Superpose a uniform stream of velocity V? and a line

Chapter 10, Problem 66P

(choose chapter or problem)

Problem 66P

Superpose a uniform stream of velocity V∞ and a line source of strength  at the origin. This generates potential flow over a two-dimensional half-body called the Rankine half-body (Fig. P10-1). One unique streamline is the dividing streamline that forms a dividing line between free-stream fluid coming from the left and ;fluid coming from the source, (a) Generate an equation for the dividing stream function ψ dividing as a function of V/L, (Hint: The dividing streamline intersects the stagnation point at the nose of the body.) (b) Generate an expression for half-height b as a function of V∞ and . (Hint: Consider the flow far downstream.) (c) Generate an equation for the dividing stream function in the form of r as a function of 0, V∞ and .(d) Generate an expression for stagnation point distance α as a function of V∞ and . (e) Generate an expression for (V/V∞) (the squared nondimensional velocity magnitude) anywhere in the flow as a function of a, r, and θ.

FIGURE P70-71