Page 102 - 48Fundamentals of Compressible Fluid Mechanics

64 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW

To demonstrate the usefulness of the this function consider the simple sit-
uation of the flow through a converging nozzle
1
2
Example 4.6:
˙ m = 1[kg/sec]
Consider a flow of gas into a
A 1 = 0.009m 2 2
converging nozzle with a mass A 2 = 0.003m
T 0 = 400K P 2 = 50[Bar]
and the
and
flow rate of 1
. The

entrance area is

and the pressure at point 2 was Fig. 4.10: Schematic of a flow of a compressible sub-

stagnation temperature is
Calculate stance (gas) thorough a converging nozzle

the the net force acting on the for example (4.6)

the exit area is

'
nozzle and pressure at point 1.
SOLUTION

measured as
The solution is obtained by getting the data for the Mach number. To obtained the
Mach number, the ratio of is needed to be calculated. To obtain this

ratio the denominator is needed to be obtained. Utilizing Fliegner’s equation (4.52),
provides the following
and

# # (

'3 )(/3&

%!(

*%

'%
#

'

(

'3 )(/3

With the area ratio of
the area ratio of at point 1 can be
calculated.

(*
*
% 3
3'

33'3'3

And utilizing again Potto-GDC provides

(

#

'

3
('

'%
(

/('(

The pressure at point 1 is

1

'%
)('(*3&