p1140 - 48 CHAPTER 11. POTENTIAL FLOW 11.40 Chapter 11,...

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48 CHAPTER 11. POTENTIAL FLOW 11.40 Chapter 11, Problem 40 For the superposition of a potential vortex and a point source, the velocity potential is φ ( r, θ )= Q 2 π f nr + Γ 2 π θ So, regarding φ as a constant, the equipotentials are given by Q 2 π f nr = φ Γ 2 π θ = f nr = 2 πφ Q Γ θ Q Therefore, the equation of an equipotential is r = r o e Γ θ /Q ,r o e 2 /Q For Q = 2 Γ ,wehave r r o = e θ / 2 o e πφ / Γ Figure 11.12 displays this equipotential for 0 θ 4 π . y x .............................................................................................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . .
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