A velocity field is given by vec$(V)=3ycos(t)hat()-9xcos(t)hat(j)$ Is this an incompressible and irrotational flow? Justify your answer. Consider a double pipe heat exchanger where a cold fluid is passed through the tube side $($outer diameter Di $)$ and the hot fluid is passed through the shell side $($anulus$).$ The inside diameter of the shell is Do$.$ Apply differential control volume analysis to derive the velocity profile of the hot fluid through anulus. Assume Newtonian incompressible fluid with constant property. Use common nomenclature.