Surface TensionDate: 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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