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Asked by Artur M. G. Lourenço on 25 May 2013

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!

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Answer by Youssef KHMOU on 26 May 2013

Edited by Youssef KHMOU on 26 May 2013

Accepted answer

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 on 27 May 2013

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 by Youssef KHMOU on 25 May 2013

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')

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Youssef KHMOU on 25 May 2013

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 on 26 May 2013

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

Artur M. G. Lourenço on 26 May 2013

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

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