seeking help with solving implicit equation

 


________________________________

	From: maxima-bounces at math.utexas.edu
[mailto:maxima-bounces at math.utexas.edu] On Behalf Of Rogers, Raymond
	Sent: Friday, January 25, 2008 2:07 PM
	To: maxima at math.utexas.edu
	Subject: Re: [Maxima] 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 

 Sorry, I misparsed the equation.  It's a little more complicated.

 

RayR