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Feedback    Next: Subsonic Fanno Flow for Up: The Practical Questions and Previous: The Practical Questions and   Index

## Subsonic Fanno Flow for Given 4fL/D and Pressure Ratio This pair of parameters is the most natural to examine because, in most cases, this information is the only information that is provided. For a given pipe , neither the entrance Mach number nor the exit Mach number are given (sometimes the entrance Mach number is give see the next section). There is no exact analytical solution. There are two possible approaches to solve this problem: one, by building a representative function and find a root (or roots) of this representative function. Two, the problem can be solved by an iterative procedure. The first approach require using root finding method and either method of spline method or the half method found to be good. However, this author experience show that these methods in this case were found to be relatively slow. The Newton-Rapson method is much faster but not were found to be unstable (at lease in the way that was implemented by this author). The iterative method used to solve constructed on the properties of several physical quantities must be in a certain range.. The first fact is that the pressure ratio is always between 0 and 1 (see Figure (9.18)). In the figure, a theoretical extra tube is added in such a length that cause the flow to choke (if it really was there). This length is always positive (at minimum is zero).

The procedure for the calculations is as the following:

1. Calculate the entrance Mach number, assuming the (chocked flow);
2. Calculate the minimum pressure ratio for (look at table (9.1))
3. Check if the flow is choked:
There are two possibilities to check it.
a)
Check if the given is smaller than obtained from the given , or
b)
check if the is larger than , 4. Calculate the based on the ,
5. calculate based on ,
6. calculate the new , based on the new ,
(remember that ),
7. calculate the corresponding and ,
8. calculate the new and improve'' the by (9.53)

Note, when the pressure ratios are matching also the will also match.

9. Calculate the improved/new'' based on the improve fanno flow!entrance Mach number calculations
10. calculate the improved as 11. calculate the improved based on the improved .

12. Compare the abs ( ) and if not satisfied
returned to stage (6) until the solution is obtained.

To demonstrate how this procedure is working consider a typical example of and . Using the above algorithm the results are exhibited in the following figure. Figure (9.19) demonstrates that the conversion occur at about 7-8 iterations. With better first guess this conversion procedure will converts much faster (under construction).    Next: Subsonic Fanno Flow for Up: The Practical Questions and Previous: The Practical Questions and   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21