ABSTRACT
The first step of the procedure outlined in Section 19.2 has been accomplished, i.e., writing the conservation equations in body-oriented coordinates. The Euler equations are readily obtained from Appendix H as
where
Chapter 17 shows there is no need to include the energy equation, which is decoupled from the others. Furthermore, there is no need to assume either a thermal or caloric state equation; i.e., the fluid may be a liquid or an imperfect gas. (Problem 20.2 derives a consistent form for the energy equation.) As Chapter 17 further indicates, a single, third-order PDE is obtained by introducing a stream function, to satisfy continuity, after which the pressure is eliminated from the momentum equations by cross-differentiation. The solution of the Euler equations, when evaluated at the wall, will be denoted with a subscript
e
. In addition, the
e
means the edge of the thin boundary layer. Uniform freestream conditions are denoted with an infinity subscript.
