One-dimensional flow: the basic equations

In all real flow situations the physical laws of conservation apply. These refer to the conservation respectively of mass, momentum and energy. The equation of state completes the set that needs to be solved if some or all of the parameters controlling the flow are unknown. If a real flow can be ‘modelled’ by a similar but simplified system then the degree of complexity in handling the resulting equations may be considerably reduced.

Historically, the lack of mathematical tools available to the engineer required that considerable simplifying assumptions should be made. The simplifications used depend on the particular problem but arc not arbitrary. In fact, judgement is required to decide which parameters in a flow process may be reasonably ignored, at least to a first approximation. For example, in much of aerodynamics the gas (air) is con­sidered to behave as an incompressible fluid (see Section 2.3.4), and an even wider assumption is that the air flow is unaffected by its viscosity. This last assumption would appear at first to be utterly inappropriate since viscosity plays an important role in the mechanism by which aerodynamic force is transmitted from the air flow to the body and vice versa. Nevertheless the science of aerodynamics progressed far on this assumption, and much of the aeronautical technology available followed from theories based on it.

Other examples will be invoked from time to time and it is salutory, and good engineering practice, to acknowledge those ‘simplifying’ assumptions made in order to arrive at an understanding of, or a solution to, a physical problem.