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Please code the graph to become like the picture as shown by using Matlab program and explain flow around a cylinder that accords to the statement exact well only the front of the cylinder. (hint: superposition of a free stream, doublet, and vortex)

Code the picture to become the graph similar to these graphs

Here some useful coding

function potential_ele01

x0=linspace(0,15,20);

y0=linspace(0,10,10);

[x,y]=meshgrid(x0,y0);

[u1,v1]=freestream(x,y,10,0);

[u2,v2]=source(x,y,5,5,100);

[u3,v3]=sink(x,y,12,5,100);

[u4,v4]=flwaroudcorn(x,y,14)

[u5,v5]=doublet(x,y,5,5,600);

[u6,v6]=vortex(x,y,5,5,50);

% u=u1;v=v1;

% u=u2;v=v2;

% u=u3;v=v3;

% u=u4;v=v4;

% u=u5;v=v5;

u=u6;v=v6;

figure(1),clf

quiver(x,y,u,v,0.5),axis equal

xlabel('x')

ylabel('y')

figure(2),clf

streamline(x,y,u,v,linspace(x0(2),x0(2),30),linspace(y0(1),y0(length(y0)),30))

xlabel('x')

ylabel('y')

axis equal

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [u,v]=freestream(x,y,U,V)

for i=1:size(x,1)

for j=1:size(x,2);

u(i,j)=U;

v(i,j)=V;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [u,v]=source(x,y,x0,y0,S)

for i=1:size(x,1)

for j=1:size(x,2);

u(i,j)=(S/2/pi)*(x(i,j)-x0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2);

v(i,j)=(S/2/pi)*(y(i,j)-y0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2);

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [u,v] = flwaroudcorn(x,y,a)

for i=1:size(x,1)

for j=1:size(x,2);

u(i,j)=2*a*x(i,j);

v(i,j)=-2*a*y(i,j);

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [u,v]=doublet(x,y,x0,y0,M)

for i=1:size(x,1)

for j=1:size(x,2);

u(i,j)=1/2*M/pi/((x(i,j)-x0)^2+(y(i,j)-y0)^2)...

-1/2*M/pi*(x(i,j)-x0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2)^2*(2*x(i,j)-2*x0);

v(i,j)=-1/2*M/pi*(x(i,j)-x0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2)^2*(2*y(i,j)-2*y0);

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [u,v]=sink(x,y,x0,y0,S)

for i=1:size(x,1)

for j=1:size(x,2);

u(i,j)=-(S/2/pi)*(x(i,j)-x0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2);

v(i,j)=-(S/2/pi)*(y(i,j)-y0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2);

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [u,v]=vortex(x,y,x0,y0,M)

for i=1:size(x,1)

for j=1:size(x,2);

u(i,j)=1/2*M/pi/((x(i,j)-x0)^2+(y(i,j)-y0)^2)*(y(i,j)-y0);

v(i,j)=-1/2*M/pi*(x(i,j)-x0)/((x(i,j)-x0)^2+(y(i,j)-y0)^2);

end

end

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