## Moving Systems

We have stated that the only stress that can exist in a fluid at rest is pressure, because the shear stresses (which resist motion) are zero when the fluid is at rest. This also applies to fluids in motion provided there is no relative motion within the fluid (because the shear stresses are determined by the velocity gradients, e.g., the shear rate). However, if the motion involves an acceleration, this can contribute an additional component to the pressure, as illustrated by the examples in this section.

### A. Vertical Acceleration

Consider the vertical column of fluid illustrated in Fig. 4-1, but now imagine it to be on an elevator that is accelerating upward with an acceleration of az, as illustrated in Fig. 4-3. Application of the momentum balance to the "slice" of fluid, as before, gives

Figure 4-3 Vertically accelerating column of fluid.

which is the same as Eq. (4-3), except that now az = 0. The same procedure that led to Eq. (4-5) now gives dP

which shows that the effect of a superimposed vertical acceleration is equivalent to increasing the gravitational acceleration by an amount az (which is why you feel "heavier" on a rapidly accelerating elevator). In fact, this result may be generalized to any direction; an acceleration in the i direction will result in a pressure gradient within the fluid in the —i direction, of magnitude paa:

0 0