xdot=goveq(r,x,flag)

% Author: Housam Binous

% Velocity Profile of Laminar Flow of Carreau fluid in a Pipe

% National Institute of Applied Sciences and Technology, Tunis, TUNISIA

% Email: [e-mail]

% governing equation is the z-component of the equation of motion in
% cylindrical coordinates and the non-Newtonian constitutive equation

function xdot=goveq(r,x,flag)

global lamda n nu0 nuI rend

if isempty(flag),

dP=100;L=50;

xdot(1)=dP/(L)-x(1)/r;
xdot(2)=-x(1)/x(3);
xdot(3)=(x(3)-nuI)/(nu0-nuI)-1/(1+(lamda*(x(1)/x(3)))^2)^((1-n)/2);

xdot=xdot';

else
    
   	M = zeros(3,3);
    
    M(1,1)=1;
    M(2,2)=1;
    
    xdot = M;

end