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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!

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# Fluid Flow: Principal Rates of Deformation/Principal Axes

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