Superpose a uniform stream of velocity V_∞ and a line source of strength V̇/L at the origin. This generates potential flow over a two-dimensional half-body called the Rankine half-body (Fig. P10–71). 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 V̇/L.

(b) Generate an expression for half-height b as a function of V_∞ and V̇/L.

(c) Generate an equation for the dividing stream function in the form of r as a function of θ, V_∞, and V̇/L. 

(d) Generate an expression for stagnation point distance a as a function of V_∞ and V̇/L. 

(e) Generate an expression for (V/V_∞)² (the squared nondimensional velocity magnitude) anywhere in the flow as a function of a, r, and θ.

FIGURE P10–71

Transcribed Image Text:

V y a b X