Page 135 - 48Fundamentals of Compressible Fluid Mechanics

5.4. SHOCK TUBE 97

Or in-terms of the pressure ratio is

(5.81)

As it was mentioned earlier the velocity at points and 3 are identical, hence
"
equation (5.81) and equation (5.75) can be combined to yield

(5.82)

%

%

After some rearrangement equation (5.82) transformed into %
%
"

(5.83)

,

#

Or in terms of Mach number of the

(5.84)

&

Utilizing the Rankine–Hugoniot relationship and the perfect gas model results in

%

%
(
(5.85)

%

%

%

Utilizing the isentropic relationship for zone 3-5 results in
%

(5.86)

"
Example 5.7:
.

Find what is the shock velocity, temperature behind the shock. what will be tem-
A shock tube with initial pressure ratio of
and the initial temperature of
?

perature behind the shock if the pressure ratio is
SOLUTION