Question

Please tell me to check the correctness of the relation h =rpg2S for the height of liquid of density 'p' and surface tension 'S' , raised in the capillary tube of radius 'r' and angle of contact zero with the liquid, if incorrect then deduce the correct form.

Answer 1

    The surface of a liquid inside a narrow capillary tube is not planar.  The water falls down in the center and is elevated at the edge where the liquid touches the walls of the capillary tube.  This is due to the attraction between the liquid and the glass molecules.

   Surface tension is defined as the force per unit length along the boundary of the surface of the liquid.  In a capillary tube of radius R, the length of the boundary is 2 π R.  That is the contact between glass and liquid. The angle of contact between the glass and liquid is Ф.

   Then the force on the risen column of liquid (of height h) above normal surface of liquid = S * (2 π R)

   The gravitational force acting downward on the column of height h
     F = mg = ρ * V * g = ρ * π R² * h * g

As the liquid column is in static equilibrium: 
        S * 2 π R = π R² ρ g h

        h = 2 S /(ρ g R)