Consider an ideal, incompressible flow described with polar coordinates (r,p,7) with corresponding velocity components u=(u,v,w), where the flow is two-dimensional (w=0). i. i. Define a stream function y and a

velocity potential o and relate them to u and v.ii. Suppose the flow is purely circular (u=0, v#0). Find v(r,q) and relate the derived constants (s) to the circulation T. This fundamental solution is called a vortex. ii. Consider an ideal, incompressible flow model of a tornado comprised of a vortex and a two-dimensional sink.i///. Find p, o, u, v and [º] for this model .ii. Sketch the streamlines. iii. Use Bernoulli's equation to find an expression for the pressure difference between points located at different radial positions, i.e., p(r.)-p(r.). What happens as r,→0?