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Next: Examples of Fanno Flow Up: Fanno Flow Previous: The Trends   Index

# The working equations

Integration of equation (9.25) yields

A representative friction factor is defined as

By utilizing the mean average theorem equation (9.36) yields

It is common to replace the with which is adopted in this book.

Equations (9.24), (9.27), (9.28), (9.29), (9.29), and (9.30) can be solved. For example, the pressure as written in equation (9.23) is represented by , and Mach number. Now equation (9.24) can eliminate term and describe the pressure on the Mach number. Dividing equation (9.24) in equation (9.26) yields

The symbol *'' denotes the state when the flow is choked and Mach number is equal to 1. Thus, when Equation (9.39) can be integrated to yield:

In the same fashion the variables ratio can be obtained

The stagnation pressure decreases and can be expressed by

Using the pressure ratio in equation (9.40) and substituting it into equation (9.44) yields

And further rearranging equation (9.45) provides

The integration of equation (9.34) yields

The results of these equations are plotted in Figure (9.2)
The Fanno flow is in many cases shockless and therefore a relationship between two points should be derived. In most times, the star'' values are imaginary values that represent the value at choking. The real ratio can be obtained by two star ratios as an example

A special interest is the equation for the dimensionless friction as following

Hence,

Next: Examples of Fanno Flow Up: Fanno Flow Previous: The Trends   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21