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Next: Combination of the Oblique Up: Prandtl-Meyer Function Previous: d'Alembert's Paradox   Index

# Examples For Prandtl-Meyer Function

Solution

First the initial Mach number has to calculated (the initial speed of sound).

The Mach number is then

This Mach number associated with

 1.3100 6.4449 0.35603 0.74448 0.47822 52.6434
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The new'' angle should be

and results in

 2.0024 26.4449 0.12734 0.55497 0.22944 63.4620
<>

Note that

The new'' width can be calculated from the mass conservation equation.

Note that the compression fan'' stream lines are not known and their function can be obtained either by the numerical method of going over small angle increments. The other alternative is using the exact solution14.1. The expansion fan'' angle changes in the Mach angle between the two sides of the bend

Reverse the example, and this time the pressure on both sides are given and the angle has to be obtained14.2.

Solution

The Mach number is determined by satisfying the condition that the pressure downstream are Mach the given one. The relative pressure downstream can be calculated by the relationship

 1.4000 7.7720 0.28418 0.60365 0.47077 54.4623
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With this pressure ratio, , require either locking in the table or using the enclosed program is required.

 1.4576 9.1719 0.26190 0.58419 0.44831 55.5479
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For the rest of the calculation the initial conditions are used. The Mach number after the bend is . It should be noted that specific heat isn't but . The bend angle is

Next: Combination of the Oblique Up: Prandtl-Meyer Function Previous: d'Alembert's Paradox   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21