# [Maxima] seeking help with solving implicit equation

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

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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

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