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)
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!
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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');
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')