Derive an expression for the rise of liquid in a capillary tube of uniform diameter and sufficient length?

The rise of liquid in a capillary tube can be derived using the capillary action formula, which is given by ( h = \frac{2\gamma \cos \theta}{\rho g r} ). Here, ( h ) is the height of the liquid rise, ( \gamma ) is the surface tension of the liquid, ( \theta ) is the contact angle, ( \rho ) is the liquid density, ( g ) is the acceleration due to gravity, and ( r ) is the radius of the capillary tube. This expression shows that the height of the liquid rise is directly proportional to the surface tension and the cosine of the contact angle, and inversely proportional to the density of the liquid, gravitational acceleration, and the radius of the tube.