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

Asked by Artur M. G. Lourenço

on 25 May 2013

### Youssef Khmou (view profile)

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

Thank you in advance for all the help!

### Youssef Khmou (view profile)

on 26 May 2013
Edited by Youssef Khmou

### Youssef Khmou (view profile)

on 26 May 2013

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
xlabel('X axis (m)');
ylabel(' Y axis (m)');
zlabel(' Velocity (m/s)');
title(' Velocity profile');```

#### 1 Comment

Artur M. G. Lourenço

### Artur M. G. Lourenço (view profile)

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.

### Artur M. G. Lourenço (view profile)

Answer by Artur M. G. Lourenço

### Artur M. G. Lourenço (view profile)

on 25 May 2013

sorry 'u' is:

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

### Youssef Khmou (view profile)

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:
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')```

Youssef Khmou

### Youssef Khmou (view profile)

on 25 May 2013

ok try this way first :

``` R=.50 ;  %radius in meters:
Vmax=20 ; % suppose that the maximum velocity of fluid is 20 m/s
V=Vmax*(1-r.^2/R^2);
VV=sqrt(V'*V);
Artur M. G. Lourenço

### Artur M. G. Lourenço (view profile)

on 26 May 2013

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

Artur M. G. Lourenço

### Artur M. G. Lourenço (view profile)

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```

### Artur M. G. Lourenço (view profile)

Answer by Artur M. G. Lourenço

on 26 May 2013

i can´t do it