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kd215

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**fluid mechanics: defition of "shear flow" [rate of deformation tensor]**

I'm studying old undergraduate chemical engineering notes for an exam in grad school. Can't recall what this really means, can anyone explain to me what "off-diagonal elements" means and why the trig function velocities would be or not be "off-diagonal elements". And can you explain what the question is talking about in general.

Problem statement: Consider the velocity field u = (

__[/x],__

__[/y],____[/z]), where:____[/x](x,y,z)=constant*y*z*sin(constant*x)...(similar functions for y and z velocities)__

and question: "Recall that the definition of "shear flow" is one for which the rate of deformation tensor [Δ][/ij] has only off-diagonal elements. Is this shear flow?" (y or n)and question: "Recall that the definition of "shear flow" is one for which the rate of deformation tensor [Δ][/ij] has only off-diagonal elements. Is this shear flow?" (y or n)