Vascular plants transport water by a passive transport system using xylem, a cell tissue which forms thin, long cylinders along branches of plants. In particular, trees use this tissue to transport water against the force of gravity to great heights.
In one model (Model 1, shown in first figure below), xylem is a tube or pipe, and water is "pulled" up by reducing the pressure at the top of the column of water in the xylem. The figure shows a tube whose bottom end is in a reservoir of water. The top end is closed and has a cavity whose pressure is less than atmospheric pressure. It turns out not to be a good model for Nature.
In another model (Model 2, shown in figure below), xylem is a narrow tube which exerts a force on water by surface tension, the same force that causes water to rise in a thin straw when it is sitting in water. In this case the forces on the column of water have to be balanced, so the downward force of gravity is equal to the upward force of surface tension. The force of surface tension is the product of the coefficient of surface tension γ (0.072 N/m for water) and the circumference of the cylinder.
In both models the height of the column is h and the radius of the tube is r, which is about 2 x 10–7 m. Use the estimate Patm = 105 N/m2 for atmospheric pressure. Use 103 kg/m3 for the density of water and 10 m/s2 for the acceleration of gravity.
How could the maximum height be increased in Model 2?