[Maxima] seeking help with solving implicit equation

Rogers, Raymond raymond-rogers at idexx.com
Fri Jan 25 13:19:22 CST 2008



	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

		: [Maxima] seeking help with solving implicit equation



		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?






		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.



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




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