Compressible Flow Equations

The one-dimensional analysis given in Section 9.3 is valid only for flow through infinitesimal streamtubes. In many real flow situations, the assumption of one-dimensionality for the entire flow is at best an approximation. In problems like flow in ducts, the one-dimensional treatment is adequate. However, in many other practical cases, the one-dimensional methods are neither adequate nor do they provide information about the important aspects of the flow. For example, in the case of flow past the wings of an aircraft, flow through the blade passages of turbine and compressors, and flow through ducts of rapidly varying cross-sectional area, the flow field must be thought of as two-dimensional or three-dimensional in order to obtain results of practical interest.

Because of the mathematical complexities associated with the treatment of the most general case of three-dimensional motion – including shocks, friction and heat transfer, it becomes necessary to conceive simple models of flow, which lend themselves to analytical treatment but at the same time furnish valuable information concerning the real and difficult flow patterns. We know that by using Prandtl’s boundary
layer concept, it is possible to neglect friction and heat transfer for the region of potential flow outside the boundary layer.

In this chapter, we discuss the differential equations of motion for irrotational, inviscid, adiabatic and shock-free motion of a perfect gas.