Page 204 - 48Fundamentals of Compressible Fluid Mechanics

166 CHAPTER 9. FANNO FLOW
9.8 The Approximation of the Fanno flow by Isothermal
Flow

The isothermal flow model has equation that theoreticians are easier to use com-
pared to Fanno flow model.
.
When the Mach number decreases the temperature approaches the stagnation
One must noticed that the maximum temperature at the entrance is L
b
). Hence, if one allow certain deviation of temperature, say
about 1%) that flow can be assumed to be isothermal. This tolerance requires
temperature (L
L
even for large

F H I
S +) . This requirement provide that somewhere (depend) in the vicinity of
b
QS_I.9
L H Q0S "-"
which requires that enough for N
that L E L
the flow can be assumed isothermal. Hence the mass flow rate is a
changes. Looking that the table or figure 9.2 or the
WYX(Z [
H "-9
results from computer program attached to this book shows that reduction of the
b
function of W`XaZ [
because N
to insert a question or exam- mass flow is very rapid.
ple about this issue in end
M Fanno flow
1
with comperison to Isothermal Flow
0.4
P / P = 0.1 iso
2 1
P / P = 0.8 iso
2
1
0.3
P / P = 0.1
2 1
P / P = 0.2
2 1
M 1 P / P = 0.5
2
1
0.2 P / P = 0.8
2 1
0.1
0
0 10 20 30 40 50 60 70 80 90 100
4fL
¾¾
Wed Mar 9 11:38:27 2005 D
Fig. 9.18: The entrance Mach number as a function of dimensionless resistance and com-
parison with Isothermal Flow
.
The results are very similar for isothermal flow. The only difference is in small
As it can be seen for the figure 9.18 the dominating parameter is W`XaZ [
.
dimensionless friction, WYXaZ [