Page 88 - 48Fundamentals of Compressible Fluid Mechanics

50 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW

SOLUTION
With known Mach number at point A all the ratios of the static properties to total
(stagnation) properties can be calculated. Therefore, the stagnation pressure at
point A is known and stagnation temperature can be calculated.
(supersonic flow) the ratios are

At

(*%

*3!(
With this information the pressure at Point B expressed
0

from the table
3'%!(*

'*3
4.2 @ M = 2

(

3

. The stagnation temperature can be “bypassed” to
#
#
calculated the temperature at point
The corresponding Mach number for this pressure ratio is 1.8137788 and

(*%
*

3

(

%(

Example 4.3:

& !# #
3
'

(

Gas flows through a converging–diverging duct. At point “A” the cross section area
# #
] and the Mach number was measured to be 0.4. At point B in the duct

0''''*3
]. Find the Mach number at point B. Assume that
is 50 [
the flow is isentropic and the gas specific heat ratio is 1.4.

the cross section area is 40 [

SOLUTION
To obtain the Mach number at point B by finding the ratio of the area to the critical
area. This relationship can be obtained by
from the Table 4.2

(
0

With the value of from the Table (4.2) or from Potto-GDC two solutions can

be obtained. The two possible solutions: the first supersonic M = 1.6265306 and
#
#
second subsonic M = 0.53884934. Both solution are possible and acceptable. The

supersonic branch solution is possible only if there where a transition at throat

where M=1.