MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

### Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

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

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!

## Products

No products are associated with this question.

## 4 Answers

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');```

## 1 Comment

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 Artur M. G. Lourenço on 25 May 2013

sorry 'u' is:

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

## 0 Comments

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')```

## 6 Comments

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```
Answer by Artur M. G. Lourenço on 26 May 2013

i can´t do it

Contact us