Basics of Fluid Mechanics, 2014a

436 CHAPTER 11. COMPRESSIBLE FLOW ONE DIMENSIONAL
Table -11.5.
The flow parameters for unchoked flow
∣
4fL
M 1 M 2
∣ D max 1
4fL
D
P 2
P 1
0.7272 0.84095 0.05005 0.05000 0.10000
0.6934 0.83997 0.08978 0.08971 0.10000
0.6684 0.84018 0.12949 0.12942 0.10000
0.6483 0.83920 0.16922 0.16912 0.10000
0.5914 0.83889 0.32807 0.32795 0.10000
0.5807 0.83827 0.36780 0.36766 0.10000
0.5708 0.83740 0.40754 0.40737 0.10000
11.7 Fanno Flow
This adiabatic flow model with friction is
named after Ginno Fanno a Jewish engineer.
This model is the second pipe flow
model described here. The main restriction
for this model is that heat transfer
is negligible and can be ignored 21 . This
model is applicable to flow processes which
are very fast compared to heat transfer
mechanisms with small Eckert number.
This model explains many industrial flow
flow ρ
direction
}
P
T
(M)
U
Û
Û
No heat transer
ρ + Δρ
P + ΔP
}
T +ΔT
(M + ΔM)
U +ΔU
c.v.
Fig. -11.19. Control volume of the gas flow in
a constant cross section for Fanno Flow.
processes which includes emptying of pressured container through a relatively short
tube, exhaust system of an internal combustion engine, compressed air systems, etc.
As this model raised from the need to explain the steam flow in turbines.
11.7.1 Introduction
Consider a gas flowing through a conduit with a friction (see Figure (11.19)). It is
advantages to examine the simplest situation and yet without losing the core properties
of the process. The mass (continuity equation) balance can be written as
ṁ = ρAU = constant
↩→ ρ 1 U 1 = ρ 2 U 2
(11.154)
21 Even the friction does not convert into heat