seeking help with solving implicit equation

 

	: [Maxima] seeking help with solving implicit equation
	
	

	Folks,

	 

	I'm writing a routine which makes use of the Colebrook equation
for calculating friction factors:

	 

	1/sqrt(f) = -2log(e/3.7D + 2.51 / (Re*sqrt(f))

	 

	In other words, the equation is implicit in the friction factor
f.

	 

	How do I properly define the equation and solve for f once I
have defined e, D, Re?  I thought it was as simple as 

	 

	1/sqrt(f):= ..etc.., define the other variables via the :
operator and solve (%,f) but this makes Maxima swear at me.  It seems
like this should be fairly straightforward root finding, but then again
I am not a mathematician and there's likely some fundamental problem
staring me full in the face.

	 

	A clue for the clueless?

	Thanks

	Len

	 

	 

	 

	Len de Vlaming

	Project Consultant

	 

If you expand the log 

1/sqrt(f) -log(sqrt(f)) = g(e,D,Re)  

which looks to be solvable as Lambert's function.

 

RayR