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the height(h) upto which a liquid can rise in a capillary tube depends on surface tension(T) of liquid, density of liquid(d), acceleration due to gravity(g) and radius of capillary. derive the relation for height if the the constant of g is -1?

the height(h) upto which a liquid can rise in a capillary tube depends on surface tension(T) of liquid, density of liquid(d), acceleration due to gravity(g) and radius of capillary. derive the relation for height if the the constant of g is -1?

Grade:12th pass

1 Answers

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
9 years ago
237-2021_capillary.png


Let the radius of the glass capillary tube be r, the coefficient of surface tension of the liquid he T, the density of the liquid be ρ, the angle of contact between the liquid and the walls of the tube be θ and the height to which the liquid rises in the tube be h.
Consider the circumference of the liquid surface where it meets the glass.

Along this line the vertical component of the surface tension force will be 2πr cosθT.

This will draw the liquid up the tube until this force by the downward force due to the column of liquid of height h, that is just balanced at equilibrium:

Therefore
2πr cosθ T = πr2ρgh which gives
h=2Tcos(theta)/r(rho)g

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