# Make a vector plot of the velocity field in polar coordinates

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Marina Markaki on 7 May 2021
Commented: Marina Markaki on 8 May 2021
After plotting contour lines of the pressure, which I did easily, I am asked to make a vector plot of the velocity field. The pressure is given as P=(c*(R1/R2)-(1-c))*log((X.^2+Y.^2).^(1/2))/log(R2/R1)+1-c and P=(c*(R1/R2)-(1-c))*log(r)/log(R2/R1)+1-c in polar coordinates, where c, R1 and R2 are constants. I was able to make the vector plots of the cartesian part using this code but I do not know how to do it in polar coordinates. Thank you.
c=0.1;
R1=1;
R2=10;
x = 1:10;
y = 1:10;
[X,Y] = meshgrid(x,y);
P=(c*(R1/R2)-(1-c))*log((X.^2+Y.^2).^(1/2))/log(R2/R1)+1-c;
p_x=(c*(R1/R2)-(1-c))*(X/(X.^2+Y.^2))/log(R2/R1);
p_y=(c*(R1/R2)-(1-c))*(Y/(X.^2+Y.^2))/log(R2/R1);
figure;
quiver(X,Y,p_x,p_y)
title('Velocity field plot')

Chad Greene on 7 May 2021
Can you use cart2pol to convert the coordinates and vector components to polar coordinates?
Marina Markaki on 8 May 2021
This is the code that I wrote but it gives me the error that U and V must be the same size.
c=0.1;
R1=1;
R2=10;
x = -10:10;
y = -10:10;
[theta,rho] = cart2pol(x,y);
P=(c*(R1/R2)-(1-c))*log(rho)/log(R2/R1)+1-c;
p_r=(c*(R1/R2)-(1-c))./(rho*log(R2/R1));
p_theta=0;
figure;
quiver(theta,rho,p_r,p_theta)
title('Velocity field plot')