The velocity field in problem one \[\mathbf{V} = A x \hat{i} - A y \hat{j}\] represents flow in a "corner", where \(A = 0.3\) s\(^{-1}\) and the coordinates are measured in meters. A square is marked in the fluid as shown at \(t = 0\).
(1) Evaluate the new positions of the four corner points when point \(a\) has moved to \(x = 2\) m after \(\tau\) seconds
(2) Evaluate the rates of linear deformation in the \(x\) and \(y\) directions.
(3) Compare area \(a'b'c'd'\) at \(t = \tau\) with area \(abcd\) at \(t = 0\).
(4) Is the flow irrotational, and is the volume of the fluid conserved?
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.