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

  • Thread starter Thread starter kingjames
  • Start date Start date
  • Tags Tags
    Matlab Plotting
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
3 replies · 7K views
kingjames
Messages
2
Reaction score
0
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
 

Discussion

Physics news on Phys.org
kingjames said:
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.
 
Mark44 said:
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??
 
Last edited:
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