Page 148 - 48Fundamentals of Compressible Fluid Mechanics

110 CHAPTER 6. NORMAL SHOCK IN VARIABLE DUCT AREAS

SOLUTION
A solution procedure similar to what done in previous example (6.1) can be used
here. The solution process starts at the nozzle’s exit and progress to the entrance.
The conditions at the tank are again the stagnation conditions. Thus, the
exit pressure is between point “a” to point “b”. It follows that there must exist a
shock in the nozzle. Mathematically, there are two main possibles ways to ob-
tain the solution. In the first method, the previous example information used and
expanded. In fact, it requires some iterations by “smart” guessing the different
shock locations. The area (location) that the previous example did not “produce”
. In here, the needed pressure
which means that the next guess for the shock location should be

2

with a larger area . The second (recommended) method is noticing that the flow

is adiabatic and the mass flow rate is constant which means that the ratio of the
(upstream conditions are known, see also equation (4.56)).

the “right” solution (the exit pressure was
&

is only

#
#

0 41

With the knowledge of the ratio

which was calculated and determines the

#
#
exit Mach number. Utilizing the Table (??) or the GDC-Potto provides the following

#
#
table is obtained

With these values the relationship between the stagnation pressures of

, is known. The exit total
pressure can be obtained (if needed). More importantly the pressure ratio exit is

'%
'
( %'%
% 3(*

)(* *%
the shock are obtainable e.g. the exit Mach number,
known. The ratio of the ratio of stagnation pressure obtained by

Looking up in the Table (5.1) or utilizing the GDC-Potto provides

#

0'

0'

0 3 % %
/(* 3

!(

) the area where the

shock (location) occurs can be found. First, utilizing the isentropic Table (??).
or
With the information of Mach number (either
2 Of course, the computer can be use to carry this calculations in a sophisticate way.