1.

The incorrect statement regarding the downwash for a single horseshoe vortex in Prandtl’s lifting line theory is____(a) Downwash has contribution from trailing vortices(b) Downwash becomes infinite at the tips(c) Downwash is given by w=\(\frac {-\Gamma}{4\pi } \frac {b}{(\frac {b}{2})^2-y^2}\)(d) The contribution of two semi-infinite trailing vortices is same as an infinite vortexThis question was addressed to me in class test.Question is taken from Prandtl’s Classical Lifting-Line Theory topic in portion Flow over Airfoils over Finite Wing of Aerodynamics

Answer»

Right choice is (d) The contribution of two semi-infinite trailing VORTICES is same as an infinite vortex

The explanation is: The downwash along the BOUND vortex is induced by the two semi-infinite trailing vortices, which is not same as that of an infinite trailing vortex. It acts downwards on the wing. When calculated USING the Biot-Savart law, it COMES equal to w=\(\frac {-\Gamma}{4\pi } \frac {B}{(\frac {b}{2})^2-y^2}\), which becomes infinite at the tips (±b/2) if we consider only a single horseshoe vortex.


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