clear, all clc;
x = linspace(-1,1);
y = linspace(-1,1);
U = 1;
for i = 1:length(x)
for j = 1:length(y)
xx(i,j) = x(i);
yy(i,j) = y(j);
rad(i,j) = sqrt(x(i)^2 + y(j)^2);
if x(i) > 0
theta(i,j) = atan(y(j)/x(i));
elseif x(i) <0 && y(j) >= 0
theta(i,j) =atan(y(j)/x(i))+pi;
elseif x(i) < 0 && y(j) < 0
theta(i,j) = atan(y(j)/x(i))-pi;
elseif x(i) == 0 && y(j) < 0
theta(i,j) = pi/2;
else
theta(i,j) = -pi/2;
end
psi(i,j) = U *rad(i,j)*sin(theta(i,j));
phi(i,j) = U*rad(i,j)*cos(theta(i,j));
end
end
contourf(xx,yy,psi,-1:0.2:1,'k','LineWidth',1.5), hold on�
contour(xx,yy,phi,-1:0.2:1,'r','LineWidth',1.5)
axis image, hold off
legend('streamlines','potential')
title('Uniform stream in x-direction')
xlabel('x-coordinate'), ylabel('y-coordinate')
axis square;