Find the dimensions of surface tension

[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?

 

[Spinnor]

From:

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

Which is from:

http://www.google.com/webhp?hl=en&t..._gc.r_pw.&fp=1fa7c254c97e187f&biw=800&bih=417


"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?

See also:

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

 

[ehild]

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?

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

[itex] h=K \frac{\gamma}{r \rho g}[/itex]

ehild

 

[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?

 

[HallsofIvy]

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

 

[lab-rat]

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