surface tension is force/length
I am going to call density rho, not P. P is confusing because usually pressure.
F = m a = rho L^3 * L/s^2
= rho L^4/s^2
so
F/L = rho L^3/s^2
but g is L/s^2
so
F/L = rho L^2 g
if our length scale is h then
Y = F/L = constant * rho h^2 g
By the way, it depends on the polarity of the molecules of fluid. Water molecules attract each other.
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the surface tension Y, of liquid depends on the density,P, acceleration of gravity,g, and the height, h. use the method of dimension to derive the actual relationship between these quantities
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