Solution to Exercise 12

12) What conditions does the following governing equation represent? Explain the features of the terms of the equation that indicate each condition.

This is Equation 67 of this book. It represents transient, confined, groundwater flow where conditions are anisotropic and heterogeneous. The K values are within the differential on the right-hand side of the equation signifying they are variables and can be different values everywhere in the domain (x,y,z), thus the equation is applicable to a heterogeneous and anisotropic system. The left-hand side has a time derivative and thus, this equation represents transient conditions, that is, the heads change with time and water can go into, or come out of, storage. If the left-hand side was set to 0, the equation would represent steady state conditions. If the equation represented unconfined conditions, there would be an h inside the derivative, and Sy would be used instead of Ss as follows (as shown in Equation 74 of this book):