Having problem with Rankine Oval Matlab

Hi I am having problems with using matlab to find the solution for Rankine Oval in Fluid Mechanics.

>> x=-10:0.01:10;

>> y=0:0.01:10;

>> [x,y]=meshgrid(x,y);

>> m=1;

>> a=1;

>> U=1;

>> psi = U*y - m/(2*pi) * atan(2*a*y./(x.^2 + y.^2 - a^2));

>> contour(x,y,psi,100);

>> grid on;

figure(1)

This is what I have made.... . the problem is I want to find the value when psi equals to zero, but I am not sure. From the book it said I need to use fzero function but it doesn't work.

It would be really nice if you guys help

Thx

[Michael Soskind]

Have you taken a look at the following answer?

A little different than your question, but possibly a good reference for the way that you are defining the oval.

Answer 1

[Star Strider]

The contour function can give you the values for ‘psi’ equal to zero:

cxy = contour(x,y,psi,[0 0]);

That will plot them, and return the (x,y) coordinates in ‘cxy’ as:

x = cxy(1,2:end);
y = cxy(2,2:end);

in the event that you need them for something else.

See the documentation on contour for details.