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A capillary tube with a square-shaped internal cross-section, each side of length 'a', is inserted vertically into a liquid of density ρ and surface tension σ. If the liquid adheres to the tube walls with a contact angle θ, approximately how high will the liquid rise inside the tube? (Ignore the surface tension effects at the corners of the tube.)

1. 2σ cosθ / (aρg)
2. 4σ cosθ / (aρg)
3. 8σ cosθ / (aρg)
4. 4σ secθ / (aρg)

Correct answer: 4σ cosθ / (aρg)

Solution

Surface-tension force pulling the column up equals sigma times the wetted perimeter times cos(theta) = sigma*4a*cos(theta). Setting this equal to the column weight rho*g*a^2*h gives h = 4 sigma cos(theta)/(a rho g). The stored answer used 2 sigma instead of 4 sigma.

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