Obtain an expression for the rise of a liquid in a capillary tube

Dear Student,
Consider a liquid whose angle of contact with the glass capillary tube is acute and so we have a concave surface as shown. Let ‘S’ be the surface tension of the liquid and ‘a’ is the radius of the capillary tube and ‘r’ is the radius of the concave surface of liquid. 'ρ' is the density of the liquid.

Pressure difference between two sides of top surface, P_a − P₀ = 2S/r

Considering points A and B, they must be at same pressure i.e.,

P₀ + hρg = P_a

Thus, height to which the liquid rises is

 
Regards