Page 251 - 48Fundamentals of Compressible Fluid Mechanics

13.4. SOLUTION OF MACH ANGLE 213

Where
(13.19)

And

(13.20)

c
(13.21)

E
, E

c
(13.22)

, E

c

E

Equation (13.19) requires that has to be a real and positive number to obtain

, E

8
real deflection angle . Clearly,
must be possible the and the negative sign is

refers to the mirror image of the solution. Thus, the negative root of must be
.
disregarded
9
Solution of a cubic equation like (13.18) provides three roots . These roots

can be expressed as
(13.23)

E ,

(13.24)

E
and E , E

(13.25)

E E
Where . E , E

(13.26)

"
(13.27)

E

is
and where the definitions of the
(13.28)
"
8 " and 1.
9 The highest power of the equation (only with integer numbers) is the number of the roots. For

example, in a quadratic equation there are two roots.
This point was pointed by R. Menikoff. He also suggested that is bounded by
.