Plot Stream Lines Using Matlab: ψ4 + ψ2 U2(x2-y2+a2) = U4x2y2

[kingjames]

ψ⁴ + ψ² U²(x²-y²+a²) = U⁴x²y²

This is the stream line equation of a flow along a vertical plate!
i need to plot the stream lines using matlab! ψ is the stream function
U is constant and 'a' is the plate length

 

[Mark44]

ψ⁴ + ψ² U²(x²-y²+a²) = U⁴x²y²

This is the stream line equation of a flow along a vertical plate!
i need to plot the stream lines using matlab! ψ is the stream function
U is constant and 'a' is the plate length

Write some MATLAB code for these calculations and we'll help you with it, but we're not going to write the code for you.

 

[kingjames]

Write some MATLAB code for these calculations and we'll help you with it, but we're not going to write the code for you.

i tried to find the roots of the equation then i have to find the derivatives with respect to x and y to be able to draw them

solve ('z^4+z^2*UINF^2*(x^2-y^2+a^2)-(UINF^4*x^2*y^2)=0','z')

ans =

1/2*(2*(x^4+2*x^2*y^2+2*x^2*a^2+y^4-2*y^2*a^2+a^4)^(1/2)-2*x^2+2*y^2-2*a^2)^(1/2)*UINF
-1/2*(2*(x^4+2*x^2*y^2+2*x^2*a^2+y^4-2*y^2*a^2+a^4)^(1/2)-2*x^2+2*y^2-2*a^2)^(1/2)*UINF
1/2*(-2*(x^4+2*x^2*y^2+2*x^2*a^2+y^4-2*y^2*a^2+a^4)^(1/2)-2*x^2+2*y^2-2*a^2)^(1/2)*UINF
-1/2*(-2*(x^4+2*x^2*y^2+2*x^2*a^2+y^4-2*y^2*a^2+a^4)^(1/2)-2*x^2+2*y^2-2*a^2)^(1/2)*UINF

one of the deravites is the folowwing (s)
x=-5:1:5
y=-5:1:5
s=1/4/(-2*(x.^4+2*x.^2*y.^2+2*x.^2*a.^2+y.^4-2*y.^2*a.^2+a.^4).^(1/2)-2*x.^2+2*y.^2-2*a.^2).^(1/2)*UINF*(-1/(x.^4+2*x.^2*y.^2+2*x.^2*a.^2+y.^4-2*y.^2*a.^2+a.^4).^(1/2)*(4*x.^2*y+4*y.^3-4*y*a.^2)+4*y)
a=1
UINF=1
plot(x,y,s)

x =

-5 -4 -3 -2 -1 0 1 2 3 4 5y =

-5 -4 -3 -2 -1 0 1 2 3 4 5

? Error using ==> mtimes
Inner matrix dimensions must agree.
i can't draw it why??

 

[Maurice M ben]

If you follow the message given by MATLAB , YOU SEE THIS:

? Error using ==> mtimes
Inner matrix dimensions must agree. HERE BECAUSE YOU FORGET A DOTE OR SOMETHING
You have missed to mesh you data
Matlab does not recognise a paire of data without this code
[x,y]=mesh(x=data, y=data) for example [x,y]=mesh(x=0:1:10, y=0:1:10) this should be written before the equations;
Also you have missed something in the equation that will plot your graph
for, example you x and y are varying and you devided 1/ by the rest of the equation you nedd to this ( 1./equation in your equation you missed the dote ) don't forget the dote after 1
Try this. I think this will help you to solve your problem, GOOD LUCK