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

 

[DeeNos]

I would first clarify the context and assumptions of the problem. Is this a two-dimensional or three-dimensional flow? Is the flow steady or unsteady? What is the physical significance of the stream function and the constant U? Once these details are established, I would approach the problem by first defining the variables and constants in Matlab. Then, I would use the built-in functions for plotting stream lines, such as "streamslice" or "streamline," to visualize the flow pattern described by the equation. It may also be helpful to plot the velocity field using the "quiver" function to better understand the behavior of the flow. Additionally, I would consider varying the value of the constant U and the plate length 'a' to investigate their effects on the stream lines. Overall, using Matlab's powerful visualization tools, I would be able to create a clear and informative plot of the stream lines described by this equation.