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The velocity induced by an infinite vortex filament, with strength Γ at some point is correctly given as______ (r, h are the distance and height to the point respectively).(a) V=\(\frac {\Gamma }{2\pi h}\)(b) V=\(\frac {\Gamma }{2\pi r}\)(c) V=\(\frac {\Gamma }{2h}\)(d) V=\(\frac {\Gamma }{2r}\)I had been asked this question in quiz.My question is from The Vortex Filament, the Biot-Savart Law, Helmholtz Theorem topic in division Flow over Airfoils over Finite Wing of Aerodynamics

Answer»

Right answer is (a) V=\(\frac {\Gamma }{2\pi h}\)

For explanation: The velocity induced at a POINT at a distance r (PERPENDICULAR distance h) from an INFINITE, straight vortex filament is calculated using Biot-Savart law. This is same as the velocity for a point vortex, which is V=\(\frac {\Gamma }{2\pi h}\) where Γ is the strength of the vortex filament.


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