Couette flow between two plate

Hi, how can i plot the velocity profile for steady couette flow between two plates? d^2u/d^2y=(1/2*miu)*dp/dx for dp/dx=[_2,_1,0,1,2] , miu=1

[Image Analyst]

How about the plot function?

plot(velocity, 'b-');

[Garland Garland]

U(y)=1/2*miu*(dp/dx)*y^2+(U_1/2*miu*(dp/dx))y The upper plate moves by U=0.01m/s

Answer 1

[Torsten]

Underlying equation is

d^2u/dy^2 = -G/mu with G = -dp/dx = const

https://en.wikipedia.org/wiki/Couette_flow

 function main
  dpdx = [-2 -1 0 1 2];
  mu = 1.0;
  U = 0.01;
  H = 0.05;
  dy = 0.001;
  np = numel(dpdx);
  y = (0:dy:H).';
  ny = numel(y);
  u = zeros(ny,np);
  for ip=1:np
    u(:,ip) = -dpdx(ip)/(2*mu)*y.*(H-y) + U*y/H;
  end
  plot(y,u)
end

[Garland Garland]

Thank you very much this was very helpful

[Torsten]

Maybe making the plot this way is better:

plot(u,y)
xlabel('Velocity u')
ylabel('Plate height h')

[Garland Garland]

Great