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Question
Derive an expression for capillary rise for a liquid having a concave meniscus.
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Solution
The pressure due to the liquid (water) column of height h must be equal to the pressure difference `(2 T)/R` due to the concavity.
∴ hρg =(2 T)/R`
Where, ρ is the density of the liquid and g is acceleration due to gravity.
Let r be the radius of the capillary tube and θ be the angle of contact of the liquid as shown in the figure.
Then radius of curvature R of the meniscus is given by,
R = `r/cos theta`
∴ hρg = `(2 T cos theta)/r`
∴ h = `(2 T cos theta)/(r rho g)`
The above equation gives the expression for capillary rise (or fall) for a liquid. Narrower the tube, the greater is the height to which the liquid rises (or falls).
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