Playing with the deformation and strain rate tensors 1)

Playing with the deformation and strain rate tensors 1) For a 2D flow (z velocity component is zero so are all derivatives with respect to the z axis) write down the components of the strain rate tensor 2) The following strain rate tensor is NOT valid for incompressible flow. Why? 3) Could the following be a strain rate tensor? If yes explain the two properties that this tensor satisfies that makes it valid. If no explain why not. a) 4) Give an example of a 3D velocity gradient (i.e. the deformation tensor) that corresponds to a purely rotational flow 5) Given the following strain rate tensors draw a square shaped fluid element and show the shape the fluid element would take after being deformed by the fluid flow a) b) c)
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