1. CHAPTER FIVE FANNO FLOW 5.1 Introduction
A course in Gas Dynamics…………………………………..….…Lecturer: Dr.Naseer Al-Janabi
CHAPTER FIVE
FANNO FLOW
5.1 Introduction
We have mentioned that area changes, friction, and heat transfer are
the most important factors affecting the properties in a flow system. Up to
this Chapter we have considered only one of these factors, that of
variations in area. We now wish to take a look at the subject of friction
losses. To study only the effects of friction, we analyze flow in a constant-
area duct without heat transfer. As before, the table permits rapid solutions
to many problems of this type, which are called Fanno flow.
5.2 Working Relations for Fanno Flow
Consider one-dimensional steady flow of perfect gas with constant
specific heats through constant area duct. In case of adiabatic, no work
exchange, the flow is Fanno flow where friction effect is considered. The
basic equations of continuity, energy, and momentum under the following
assumptions, are derived:
The stagnation temperature will be proved to be constant along the duct
while the stagnation pressure will suffer from losses due to friction. The
entropy is expected to increase.
• State equ.

2. velocity” or “mass flux”. • Energy
A course in Gas Dynamics…………………………………..….…Lecturer: Dr.Naseer Al-Janabi
• Continuity
The flow area is constant. G is a constant, which is referred to as the “mass
velocity” or “mass flux”.
• Energy
We start with S.F.E.E.
For adiabatic and no work, this becomes
If we neglect the potential term, this means that

3. From continuity equation
A course in Gas Dynamics…………………………………..….…Lecturer: Dr.Naseer Al-Janabi
From continuity equation
• Entropy
Substitute for Temperature and pressure ratio, from above:

4. work flow of a perfect gas, we start from the following thermodynamic
A course in Gas Dynamics…………………………………..….…Lecturer: Dr.Naseer Al-Janabi
To derive an expression for stagnation pressure ratio for adiabatic, no-
work flow of a perfect gas, we start from the following thermodynamic
relation for stagnation (total) properties
Since for adiabatic flow and from energy
equation, then
• Momentum

5. Friction factor, f, is four times friction coefficient, Cf.
A course in Gas Dynamics…………………………………..….…Lecturer: Dr.Naseer Al-Janabi
The external forces that act on the element are the pressure and shear
forces as shown in figure (5.1)
Figure 5.1 Control volume for isolated, constant area duct with
frictional flow
τ is shear stress due to wall friction and Asur duct surrounding surface
area. The hydraulic diameter;
Surface area is
Friction factor, f, is four times friction coefficient, Cf.

6. Substitute for τ and Asur
A course in Gas Dynamics…………………………………..….…Lecturer: Dr.Naseer Al-Janabi
Substitute for τ and Asur
From state equation and the definition of Mach number
Taking logarithmic of this expression and then differentiating gives
Substitute for dp⁄p and dV⁄V gives
Then