# 3D matrix and 3d plot in matlab

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H-M on 17 May 2020
Commented: Walter Roberson on 2 Jun 2020
I want to use the repmat function to copy the velocity profile along a pipe for 30 times in order to make the geometry of pipe.
my code below generate the velocity profile for Poisuielle flow inside the pipe using meshgrid and mesh functions.
R = 0.003/2; %pipe dia.
yy=linspace(-R,R,50);
xx=yy';
r=sqrt(xx.^2+yy.^2);%pipe redius as function of x , y
z=-(f1.a0)*(R^2-(xx.^2+yy.^2))/0.016;% velocity profile in z direction(along the pipe),f1.a0=constant
[X1,Y1]=meshgrid(xx,yy);
figure
mesh(X1,Y1,z)
colorbar
contour(X1,Y1,z)
##### 2 CommentsShowHide 1 older comment
darova on 20 May 2020
Can you make a simple sketch in paint? Walter Roberson on 20 May 2020
f1.a0 = -3; %to have **some** value
R = 0.003/2; %pipe dia.
yy=linspace(-R,R,50);
xx=yy;
d = linspace(0,1,30); %distance along pipe
[XX,YY,DD] = meshgrid(xx, yy, d);
r = sqrt(XX.^2+YY.^2);%pipe redius as function of x , y
VV = -(f1.a0)*(R^2-(XX.^2+YY.^2))/0.016;% velocity profile in z direction(along the pipe)
levels = linspace(min(VV(:)), max(VV(:)), 10);
for K = 1 : length(levels)
isosurface(XX, YY, DD, VV, levels(K));
end
xlabel('x');
ylabel('y');
zlabel('distance along pipe');
title('velocity profile')
colorbar;
Walter Roberson on 2 Jun 2020
I just noticed an unnecessary calculation. You never use the r you calculate. I suggest
r2 = XX.^2+YY.^2; %pipe radius squared as function of x , y
VV = -(f1.a0)*(R^2-r2)/0.016;% velocity profile in z direction(along the pipe)
This should not change the calculation.
With the code that uses x and y coordinates arranged in a square, the corners have negative velocity not 0. Are you trying to model a circular pipe? If so then I would suggest using polar coordinates.