Expression for height of a liquid in capillary tube
Answers
P2=P1+αgh
where
P2=pressure at calculation point
P1=pressure at height h
α=density of liquid
Consider a narrow glass tube of diameter of d dipped in a liquid (say water). Water in the tube will rise above the adjacent liquid level. It is called capillary rise.
Let σ = Surface tension of liquid.
ϴ = Angle of contact between the glass tube and the liquid surface.
h = Height of liquid column in glass tube.
Under equilibrium, two forces are acting on the water inside. The first one is weight of water column and second is the upward force acting on water due to surface tension. The weight of liquid of height h should be balanced by the force at liquid surface. This force at surface of liquid is due to surface tension.
The weight of liquid of height h in the tube = Volume x ρ x g
= (π/4)d2 x h x ρ x g
Here ρ = density of liquid
g = acceleration due to gravity.
The vertical component of surface tensile force = surface tension x circumference x cosϴ
= σ x πd x cosϴ
At equilibrium, the weight of liquid balanced by the vertical component of tensile force.
For water and glass tube, the angle ϴ is almost zero. ie cosϴ ≈ 1
Then the equation for capillary rise of water in the glass tube is h = 4 σ /(ρgd)
Expression for Capillary fall