{surface \; tension}## is not known either. We can write net surface tension force as

##F_{surface \; tension} = \int_0^H 2 \pi r (\sin \arctan \frac{dy}{dr(y)}) dy ##

Is there something else we could use to analyze the shape of the water surface ##r(y)##?

A related question as I am thinking about this is how to apply minimization of potential energy? Maybe variational principle could yield the ideal curve ##r(y)##? This then reminds me how we generally approach wetting inside of a glass tube, there we simply use a force balance and I don't see how we could use energy minimization principle for the internal wetting setup.

Looking for ideas how you might approach this, thanks!

##F_{surface \; tension} = \int_0^H 2 \pi r (\sin \arctan \frac{dy}{dr(y)}) dy ##

Is there something else we could use to analyze the shape of the water surface ##r(y)##?

A related question as I am thinking about this is how to apply minimization of potential energy? Maybe variational principle could yield the ideal curve ##r(y)##? This then reminds me how we generally approach wetting inside of a glass tube, there we simply use a force balance and I don't see how we could use energy minimization principle for the internal wetting setup.

Looking for ideas how you might approach this, thanks!