Problem 3: Fluid Deformation and Rotation in Flow
A flow in the narrow gap between large parallel plates is shown. The velocity field in the narrow gap is given by \[\mathbf{V} = \frac{U}{h} y \hat{i}\] where \(U = 4\) mm/s and \(h = 4\) mm. At \(t = 0\) line segments $ac$ and $bd$ are marked in the fluid to form a cross as shown.
(1) Evaluate the positions of the marked points at $t = 1.5$ s and sketch for comparison using appropriate software.
(2) Calculate the rate of angular deformation and the rate of rotation of a fluid particle in this velocity field. Comment on your results.
1 This problem set contains 6 problems, and your final score will be based on the 4 problems on which you earned the highest scores.