Shear stress from velocity profile
I was trying to calculate the shear stress due to fluid flow inbetween two parallel plates from the velocity profile taken from the middle of the flow channel (along vertical axis 'y') using comsol. The solution i got is two times the analytical solution i have calculated. The analytical equation i have used here is
where tou is shear stress, umax is the max velocity
h is half of the distance between plates.
The calculation with velocity profile from comsol is done by
du/dy, i calculated with excel from the u,y values in the velocity profile.
the velocity profile is parabolic and looks laminar.
is that i am doing something wrong?
I don't remember the formulas but, if i understand well your problem, it is impossible that for the parabolic velocity profile the derivative at wall is equal to the one from the linear profile. Hence you should check your analytical formula for the stress (just take by yourself the derivative of the analytic velocity profile)
I agree with the previous poster. I think your analytical solution is incorrect. Using a back of the envelope calculation I get a significantly different solution for the shear stress. I am assuming a laminar parabolic flow so depending on conditions my solution may not apply. Also since I mean the back of envelope quite literally I may have made an error.
Assuming your analytical solution is correct I would consider using a finer mesh. I would suggest that you plot your velocity profile against the analytical solution. The profile can look parabolic without truly being parabolic. The problem may simply be that grid resolution or insufficient convergence.
Lastly, your analytical solution may not valid for your Re.
I hope this is helpful. Have a good day.
Thanks very much Paolo & Charles, i think i did a mistake in my analytical equation...it is supposed to be Tou=2*Umax/h*viscosity i dont know in many books they just refer to Umax/h...
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