How to plot to get the figure?

%Creation of streamline around the circle
a = 6;   % Radius of Circle
V_i =50;    % Velocity
G = 20;     % Gramma (Circulation)
x=[-a*2:a/3:a*2];
[x]=meshgrid(x);
y=x';

for i=1:length(x);
   for k=1:length(x);
      if sqrt(x(i,k).^2+y(i,k).^2)<a;
         x(i,k)=0;
         y(i,k)=0;
      end
   end
end

r=sqrt(x.^2+y.^2);
% theta=atan2(y,x);
theta =pi-asin(-G/(4*pi*a*V_i));
ur=V_i*cos(theta).*(1-a^2./(r.^2));
ut=-V_i*sin(theta).*(1+a^2./(r.^2))-G./(2*pi*r);
u=ur.*cos(theta)-ut.*sin(theta);
v=ur.*sin(theta)+ut.*cos(theta);

%Creating The Filled Circle
t_r  = 0:.1:2*pi;
xxx = a*cos(t_r);
yyy = a*sin(t_r);

%Vectors and Filled Circle plotting
figure(2)
hold on
quiver(x,y,u,v)
fill(xxx,yyy,'y')
axis square
title('streamline')
grid off

[Myo Gyi]

Somebody help me please. I want to make three figure. I have no idea to get these figure.

https://ocw.mit.edu/courses/mechanical-engineering/2-25-advanced-fluid-mechanics-fall-2013/potential-flow-theory/MIT2_25F13_SolutionMagnus.pdf

[Myo Gyi]

Help me please.

http://www.flowillustrator.com/fluid-dynamics/case-studies/asymmetric-potential-flow-past-a-cylinder.php

Answer 1

[darova]

I just used these formulas from this page

The code i used

clc,clear

[x,y] = meshgrid(-3:0.2:3);

a = 1;                  % cylinder radius
U = 1;                  % flow velocity
G = 2.5*pi;             % circulation

xmy = x.^2 - y.^2;
xpy = x.^2 + y.^2;
u = U*(1 - xmy*a^2./xpy.^2) + G/pi*y./xpy;  % horizontal velocity
v = -2*U*x.*y*a^2./xpy.^2 - G/pi*x./xpy;    % veftical velocity

[xc,yc] = pol2cart(deg2rad(0:10:360),1);
plot(xc,yc,'r','linew',2)
streamline(x,y,u,v,x(:,1),y(:,1))
streamline(x,y,u,v,x(1,:),y(1,:))

Results

[Myo Gyi]

Thank You very much for your answer sir.. But I want to make the above figure, using the equation of Gramma = 4piU sir.. Thanks a lot.