Question: 1. Define vorticity in a fluid and obtain an expression for it at a point with polar coordinates (r, θ), the motion being assumed two-dimensional. From the definition of a line vortex as irrotational flow in concentric circles determine the variation of velocity with radius and thus obtain the stream function (ψ), and the velocity potential (φ), for a line vortex. (U of L)
2. A sink of strength 120 m2 s-1 is situated 2 m downstream from a source of equal strength in an irrotational uniform stream of 30 m s-1. Find the fineness ratio of the oval formed by the streamline ψ = 0.