Question

The incorrect statement regarding Helmholtz theorems is____

(a) Valid for all inviscid flows

(b) Γ remains constant along vortex filament

(c) Describes vortex behavior

(d) Vortex filament forms a closed loop or extends till the boundaries of the fluid

The question was posed to me in an internship interview.

My question is based upon The Vortex Filament, the Biot-Savart Law, Helmholtz Theorem topic in section Flow over Airfoils over Finite Wing of Aerodynamics

Answer 1

Correct option is (a) Valid for all inviscid flows

To explain I would say: The Helmholtz theorems are valid for inviscid, incompressible flows and describe the vortex behavior. According to these theorems, the strength of vortex filament is constant along its length and a vortex filament cannot end in a fluid. According to the latter one, the filament must form a closed loop or extend till the boundaries of the fluid.