Page 117 - 48Fundamentals of Compressible Fluid Mechanics

5.1. SOLUTION OF THE GOVERNING EQUATIONS 79

In the same way the relationship between the density ratio and pressure ratio is

(5.26)

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5.1.3 Speed of Sound Definition
There can be several definitions of speed of sound that associated with the shock
wave.
5.1.3.1 The Maximum Conditions
The maximum speed of sound
is when the highest tempera- Shock Wave relationship
ture is achieved. The maxi- M and P /P as a function of M x
y
0x
0y
1
mum temperature that can be
achieved is the stagnation tem- 0.9
perature 0.8 M y
P /P
0.7 0y 0x
(5.27) 0.6
M y 0.5

The stagnation speed of sound

0.4

is
0.3
(5.28) 0.2
" ,
Based on this definition a new 0.1

Mach number can be defined 0 1 2 3 4 5 6 7 8 9 10
Fri Jun 18 15:47:34 2004 M x
(5.29)
2
Fig. 5.3: The exit Mach number and the stagnation
pressure ratio as a function of upstream Mach

number
5.1.3.2 The Star Conditions
The speed of the sound at the critical condition also can be a good reference
velocity. The speed of sound at that velocity
(5.30)

In the same manner additional Mach number can be defined as

(5.31)