Page 87 - 48Fundamentals of Compressible Fluid Mechanics

4.2. ISENTROPIC CONVERGING-DIVERGING FLOW IN CROSS SECTION 49

be calculated utilizing the pressure ratio. With known Mach number, the temper-
ature, and velocity can be calculated. Finally, the cross section can be calculated
with all these information.
In the point where the static pressure known

&

From Table (4.2) or from Figure (4.3) or utilizing the enclosed program from Potto-

GDC, or simply using the equations shows that

3

With these values the static temperature and the density can be calculated.

3
'3

3

'

%%'3'

%'3

3 %

%'3
'
'
% (/

!(/3

#

*

#

The velocity at that point is
3 %%'
# % #

%(
3

The tube area can be obtained from the mass conservation as

1

(4.44)
# # #

/(

%'%3'
'%
%!(
#

% 3

For a circular tube the diameter is about 1[cm].

Example 4.2:
3 and the static pres-
4
sure is 2 [Bar] . Downstream at point B the pressure was measured to be 1.5[Bar].
The Mach number at point A on tube is measured to be
Calculate the Mach number at point B under the isentropic flow assumption. Also,

and assume a perfect gas model.
estimate the temperature at point B. Assume that the specific heat ratio
3 Well, this question is for academic purpose, there is no known way to this author to directly measure
the Mach number. The best approximation is by using inserted cone for supersonic flow and measure
the oblique shock. Here it is sub sonic and that technique is not suitable.
4 This pressure is about two atmospheres with temperature of 250[K]