numerical root finding procedures

trying to solve the part under else. eover and Re are known, but still leaves me with (f) on both side of the original colebrook equation. 1/sqrt(f) = -2*log10(eoverD/3.7 + 2.51/Re/sqrt(f)). Please help, a bit stuck.

Re = V*D1 / nu;
% Check for laminar flow.
if Re < 2300
F = 64 / Re;
else
    F(f)=1/sqrt(f)+2*log10(eoverD/3.7 + 2.51/Re/sqrt(f));
end

[the cyclist]

You have written this a bit confusingly. I think it is a bit clearer to write your code as

Re = V*D1 / nu;
% Check for laminar flow.
if Re < 2300
f = 64 / Re;
else
  % Here I need to calculate "f" such that it solves the equation
  % 0 = 1/sqrt(f)+2*log10(eoverD/3.7 + 2.51/Re/sqrt(f));
end

Notice how I get rid of the confusing use of capital F.

See my suggestion for solving this in my answer below.

[harley]

thanks for that, when i run i get in the command window;

Exiting fzero: aborting search for an interval containing a sign change because complex function value encountered during search. (Function value at -0.28 is -9.229-3.1086i.) Check function or try again with a different starting value.

code is

D = 0.1; 
e = 0.0015e-3; 
nu = 1.01e-6; 
eoverD = e/D;
%
V = 2; 
%
Re = V*D / nu;
% 
if Re < 2300
f = 64 / Re;
else
   darbyFormula = @(x) 1/sqrt(x)+2*log10(eoverD/3.7 + 2.51/Re/sqrt(x));
f = fzero(darbyFormula,1);
end

[harley]

got it working, thanks

Answer 1

[the cyclist]

You should be able to use the function fzero() to solve for f in your implicit equation.

>> doc fzero

for details.

I think this will do it, but definitely check:

darbyFormula = @(x) 1/sqrt(x)+2*log10(eoverD/3.7 + 2.51/Re/sqrt(x));

f = fzero(darbyFormula,1)

Answer 2

[Walter Roberson]

If you do some algebraic manipulation, you get

x = 0.3340248829e22 / (-0.5020000000e11 * lambertw(.4586822894 * Re * exp(.1239681863 * eoverD * Re)) + 6223202955 * eoverD * Re)^2

with no searching (provided that eoverD already has a value)

lambertw is in the Symbolic Toolbox. If you do not have that, then see http://www.mathworks.com/matlabcentral/newsreader/view_thread/32527