Colebrook equation is an

So, one of the methods to solve this equation is Newton-Raphson method. Colebrook equation can be re-written in residual form like the following

The following

The following capture shows the result obtained by the function used in Scilab

and the following capture is the result obtained by the online calculator in this link http://www.engineeringtoolbox.com/colebrook-equation-d_1031.html

__implicit equation__used to calculate the Darcy-Weisbach friction factor which is used to calculate the pressure drop in pipes.So, one of the methods to solve this equation is Newton-Raphson method. Colebrook equation can be re-written in residual form like the following

The following

*Scilab*function is used to calculate Darcy-Weisbach friction factor for a fully-developed turbulent flow.function [f, #of_iterations]=Colebrook_f(epslon, d, Re, NMax)
R='1/sqrt(f)+2*log10((epslon/d)/3.7+2.51/(Re*sqrt(f)))'; // Residual expression
D='-0.5*f**(-1.5)*(1+(5.02/(log(10)*Re))/((epslon/d)/3.7+2.51/(Re*sqrt(f))))'; // derivative expression: partial ... derivative of residual with respect to friction factor

f=0.02; // Initial guess of Darcy-Weisbach friction factor
for i=1:NMax, // loop stops after reaching stop criteria
RV=eval(R); // Residual value evaluation
DV=eval(D); // Derivative value evaluation
f_new=f-RV/DV; // computing the new value of f using Newton-Raphson method
if RV <=0.0001 then // If residual is less than the accepted error
break
else f=f_new;
end
end
#of_iterations=i;
endfunction

and the following capture is the result obtained by the online calculator in this link http://www.engineeringtoolbox.com/colebrook-equation-d_1031.html