Question

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 1

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.