Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A1 / a / Solution

For complete wetting, the meniscus has curvature radius equal to the capillary radius $r=d/2$. The Young–Laplace equation gives the supporting pressure difference $\Delta p=2\gamma /r=4\gamma /d$. Balance it against the hydrostatic pressure $\rho gh$. Taking the sap's mass density to be water-like, $\rho \simeq 10^3\mathrm{kg}{\mathrm{m}}^{-3}$, givesThis is the height supported by the stipulated capillary-pressure model. The density assumption is needed because the surface tension and capillary diameter alone do not determine a height.