# Aerodynamics Questions and Answers – The Vortex Filament, Biot-Savart Law, Helmholtz Theorem

«
»

This set of Aerodynamics MCQs focuses on “The Vortex Filament, Biot-Savart Law, Helmholtz Theorem”.

1. Is vortex filament is a very thin strip?
a) True
b) False

Explanation: A vortex filament is a very thin strip of vorticity in x-y plane. The small thickness assumption will be used to characterize the filament by its center line curve. Mass conservation and material transport of vorticity are used to describe variation in local thickness and vorticity.

2. Is thin strips of vorticity are unstable to disturbances and tend to roll up?
a) False
b) True

Explanation: Vortex filament is well known that thin strip of vorticity are unstable to disturbance and tend to roll up. Here we test this using our model, we study two cases a parabolic vortex filament and a circular vortex filament.

3. Is weak external velocity, rolling up of the vortex filament?
a) True
b) False

Explanation: The weak external velocity, rolling up of the vortex filament occurs as expected, but in the presence of strong external velocity field, the filament is extremely stretched out and flattened, preventing all rolling up activities.

4. Is circular filament is of constant thickness?
a) True
b) False

Explanation: The closed filaments, a circular filament of constant thickness and vorticity is in self equilibrium, this is easily verified using z=e, consider straight filaments placed on the z-axis with constant vorticity along the curve.

5. Is vortex filament equation can be modified to include the effects of point vortices?
a) False
b) True

Explanation: The vortex filament equation can be modified to include the effects of point vortices, here we place two point vortices symmetrically inside a circular vortex filament. Initially, the point vortices just rotate about the center of the circular vortex filament.

6. Is Helmholtz’s theorems apply to inviscid flows?
a) True
b) False

Explanation: Helmholtz’s theorems apply to inviscid flows, in observation of vortices in real fluid the strength of the vortices always decays gradually due to the dissipative effect of viscous forces. Thus, it only applied to inviscid flows.

7. Is strength of a vortex tube vary with time?
a) False
b) True

Explanation: The strength of a vortex tube does not vary with time, fluid elements lying on a vortex line at some instant continue to lie on that vortex line. More simply, vortex lines move with the fluid, also vortex lines and tubes must appear as a closed loop.

8. Is Biot-savart law is used for computing the resultant magnetic field?
a) True
b) False

Explanation: The biot-savart law is used for computing the resultant magnetic field at position r in 3D –space generated by a steady current. Steady current is a continual flow of charges which does not charge wit time and the charge neither accumulates nor depletes at any point.

9. Is integral is usually around a closed curve?
a) True
b) False

Explanation: The integral is usually around a closed curve since stationary electric currents can only flow around closed paths when they are bounded. However, the law also applies to infinitely long wires as used in the definition of the SI unit of electric current.

10. Is 2D version of Biot-Savart equation is used, when the sources are invariant in one direction?
a) True
b) False 