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### Surface Tension

```
Date: 11/09/2000 at 20:14:38
From: Derek Schimpf
Subject: Calculating the force of surface tension

Dr. Math,

The unit of surface tension is N/m. If I want to calculate the force
in newtons exerted by a liquid, do I multiply the surface tension by
the distance that the surface has been deformed (without breaking the
surface)?

Thanks.
Derek
```

```
Date: 11/10/2000 at 06:34:23
From: Doctor Mitteldorf
Subject: Re: Calculating the force of surface tension

Dear Derek,

It's not that simple. The force can be related to the radius of
curvature, which may be different at different points along your
surface. The geometry of the problem is often the complicating factor.

Surface tension is the amount of force on a given liquid area. You'd
think it would be newtons per meter squared, N/m^2. How did it get to
be N/m?

The reason is that surface tension depends on the curvature of the
surface, and the units of curvature are 1/m. Think of curvature as
being the reciprocal of the radius of curvature.

To get the force, multiply the surface tension times the area times
the reciprocal of the radius of curvature.

The complication comes in the geometry. A 2-dimensional surface can
have 2 principal radii of curvature, because it curves differently in
2 directions. A free surface, like a soap bubble, will obey a
"constant curvature" rule that says the sum of these two reciprocals
is the same everywhere. It's the sum of the two reciprocals that gives
you the effective curvature that you can use to calculate a force.

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
```
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