Problem 3.8. If a trace (say a dye) of concentration c is introduced into a fluid flow and the dye does not diffuse, then c satisfies the conservation equation De 0 (3.10) where D/De denotes the substantial derivative, which simply states that the dye follows the fluid. Assume the velocity field is given by u (x ) = (3.12) (a) Sketch the streamlines of the flow. In which direction is the local fluid velocity? (b) Now assume a thin cylindrical ring of dye (see figure above) of initial thicknessb, and radius R (with b