5.1 Fluid Equations

In the introductory discussion in Chapter 3 we simply used the impulse-momentum relation to illustrate the basic idea involved in the dynamics of wave motion. To go further, the differential equations of fluid motion are more appropriate and we proceed accordingly.

The thermodynamic state of a fluid is described by three variables, such as pressure, density, and temperature and the motion by the three components of velocity. Thus, there is a total of six variables which have to be determined as functions of space and time to solve a problem of fluid motion. Therefore, six equations are needed. They are conservation of mass (one equation), conservation of momentum (three equations, one for each component), conservation of energy (one equation), and one equation of state for the fluid.

In describing the motion of a fluid, we shall use what is known as the Eulerian description. The velocity and the thermodynamic state (such as pressure) at a fixed position of observation are then recorded as functions of time. Different fluid particles pass the observer as time goes on. (In the Lagrangian description, the time dependence is expressed in a coordinate frame that moves and stays with the fluid element under consideration.)