Problem to plot a difficult graph

Posted on 2008-11-17 12:15 By gertjanglissenaar (1)

Categories:

Math Advice (Student)

Hello all,

For a project of groundwater contaminations i need to plot the following graph.

18^2-y^2 = Q*(ln((3000*(18-y))*sqrt(0.412e-4))-ln(sqrt(x)))/(0.412e-4*Pi)

where as X stands for the distance of a waterfilter and Y stands for the water level.

I tried to plot this with maple but i cant find the solution for this.

Thanks for your time,

Gertjan

If a 2D plot is meant

Comment on 2008-11-17 13:23 from jakubi ( Maple Rating 4

943)

by setting a value for Q, you can do something like:

f:=18^2-y^2 = Q*(ln((3000*(18-y))*sqrt(0.412e-4))-ln(sqrt(x)))/(0.412e-4*Pi);
g:=solve(f,x);
plot(subs(Q=1,g),y=0..10);

implicitplot

Comment on 2008-11-17 17:45 from Robert Israel ( Maple Rating 4

1554)

To plot a curve of the form f(x,y) = g(x,y), you can use implicitplot in the plots package.

I'll take Q = 10000.

> plots[implicitplot](18^2-y^2 = 10000*(ln((3000*(18-y))*sqrt(0.412e-4))-ln(sqrt(x)))/(0.412e-4*Pi),
   x=0..20, y = 17 .. 18,gridrefine=3,crossingrefine=3);

graphical viewing using animation or 3d

Comment on 2008-11-19 14:38 from Doug Meade ( Maple Rating 4

739)

I think you have missed on your guesses for interesting values of Q. Rather than getting individual plots for fixed values of Q, I let Maple create an animation of this curve as a function of the parameter Q. Here's the basic idea, building upon Robert's use of implicitplot:

with( plots ):
animate( implicitplot, [18^2-y^2 = 10^q*(ln((3000*(18-y))*sqrt(0.412e-4))-ln(sqrt(x)))/(0.412e-4*Pi),
   x=0..5000, y = 0 .. 20,gridrefine=3,crossingrefine=3], q=-2..-1 );

Note that I replaced Q with 10^q and modified the viewing window. In my code, I'm looking at Q between 0.01 and 0.1. (I'm having trouble uploading a file to MaplePrimes right now, so I can't show you what this produces.) Further refinements are probably called for, but I don't know enough about the specifics of your problem to begin to guess what you want to see.

You could also look at your equation in 3D. I don't see that the gridrefine and gridcrossing options are available in implicitplot3d, so it's a little more difficult to get a good picture.

implicitplot3d(18^2-y^2 = 10^q*(ln((3000*(18-y))*sqrt(0.412e-4))-ln(sqrt(x)))/(0.412e-4*Pi),
   x=0..2000, y = 0 .. 20, q=-2..-1, axes=boxed );

Doug

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