# Parameter Selection with the Secant Method

### Assignment :

Complete HW 11 and
Prepare for the second exam

Last time you adjusted an area in the input deck choke1.inp to obtain a requested
mass flow of
5 kg/s . Most people had to run TRACE a significant (order of 10)
number of times to obtain the requested precision. Today I'll show you
a systematic way to approach this task. Start by reading my
general discussion of the Secant Method
to obtain a solution to a nonlinear
equation in the form "f(x)=0". For this application the function "f" is
the difference between the
desired mass flow (5 kg/s) and the flow rate produced by the
combination of TRACE and its input choke1.inp
. The independent variable "x" is the area to be adjusted. When f(x) is
a know
closed form function you can implement the Secant method as a
relatively simple program. However,
our function (TRACE) is a little complex for this approach. The
quickest way out is to
build a table (or spread sheet) with the key terms in the Secant
method's formula. Enter relevant
results from the output or graphics files (.out via text editor or .xtv
via APTplot) into the table by hand, compute the area change
for the next run, and enter
the new area into your input file, repeating this process until the
result is
obtained to the desired
accuracy.

**Maintained by John Mahaffy : jhm@psu.edu
**