11.10 Problem Set

Using the example of a leaf with dimensions 0.05 m by 0.05 m, this module demonstrated that under certain circumstances an increase in wind speed will increase transpiration while in other cases an increase in wind speed will decrease transpiration. Find examples of these two cases for a Douglas fir needle with D = 0.001 m, W = 0.02 m.
Your light plane has just been forced down at 5000 feet in the Andes mountains. It is a hot (35°C), still (wind speed = 0.1 m sec^-1), and dry (relative humidity = 20 percent) day in late summer. To pass the time until you are rescued, you look at the surrounding flora and become interested in leaf sizes. The sun is shining brightly and you guess that, without as much atmosphere to absorb the radiation, the plant leaves must be absorbing about 800 W m^-2 of radiant energy. You also note that the ground is dry so you surmise that the plants are water stressed and must have internal diffusive resistances of about 2000 s m^-1. Assuming that these are the conditions which determine plant survival in this area, and assuming that plant leaves cannot tolerate temperatures in excess of 45°C for extended periods, what are the shape and size of the largest leaves you expect to find?
Equation (11.7) in the module indicates how a leaf dissipates the radiant energy it absorbs. The three terms on the right-hand side of (11.7) correspond to reradiation; loss of sensible heat by convection; and loss of latent heat through transpiration. For each of the three situations listed below, find the relative contribution of each of these mechanisms to the dissipation of the incident radiant energy.

In Figure 11.3, the situation indicated by the intersection of the \(r_l\) = 200 s m^-1 and V = 0.1 m s^-1 lines.
In Figure 11.3, the situation indicated by the intersection of the \(r_l\) = 0 s m^-1 and V = 2 m s^-1 lines.
In Figure 11.8, the situation indicated by the intersection of the \(r_l\) = 5000 s m^-1 and \(T_a\) = 0°C lines.