Page 184 - 48Fundamentals of Compressible Fluid Mechanics

146 CHAPTER 9. FANNO FLOW
9.4.1 Example 6879;:=< ?A@&BC=D

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EGF

Fig. 9.3: Schematic of example 1 .0/$12-345 "!$#&%(' )*+-,
Example 9.1:
Air flows from a reservoir and enters a uniform pipe with a diameter of 0.05 [m]
and length of 10 [m]. The air exits to the atmosphere. The following conditions
4
. Assume that
and that the flow from the reservoir up

temperature L MH (*
ON
PHRQS
prevail at the exit: 8HJI K
to the pipe inlet is essentially isentropic. Estimate the total temperature and total

QUQ=V
the average friction factor to be HTQ0S
pressure in the reservoir under the Fanno flow model.

SOLUTION
For isentropic flow to the pipe inlet, temperature and total pressure at the pipe inlet
are the same as the those in the reservoir. Thus, finding the total pressure and
temperature at the pipe inlet is the solution. With the Mach number and temper-
ature known at the exit, the total temperature at the entrance can be obtained by
) the following is obtained.

knowing the WYX(Z [
. For given Mach number (N H\QS

I
S Q
Q
Q^S Q
QUQ
Q
Q0S Q0I-V I I=S_I
So the total temperature at the exit I=S Q QS I-V ] ]
I
S Q
I %
V 3
(
L

QUQ
H &
H
Q0S
L H
L
L

is added as

To ”move” the other side of the tube the W`XaZ [
IUS Q
(
V
I(Q
QS Q
Q=V
QS QI-V I
S I
WYX(Z [ cb H W`XaZ [ WYXaZ [ H

4 This property is given only for academic purposes. There is no Mach meter.

# #

QS Q