Basics of Fluid Mechanics, 2014a

11.7. FANNO FLOW 445
10 2 0 1 2 3 4 5 6 7 8 9 10
10
10 -1 1
4 fL
D
P/P ∗
P 0 /P 0
∗
ρ/ρ ∗
U/U ∗
T/T ∗
10 -2
M
Fig. -11.20. Various parameters in Fanno flow shown as a function of Mach number.
11.7.5 Examples of Fanno Flow
Example 11.18:
Air flows from a reservoir and enters a uniform pipe with a diameter of 0.05 [m] and length of 10 [m].
P 0 =?
T 0 =? ◦ C
M 2 =0.9
D=0.05[m]
L=10[m]
T 2 =27 ◦ C
P 2 =1[Bar]
Fig. -11.21. Schematic of Example 11.18.
The air exits to the atmosphere.
The following conditions prevail at
the exit: P 2 =1[bar] temperature
T 2 =27 ◦ CM 2 =0.9 23 . Assume
that the average friction factor to
be f =0.004 and that the flow
from the reservoir up to the pipe
inlet is essentially isentropic. Estimate
the total temperature and total pressure in the reservoir under the Fanno flow
model.
Solution
For isentropic, the flow to the pipe inlet, the temperature and the total pressure at the
pipe inlet are the same as those in the reservoir. Thus, finding the star pressure and
temperature at the pipe inlet is the solution. With the Mach number and temperature
known at the exit, the total temperature at the entrance can be obtained by knowing
the 4fL
D
. For given Mach number (M =0.9) the following is obtained.
23 This property is given only for academic purposes. There is no Mach meter.