Consider two-dimensional flow near a solid wedge with angle , as in Fig. P5.5. The flow along the top of this indefinitely long object can

Consider two-dimensional flow near a solid wedge with angle βπ, as in Fig. P5.5. The flow along the top of this indefinitely long object can be described using the (x, y) coordinates shown. If the fluid has negligible viscosity, then for x ≥ 0 it is found that

where C is a constant and m = β/(2 − β).

(a) Determine v_y(x, y).

(b) For what values of m and β (if any) is such a flow irrotational?

(c) Calculate the stream function ψ(x, y) for m = 1⁄3 (a 90° wedge) and plot streamlines that correspond to several values of ψ⁄C.

vx (x) = Cx (P5.5-1)