You have been given the task of determining, for a redwood tree \(100 \mathrm{~m}\) tall, the mechanisms that allow the tree to grow to such a height and the mechanisms that prevent it from growing any taller. Using your knowledge of fluid dynamics, you determine that capillary rise causes water to rise a height \(b\) through a tree's xylem (the hollow tubelike cells in trees that carry water), and for a xylem radius \(r\), this height is approximately given by \(h=\left(0.137 \mathrm{~J} / \mathrm{m}^{2}\right) /\left(ho_{\text {water }} g r\right)\). Using a microscope, you observe that the xylem has a diameter of about \(5 \mu \mathrm{m}\). You are convinced that a mechanism other than capillary rise is needed to enable the water to rise to the top leaves.