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Next: Non-Dimensionalization of the Equations Up: Fanno Flow Previous: Introduction   Index

# Model

The mass (continuity equation) balance can be written as

 (9.1)

The energy conservation (under the assumption that this model is adiabatic flow and the friction is not transformed into thermal energy) reads

Or in a derivative form

Again for simplicity, the perfect gas model is assumed9.3.

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

It is convenient to define a hydraulic diameter as

Or in other words

It is convenient to substitute for and yet it still will be referred to the same name as the hydraulic diameter. The infinitesimal area that shear stress is acting on is

Introducing the Fanning friction factor as a dimensionless friction factor which is some times referred to as the friction coefficient and reads as the following:

By utilizing equation (9.2) and substituting equation (9.10) into momentum equation (9.6) yields

Dividing equation (9.11) by the cross section area, and rearranging yields

The second law is the last equation to be utilized to determine the flow direction.

Next: Non-Dimensionalization of the Equations Up: Fanno Flow Previous: Introduction   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21