Make a vector plot of the velocity field in polar coordinates

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Marina Markaki 2021-5-7

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评论： Marina Markaki 2021-5-8

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')

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Answer 1

Chad Greene 2021-5-7

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https://ww2.mathworks.cn/matlabcentral/answers/824400-make-a-vector-plot-of-the-velocity-field-in-polar-coordinates#answer_694565

Can you use cart2pol to convert the coordinates and vector components to polar coordinates?

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Marina Markaki 2021-5-8

在 MATLAB Online 中打开

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')