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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)

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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