MATLAB: How to 2D plot using the equation of fi and zi

2d plot

Best Answer

The wikipedia page plots only the polar sector 2*pi/(2*n) of the stream lines / potential

The second plot is the full picture.

n = 3/2;
A = 1;
x=linspace(-1,1,21);
y=linspace(-1,1,21);
[X,Y]=ndgrid(x,y);
Z=X+1i*Y;
W = A*Z.^n;
phi = real(W);
psi = imag(W);
close all
subplot(2,1,1);
hold on
plot(phi,psi,'b');
plot(phi.',psi.','g');
axis equal
subplot(2,1,2);
hold on
contour(x,y,phi.',20,'b');
contour(x,y,psi.',20,'g');
axis equal

Related Solutions

MATLAB: How to change the legend color

First, create a handle to the legend object, then change whatever properties you want using the options in Legend Properties.

Example (with your code) —

n = 2/3;
A = 1;
r = linspace(0,0.4,30);
th = linspace(0,2*pi,100);
[R, TH] = meshgrid(r,th);
fi = A*R.^n.*cos(n*TH);
zi = A*R.^n.*sin(n*TH);
[X,Y] = pol2cart(TH,R);
contour(X,Y,fi,'r')
hold on
contour(X,Y,zi,'b')
hold off
xlabel x-axis
ylabel y-axis
title('n = 2/3: flow around a right corner')
hl = legend('\phi','\psi');
set(hl, 'TextColor','r', 'Color','g', 'EdgeColor','b')

Experiment to get the result you want.

MATLAB: Is it always showing an error as phi is an undefined function for input argument type char ?

Sofiya, in your code above some of the variable names contain empty spaces (if the copy-paste worked), which is not valid. E.g.

 phi UniFlow

needs to be changed to, e.g.,

 phi_UniFlow

Check out:

 U = 1; % Uniform stream % GRID:
 x = -2:.02:2;
 y = -2:.02:2; 
 for m = 1:length(x) 
    for n = 1:length(y) 
        xx(m,n) = x(m); 
        yy(m,n) = y(n); % Velocity potential function: 
        phi_UniFlow(m,n) = U * x(m); % Stream function:
        psi_UniFlow(m,n) = U * y(n); 
    end
 end % Plots % Uniform stream in x direction: 
 contour(xx,yy,psi_UniFlow,[-2:.5:2],'k'),
 hold on 
 contour(xx,yy,phi_UniFlow,[-10:1:5],'r') 
 axis image
 hold off 
 title('Uniform stream in x direction') 
 xlabel('x')
 ylabel('y')

Best Answer

Related Solutions

MATLAB: How to change the legend color

MATLAB: Is it always showing an error as phi is an undefined function for input argument type char ?

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