A Short Proof of the Prandtl-Meyer Expansion Formula

Extract

Most teachers of gasdynamics with whom the writer has discussed the Prandtl-Meyer analysis find difficulty in giving a lucid exposition to students; the standard treatment tends to be long, and mathematical rather than physical, so that steps in the process of integration are difficult to remember. Lockwood Taylor gives a short treatment; but he begins from Ackeret's formula, which is in effect the differential equation to be treated; and he avoids the actual integration. These considerations have prompted the writer to publish the following treatment, which though self-contained is quite short, and—being mostly graphical—gives some insight into the physics of the problem.