HP27S Inherent problem with the equation solver Message #1 Posted by Bruce Cohen on 24 Oct 2004, 5:31 a.m.
I was trying to transfer a conduit flow equation from my HP42S solver to my HP27S just to see how complicated it would be, since there is no way to store intermediate calculations. As you can see by the equation, this was not a trivial task. When I finished and had the equation working properly, I did a test calculation, solving for each of the variables to detect physically impossible solutions. The results of this test has revealed this problem.
PROBLEM: THIS DOG WON'T HUNT!
The consequences of an overly agressive direct solver prevents the discovery of the desired roots of some equations.
The variable E~IN is second order in the equation below; but, since it only appears once in the equation, the direct solver is able to isolate it to one side of the equation. This allows rapid answers for one root but with no way to calculate the other root, since direct solutions don't permit the use of guesses to "HUNT" for the other root.
VARIBLES
!RE 395,319.5445 Reynolds number  dimensionless
!V~FT/S 6.3828 Fluid velocity  feet per second
!Q~GAL 2,611.2000 Pipeline volume  gallons
F~GPM 1000 Flowrate  gallons per minute
D~#/GAL 8.34 Density  pounds per gallon
ID~IN 8.0 Pipe inside diameter  inches
L~FT 1000 Pipe length  feet
E~IN .0018 Roughness  inches
VIS~CP 1.0 Viscosity  centipoise
P~PSI 12.0034 calc Pressure  pounds per square inch
K 20.0 Fitting coefficents  dimensionless
Variables preceeded by a (!) are outputs only.
After solving for P~PSI, solve for E~IN and you get the answer E~IN=280,727.6311 which is the physically meaningless root.
EQUATION  The equation is entered into the HP27S solver as a single string, the line breaks are for readability.
HYDRAULICS
:IF(S(!RE):F~GPMx379.2034xD~#/GAL÷ID~IN÷VIS~CP!RE
:IF(S(!V~FT/S):F~GPMx0.4085÷ID~IN^2!V~FT/S
:IF(S(!Q~GAL):ID~IN^2x0.0408xL~FT!Q~GAL
:(IF(F~GPMx379.2034xD~#/GAL÷ID~IN÷VIS~CP>2300:0.0772÷LOG((E~IN÷3.7÷)^1.111+6.9÷(F~GPMx379.2034xD~#/GAL÷ID~IN÷VIS~CP))^2
:16÷(F~GPMx379.2034xD~#/GAL÷ID~IN÷VIS~CP))x24xL~FT÷ID~IN+K÷2)x(F~GPMx.0485÷ID~IN^2)^2÷618.87P~PSI÷D~#/GAL)))
This problem seems to be affected by the number of times a variable appears in an equation.
For example:
A=LOG((X^PI)^5.124)^1.23 Yields a direct solution
A=X+X requires an iterative solution
