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A perfectly wetting liquid of surface tension S and density rho is in contact with a vertical wall. Measured at a height y above the horizontal free surface far from the wall, what is the radius of curvature of the liquid meniscus near the wall?
- S/(y*rho*g)
- 2*S/(y*rho*g)
- 4*S/(y*rho*g)
- S/(2*y*rho*g)
Correct answer: S/(y*rho*g)
Solution
The meniscus climbing a flat wall is curved in one direction only, so the Laplace pressure across it is S/R. At height y above the flat free surface, the liquid pressure just beneath the surface is lower than atmospheric by rho*g*y. This pressure deficit is supplied by surface curvature: S/R = rho*g*y, giving R = S/(rho*g*y).
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