Calculating Radius of a Capillary Tube: Capillary Action: Tree Sap

The height to which a liquid will rise as a result of capillary action is given by $h=\frac{\mathrm{2\gamma }\text{cos}\theta }{\rho \text{gr}}$, and every quantity is known except for $r$.

Solving for $r$ and substituting known values produces

This result is unreasonable. Sap in trees moves through the xylem, which forms tubes with radii as small as $2\text{.}5\times {\text{10}}^{-5}\text{m}$. This value is about 180 times as large as the radius found necessary here to raise sap $\text{100 m}$. This means that capillary action alone cannot be solely responsible for sap getting to the tops of trees.