3D matrix and 3d plot in matlab

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.

Please help me how to write the repmat to generate the pipe geometry.

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)

[darova]

Here is the result of your code

Can you explain more what are you trying to achieve?

[darova]

Can you make a simple sketch in paint?

Answer 1

[Walter Roberson]

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;

[H-M]

Thanks Walter for your answer.

My goal is to stack the velocity profile together to make a pipe geometry.The final geometry should be in the form of 3d matrix

[Walter Roberson]

VV is the 3d array you asked for, under the assumption that the flow is the same at each distance along the pipe. The isosurface loop is for visualization that the geometry is as desired.

[Walter Roberson]

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.