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

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

[Youssef Khmou]

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');

[Artur M. G. Lourenço]

O/ Thank you so much! From here I think I can move forward only. Just leave it on the lack horinzontal and insert my data. Thank you again.

Answer 2

[Artur M. G. Lourenço]

sorry 'u' is:

u = (-a^2 - r^2) / 4 * mi

Answer 3

[Youssef Khmou]

hi here is an example before staring to answer the problem :

the veolcity is defined as :

V(r)= Vmax*(1-r²/R²), R is the radius of the tube :

 R=.50 ;  %radius in meters:
 r=linspace(-R,R,30);  %  varying radius
 Vmax=20 ; % suppose that the maximum velocity of fluid is 20 m/s

 V=Vmax*(1-r.^2/R^2);
 figure, bar(r,V);
 figure, plot(V,r); xlabel(' Velocity'),ylabel(' varying radius')

[Artur M. G. Lourenço]

hi thanks! I think I have to solve algebraically before using integral

[Youssef Khmou]

hi can you explain more the issue? you mean 3D paraboloid like in the figure?

[Artur M. G. Lourenço]

hi yes just it

[Youssef Khmou]

ok try this way first :

 R=.50 ;  %radius in meters:
 r=linspace(-R,R,30);  %  varying radius
 Vmax=20 ; % suppose that the maximum velocity of fluid is 20 m/s
 V=Vmax*(1-r.^2/R^2);
 VV=sqrt(V'*V);
 figure, surf(r,r,VV), shading interp,

[Artur M. G. Lourenço]

almost! Missing only the base should be circular. I am trying here to change that!

[Artur M. G. Lourenço]

see this, my graph looks like a half of cylinder

 [x, y, z] = ellipsoid(0,0,0,5.9,3.25,3.25,30);
 surfl(x, y, z)
 colormap copper
 axis equal

Answer 4

[Artur M. G. Lourenço]

i can´t do it