3 We covered the idea of a streamfunction in Cartesian (x,y) coordinates. In a similar fashion, when using polar coordinates, (r, ) one may define an appropriate streamfunction to represent the velocity (Ur, Up). From our general notes on NS eqs, we have the mass balance in 2D polar coordinates gives: 1 a Vu= = 0 rae Define a stream function 1 ur = ue = raa ar 1 due rar (ru) + (a) Show that for any choice y(r, o) the mass balance is satisfied. Find the streamfunctions for the following velocity fields: (b) u = U(1 y2/h2), v , v = 0 (c) Ur = 0 ; Ug = -C/r