Area-Mach Number Relation

Подпись: 1 M2 Подпись: 2 y+T Подпись: (2.93)

For an isentropic flow of a perfect gas through a duct, the area-Mach number relation may be expressed, assuming one-dimensional flow, as:

where A* is called the sonic or critical throat area.

2.13.4.2 Prandtl-Meyer Function

Подпись: Y + 1 t v = arc tan Y - 1 Подпись: Y 1 (M2 — 1) — arc tanv^M2 — 1 Y + 1 Подпись: (2.94)

The Prandtl-Meyer function v is an important parameter to solve supersonic flow problems involving isentropic expansion or isentropic compression. Basically the Prandtl-Meyer function is a similarity parameter. The Prandtl-Meyer function can be expressed in terms of M as:

From Equation (2.94) it is seen that, for a given M, v is fixed.