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Expression for Capillary Rise

Let h be the capillary rise in fall in a tube of diameter ‘d’ centre surface tension force in upward direction.

Capillary rise

P = πd σ cos Ѳ

Weight of liquid column = V. γ

= ( π/4d2 x h) γ

Where γ  = specific weight of liquid

Under equilibrium, the weight of liquid column will be balanced by surface tension force 'σ '

Weight of liquid = Surface tension

π/4d2 hγ = πdσcosѲ

h = 4σcosѲ / γd

For pure water in contact with clean glass and air, Ѳ = 0

h = 4σ / γd

For mercury and glass, Ѳ  = 1400

Capillary rise in a gap between two closed spaced parallel plates:

h = 2σcosѲ / γt              Where ‘t’ is the gap between the plates.

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