Page 288 - 48Fundamentals of Compressible Fluid Mechanics

250 CHAPTER 14. PRANDTL-MEYER FUNCTION

which satisfied equation (14.27) (because ). The arbitrary con-
. The tangential velocity

obtains the form
stant in equation (14.28) is chosen such that "

%
(14.29)

"

"

The Mach number in the turning area is

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$

(14.30)
"
"
"
"
"

"
equations (14.29)
and (14.28) results for the Mach number and "

Now utilizing the expression that were obtained for "
$
%

" *
(14.31)

or the reverse function for is

!
(14.32)

What happened when the upstream Mach number is not 1? That is when

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initial condition for the turning angle doesn’t start with but at already at

different angle. The upstream Mach number denoted in this segment as, .

For this upstream Mach number (see Figure (14.2))
(14.33)

*

The deflection angle * , has to match to definition of the angle that chosen here

when ) so

(
(14.34)

*

(14.35)

These relationship are plotted in Figure (14.6).

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14.2.2 Comparison Between The Two Approaches, And Limita-

tions
The two models produce the exact the same results but the assumptions that con-
struction of the models are different. In the geometrical model the assumption was