Implicit Functions and Iterative Processes in Hydraulics

In hydraulics you can use the Colebrook Equation to find friction factor. This is an implicit function.

http://en.wikipedia.org/wiki/Darcy_friction_factor_formulae#Colebrook_equation

How does MATLAB handle implicit functions? This method is used in an iterative approach. How would I start picking this equation apart to write a code for an implicit function?

Thank you

Answer 1

[Andrew Newell]

MATLAB handles implicit functions by changing f(x)=g(x) into f(x)-g(x)=0 and solving for x. Here is an example inspired by your link:

A = 0.1; B = 1;
fcn = @(x) 1./x+2.*log10(A + B./x);
xp = 1:.1:10; yp = fcn(xp); plot(xp,yp)
sqrtf = fzero(fcn,2);
f = sqrtf^2;
disp(['f = ',num2str(f)])

I have used an anonymous function, but you can also define functions in a variety of other ways (see Types of functions).

Answer 2

[Sean de Wolski]

Some recommended reading:

http://www.mathworks.com/matlabcentral/fileexchange/8553-optimization-tips-and-tricks

Number 32 (33 in the actual HTML)