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Fluid Flow: Principal Rates of Deformation/Principal Axes 
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#1
Mar1907, 08:26 AM

P: 9

Hi all,
I've been stumped on this problem for over a month. Any guidance would alleviate my overwhelming frustration. Here is the original problem statement: Find the principal rates of deformation and principal axes for the flow given by: u = (x,y) and v = 0, satisfying the continuity equation (density = rho = constant) [tex] \frac{\partial u_i}{\partial x_i} = 0[/tex] Attached to this post is my attempt to work out the solution. I'm not sure how to proceed on, so your help would be greatly appreciated. Thanks! 


#2
Mar1907, 10:14 AM

P: 11

Anyhew, your solution seems correct up till and including the principal directions (with the note that u=u(y) only, i.e. 2D shear flow). When I calculate the principal values and directions in the old fashion way (as eigenvalues/eigenvectors of the strain rate tensor), I get the same directions, but principal values are +/ du/dy. Cheers //Rope 


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