The Concorde 264 supersonic airliner. Flying more than twice as fast as the speed of sound, as
discussed in the present chapter, the Concorde is a milestone in commercial aviation. However,
this great technical achievement is accompanied by high expense for the traveller. (Courtesy of
Don Riepe/Peter Arnold, Inc.)
Motivation. All eight of our previous chapters have been concerned with “low-speed’’
or “incompressible’’ flow, i.e., where the fluid velocity is much less than its speed of
sound. In fact, we did not even develop an expression for the speed of sound of a fluid.
That is done in this chapter.
When a fluid moves at speeds comparable to its speed of sound, density changes be-
come significant and the flow is termed compressible. Such flows are difficult to obtain
in liquids, since high pressures of order 1000 atm are needed to generate sonic veloci-
ties. In gases, however, a pressure ratio of only 21 will likely cause sonic flow. Thus
compressible gas flow is quite common, and this subject is often called gas dynamics.
Probably the two most important and distinctive effects of compressibility on flow
are (1) choking, wherein the duct flow rate is sharply limited by the sonic condition,
and (2) shock waves, which are nearly discontinuous property changes in a supersonic
flow. The purpose of this chapter is to explain such striking phenomena and to famil-
iarize the reader with engineering calculations of compressible flow.
Speaking of calculations, the present chapter is made to order for the Engineering
Equation Solver (EES) in App. E. Compressible-flow analysis is filled with scores of
complicated algebraic equations, most of which are very difficult to manipulate or in-
vert. Consequently, for nearly a century, compressible-flow textbooks have relied upon
extensive tables of Mach number relations (see App. B) for numerical work. With EES,
however, any set of equations in this chapter can be typed out and solved for any vari-
able—see part (b) of Example 9.13 for an especially intri