Suppose water rise predicted by capillarity formula exceeds height of capillary tube. Does water overflow? Explain with mamatical expression.

We know that Capillary action occurs when the force of adhesion between molecules of liquid and walls of a capillary tube (container) is stronger than the force of cohesion between molecules of a liquid. Due to this the liquid has the ability to flow in narrow spaces, or even against gravity.

The height 

h of a liquid column is given as

`h=(4 sigma cos theta)/(rho g d)`

where 

`sigma` is the liquid-air surface tension. 

`theta` is angle of contact, 

`rho` is the density of liquid, 

`g`  is acceleration due to gravity, and 

`d` is the diameter of capillary tube.

When length of tube is less than the height of cap....

We know that Capillary action occurs when the force of adhesion between molecules of liquid and walls of a capillary tube (container) is stronger than the force of cohesion between molecules of a liquid. Due to this the liquid has the ability to flow in narrow spaces, or even against gravity.

The height 

h of a liquid column is given as

`h=(4 sigma cos theta)/(rho g d)`

where 

`sigma` is the liquid-air surface tension. 

`theta` is angle of contact, 

`rho` is the density of liquid, 

`g`  is acceleration due to gravity, and 

`d` is the diameter of capillary tube.

When length of tube is less than the height of capillary rise, the liquid molecules on reaching top of the capillary come into contact with horizontal surface of the tube. The surface tension becomes horizontal. There is no vertical force to pull the liquid up and it stops rising.

Also at each point at the capillary edge there exits a point diametrically opposite at which the surface tension is equal and opposite.

Thus an equilibrium is established, and the liquid does not spill over.