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

2013 5 25
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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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Youssef Khmou
Youssef Khmou 2013-5-26
编辑：Youssef Khmou 2013-5-26

0 个投票

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');

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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.

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Youssef Khmou
Youssef Khmou 2013-5-25

0 个投票

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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hi thanks! I think I have to solve algebraically before using integral
Youssef Khmou
Youssef Khmou 2013-5-25
hi can you explain more the issue? you mean 3D paraboloid like in the figure?
Youssef Khmou
Youssef Khmou 2013-5-25
编辑：Youssef Khmou 2013-5-25
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,
almost! Missing only the base should be circular. I am trying here to change that!
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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