The Euler equations

For some applications in aerodynamics it can be an acceptable approximation to neglect the viscous stresses. In this case Eqns (2.66) simplify to

(2.68a)

(2.68b)

These equations are known as the Euler equations. In principle, Eqns (2.68a, b), together with the continuity Eqn (2.46), can be solved to give the velocity components и and v and pressure p. However, in general, this is difficult because Eqns (2.68a, b) can be regarded as the governing equations for и and v, but p does not appear explicitly in the continuity equation. Except for special cases, solution of the Euler equations can only be achieved numerically using a computer. A very special and comparatively simple case is irrotational flow (see Section 2.7.6). For this case the Euler equations reduce to a single simpler equation – the Laplace equation. This equation is much more amenable to analytical solution and this is the subject of Chapter 3.