Page 176 - 48Fundamentals of Compressible Fluid Mechanics

138 CHAPTER 9. FANNO FLOW
9.2 Model

The mass (continuity equation) bal-
ance can be written as

(9.1)

The energy conservation (under the assumption of this model as adiabatic
flow and the friction in not transformed into thermal energy) reads
(9.2)

(9.3)

Or in a derivative form
(9.4)

3
Again for simplicity, the perfect gas model is assumed .
(9.5)

It is assumed that the flow can be approximated as one dimensional. The

force acting on the gas is the friction at the wall and the momentum conservation
reads
(9.6)

' ) )

It is convenient to define a hydraulic diameter as
Cross Section Area
(9.7)
wetted perimeter

Or in other words
#
(9.8)

3 The equation of state is written again here so that all the relevant equations can be found when this

chapter is printed separately.