In fluid mechanics, the circulation around a curve C is defined as r = u. dx, where u(x) is the velocity of the fluid at position x. When C is a closed curve, I' quantifies how much the fluid is flowing around C. Circulation is useful for studying vortices, like hurricanes and tornadoes, and other rotational flows. Consider the following two velocity fields: A. flow into a drain: ax ay u(x, y) = - 2 2 + 2 ' 2 2 + 32 where a > 0 is a constant. B. vortex: (-By, 12x) , Vx2+ 32 ro, where ro > 0, S, b are constants. 1. Assume that the vortex (B) velocity u is continuous. What does this imply about the constants , b, and ro? 2. Sketch the field portrait of A and B. 3. The field portrait illustrates the direction of u but not its magnitude, i.e. the speed of the fluid. How does the fluid speed depend on the distance from the origin in A and B