MATLAB: Distribution graph velocity : how to make simple paraboloid of revolution

Question

Hello Guys,

I have a simple problem. You remember the mechanics of fluids? To calculate the velocity distribution in a circular tube (actual fluid) use the equation "u" and then to further develop the known Hagen-Poiseuille equation. If we consider the tube without inclination have this equation:

 u = (-N 2 - R 2) / 4 * mi

if I assign values to 'r' and 'mi', we have a paraboloid of revolution that describes the velocity distribution of the fluid in the tube. How can I make this chart in matlab?

See the example:

 a = [-50:50];
 u = -((a.^2-(0.001^2))/(4*1.485));
 plot(u,a)

or

 syms x
 ezplot(-((a^2-0.001^2)/(4*1.485)))

I put an fig in attach

https://docs.google.com/file/d/0B9JmyPHF_ZMPTFVmOWw3bk9FR1E/edit?usp=sharing

Thank you in advance for all the help!

Answer 1

hi,

i think your method works for this type of problems, try :

 N=40;         % Discretization
 Vmax=20;      % 20m/s
 xc=0;
 yc=0;
 zc=0;
 R=0.5;        %  radius of the tube
 [x,y,z]=ellipsoid(xc,yc,zc,R,R,Vmax,N);
 z(z<0)=0;     %  trick to truncate the unwanted elements
 figure, surf(x,y,z), shading interp
 xlabel('X axis (m)');
 ylabel(' Y axis (m)');
 zlabel(' Velocity (m/s)');
 title(' Velocity profile');