# Find the dimensions of surface tension

1. Sep 9, 2011

### lab-rat

I would really appreciate some help with this!

h= (L)
r=(L)
p=(ML-3)
g=(LT-2)

I just don't know what to do with the directly proportional sign. Should I isolate the surface tension before or after adding the constant?

2. Sep 9, 2011

### Spinnor

From:

http://www.wikihow.com/Determine-Whether-Two-Variables-Are-Directly-Proportional

Which is from:

"Understand what the phrase directly proportional means. A very common misconception is that two variables are directly proportional if one increases as the other increases. Two variables are said to be directly proportional if, and only if, their ratio is a constant for all values of each variable. Thus when one variable is divided by the other, the answer is always a constant. "

So in the formula for surface tension I think that the proportional sign can be replaced with an equals sign when the formula is multiplied by a dimensionless constant?

http://en.wikipedia.org/wiki/Surface_tension#Two_definitions

3. Sep 10, 2011

### ehild

The directly proportional sign means a multiplicative constant K which is dimensionless. So

$h=K \frac{\gamma}{r \rho g}$

ehild

4. Sep 10, 2011

### lab-rat

So from there I can isolate surface tension and find its dimensions?

surface tension = (L)(L)(ML-3)(LT-2) / k

=M/kT2

Now how do I find the SI units with a constant in there?

5. Sep 10, 2011

### HallsofIvy

Staff Emeritus
As ehild said, that constant is dimensionless so you can just ignore it.

6. Sep 10, 2011

### lab-rat

Oh ok, so the SI units would be kg/s2 ?