In this chapter we consider stresses in a fluid. We start by setting the forces resulting from these stresses in their proper perspective, i.e., in relation to body forces, together with which they raise accelerations. This results in a set of momentum equations, which are needed later.

We then consider the relations between the various stress components and proceed to inspect stress in fluids at rest and in moving fluids.

The Momentum Equations

In this section we establish relations between body forces, stresses and their corresponding surface forces and accelerations. Newton's second law of motion is used, and the results are the general momentum equations for fluid flow.

Consider a system consisting of a small cube of fluid, as shown in Fig. 2.1. A system is defined in classical thermodynamics as a given amount of matter with well-defined boundaries. The system always contains the same matter and none may flow through its boundaries.

As a rule a fluid system does not retain its shape, unless, of course, the fluid is at rest. This does not prevent the choice of a system with a certain particular shape, e.g., a cube. The choice means that imaginary surfaces are defined inside the fluid such that at the considered moment they enclose a system of fluid with a given shape. A moment later the system may have a different shape, because the shape is not a property of the fluid or of the location.