Читать книгу The Mathematics of Fluid Flow Through Porous Media - Myron B. Allen III - Страница 23

For the body force, which is gravity in all of the problems examined here, we adopt the constitutive relationship . Here m denotes the gravitational acceleration, which varies across Earth's surface, and we adopt a Cartesian coordinate system in which points away from Earth's center, as shown in Figure 2.8.

An alternative way of writing this expression proves useful in subsequent sections. Define the depth function as the mapping that assigns to each spatial point its depth below some datum, at which , as drawn in Figure 2.8. We often take the datum to be Earth's surface, but other choices are possible. Observe that

which has dimension . Therefore, we write the constitutive equation for the body force as .