Re: T-89/92 Solver?

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: T-89/92 Solver?
From: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
Date: Thu, 29 Oct 1998 17:36:41 -0500
Reply-To: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>

>  I am trying to solve the following equation:
>
>  1/f^.5=-2.0*Log(e/d/3.7+2.51/(Re*f^.5))
>
>  Given Re, e, d, can the Ti-89/92 solve this for f?  I have tried using
>  solve() and zeros().  Solve() just tries to rearange the equation for f
>  (not possible).  Zeros didn't seem to work either.
>
>  BTW, this is the Colebrook eqn, if you are wondering.
>
>  Thanks,
>
>  Mark

Putting  1/f^.5 = x  and  e/d/3.7 = A  and  2.51/Re = B
the equation becomes

        x = -2*log(A + Bx)

It should be clear that there is no explicit algebraic or elementary
transcendental solution for x in terms of A and B. The best you can do is
aim for a numerical solution (or you could graph it).

Making substitutions like this to "help" the software is the best way to
approach solving a really messy equation like this. It's one of the
techniques we are going to be teaching students when the use of inexpensive
symbolic calculators becomes common (a year or two from now?).

RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623

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