Question

obtain by dimensional analysis an expression for the surface tension of a liquid rising in a capillary tube Assume that the surface tension T depends on mass m of the liquid and pressure p of the liquid and radius r of the liquid

Answer 1

THE DIMENSION OF SURFACE TENSION IS [M L0T -2].

NOW EQUATE THE DIMENSION OF MASS ,PRESSURE AND RADIUS.

[ML0 T -2 ] = [M]A [ML -1 T -2]B [L]C

= MA+BL-B+CT -2B

SO WE GET

A+B=1, -B+C=0 AND -2B=-2

SAOLVING THIS WE GET,

B =1 , A=0 AND C=1

SO THE EXPRESSION FOR THE SURFACE TENSION IS

m0 p1 r1

Answer 2

It has no component perpendicular to the horizontal surface. As a result, there is no pressure difference between the liquid side and the vapour side. ... Thus, there is always an excess of pressure on the concave side of a curved liquid surface over the pressure on its convex side due to surface tension.