What do you mean by capillarity. Derive relation for the rise of liquid in a capillary tube on the basis of balancing force and explain the rise of liquid in a tube of insufficient length.

Explanation

Capillarity: Capillarity is the phenomenon of rise of fall of liquid in a capillary tube.
Derivation : A uniform glass capillary of uniform internal radius r is dipped into a liquid vertically Water rises in the capillary upto a height h. In this situation, the tota upward force acting on the periphery is
`F = 2pi r T cos R `
` theta =` Angle of contact
T = Surface tension of the liquid.
Volume of the liquid in the capillary.
= volume of the liquid in the cylinder of height h + volume of the liquid under the curved surface AEB.
= volume of the liquid in the cylinder of height h + volume of the cylinder ABCD - volume of the hemisphere AEB
`= pi r ^(2) + pi r ^(2) r - (1)/(2) xx (4)/(3) pi r ^(3)`
`= pi r ^(2) ( h + (r)/(3))`
weight of liquid `= pi r ^(2) (h + (r)/(3)) rho g`
where `rho = `density of the liquid.
For equilibrium, F = weight of the liquid
`2pi r T cos theta = pi r ^(2) (h + (r)/(3)) rho `
`T = (r (h + (r)/(3))rho g )/( 2 cos theta)`
Neglecting ` (r)/(3)` in comparison to h
`T = (rh rho g )/( 2 cos theta) `
`therefore h = ( 2 T cos theta)/( r rho g )`