Page 119 - 48Fundamentals of Compressible Fluid Mechanics

5.2. OPERATING EQUATIONS AND ANALYSIS 81

Potto-GDC for or value of the specific heat ratio. For finding the Mach number for
is only a few mouse clicks way to following
table.

pressure ratio of 8.30879 and

To illustrate the us- Shock Wave relationship

%

)( (/3
P /P , r/r and T /T as a function of M
age of the above equations, y y y x y x x
120.0
an example is provided.
110.0

3
%

'%'%
100.0
Example 5.1: P /P x
y
90.0
Air flows with a Mach num- T /T x
y
80.0 r/r
ber of

, at pres- y x
70.0
sure of 0.5 [bar] and tem-
60.0
perature 0
C goes through

50.0

a normal shock. Calculate
40.0
the temperature, pressure,
30.0
total pressure and velocity
20.0
downstream of the shock.
10.0
0.0
SOLUTION 1 2 3 4 5 6 7 8 9 10
Analysis: Fri Jun 18 15:48:25 2004 M x
First, the known informa- Fig. 5.4: The ratios of the static properties of the two sides
of the shock
. Using
these data, the total pressure can be obtained (through an isentropic relationship

and
(/
the velocity can

readily be calculated. The relationship that was calculated will be utilized to ob-

tion

,
0
Table (4.2), i.e.
is known). Also with the temperature,

tain the ratios for downstream of the normal shock.

(
(

%( (/

'
1

(
!( '
# #

%

(*
3!(

%(

Now the velocity downstream is determined by the inverse ratio of

%( . # # %

3& 1

'
'
# #

3/
%( ( 3& 1

%'
'