# Math Help - Effects of surface tension

1. ## Effects of surface tension

Hello!

What I have understood about surface tension is that it lays a pressure on the surface in proportion to the bending of it, the angular change per meter surface , which has the unit $[rad/m^{-1}]=[m^{-1}]$. And pressure has the unit $N/m^2$. So surface tension would have the unit $\left[\frac{N/m^2}{m^{-1}}\right]=[N/m]$, which it has. Now, is it so that the pressure applied to the surface is given by

$P=S\cdot\frac{\delta^2 y}{\delta x^2}$

Where S is the surface tension, and x and y have the unit $[m]$, so $\frac{\delta^2y}{\delta x^2}$ has the unit $[m^{-1}]$. $\frac{\delta^2 y}{\delta x^2}$ is the same as $\frac{\delta\alpha}{\delta x}$, where $\alpha$ is the angle ( $\alpha = \frac{\delta y}{\delta x}$ for small $\alpha$)

2. Originally Posted by TriKri
Hello!

What I have understood about surface tension is that it lays a pressure on the surface in proportion to the bending of it, the angular change per meter surface , which has the unit $[rad/m^{-1}]=[m^{-1}]$. And pressure has the unit $N/m^2$. So surface tension would have the unit $\left[\frac{N/m^2}{m^{-1}}\right]=[N/m]$, which it has. Now, is it so that the pressure applied to the surface is given by

$P=S\cdot\frac{\delta^2 y}{\delta x^2}$

Where S is the surface tension, and x and y have the unit $[m]$, so $\frac{\delta^2y}{\delta x^2}$ has the unit $[m^{-1}]$. $\frac{\delta^2 y}{\delta x^2}$ is the same as $\frac{\delta\alpha}{\delta x}$, where $\alpha$ is the angle ( $\alpha = \frac{\delta y}{\delta x}$ for small $\alpha$)
If I am understanding you correct then you are right. There is also another feature of surface tension: the surface formed contains the least possible amount of energy. In this way you can predict the equation for the surface. (There's a partial differential equation for this, but I don't remember it and I'm too lazy right now to look it up. )

-Dan

3. I found a picture on the wikipedia article which made it a bit clearer to me

I haven't thought of surface tension this way before, like something is pulling sideways in the surface. This clearly motivates the tension part of the name.