0Generally speaking, fluids are acted upon by two distinct types of force. The first type is long range in nature—that is, such that it decreases relatively slowly with increasing Mathematical Models of Fluid Motion 3 ing distance between interacting elements—and is capable of completely penetrating into the interior of a fluid. Gravity is an obvious example of a long-range force. One consequence of the relatively slow variation of long-range forces with position is that they act equally on all of the fluid contained within a sufficiently small volume element. In this situation, the net force acting on the element becomes directly proportional to its volume. For this reason, long-range forces are often called volume forces. In the following, we shall write the total volume force acting at time t on the fluid contained within a small volume element of magnitude dV, centered on a fixed point whose position vector is r
