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# MCQs on The Vortex Filament, the Biot-Savart Law, Helmholtz Theorem – 1

1 - Question

In Biot-Savart law, the circulation taken about any path enclosing the vortex filament is____

a) Constant

b) Depends on the local strength

c) Zero

d) Path-dependent

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aExplanation: The circulation taken about any path enclosing the vortex filament is a constant. This is true for a straight as well as curved filament. (Kelvin’s circulation theorem).

2 - Question

A curved vortex filament does not exist.

a) True

b) False

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bExplanation: The filament can take any shape, curved, straight, round etc. Hence, the given statement is false. In general, we assume a curved vortex filament.

3 - Question

Which is the incorrect analogyout of the following regarding Biot-Savart law?

a) Induced velocity: Magnetic induction

b) Vortex Filament: Current-carrying Wire

c) Vorticity: Velocity

d) Aerodynamics: Electromagnetism

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cExplanation: The Biot-Savart law holds an analogy in aerodynamics and electromagnetism. The induced air current (induced fluid velocity) for a vortex filament can be thought analogous to the induced magnetic field (magnetic induction) for a current-carrying wire. The circulation can be thought of as magnetic flux and vorticity is like the current.

4 - Question

Biot-Savart law can be used to describe inviscid, incompressible flows.

a) True

b) False

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aExplanation: Biot-Savart law is a consequence of potential theory and potential theory provides description for electromagnetic fields and inviscid, incompressible flows as well. Thus, it is true.

5 - Question

Select the incorrect statement regarding the terminology used in the study of incompressible flow over finite wings.

a) Induced drag is finite

b) Circulation is constant

c) Downwash is absent

d) Vorticity induces velocity

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cExplanation: Due to the presence of downwash, lift is no more vertical. The induced drag is caused by the non-vertical component of lift. Circulation is constant, as the Kelvin’s circulation statement states. The vortex filament induces velocity, which depends on the strength of vortex (constant circulation).

6 - 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=Γ2πh

b) V=Γ2πr

c) V=Γ2h

d) V=Γ2r

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aExplanation: 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=Γ2πh where Γ is the strength of the vortex filament.

7 - Question

Identify the correct expression for the induced velocity by a semi-infinite vortex filament at a point. (Where symbols have their usual meaning)

a) V=Γ4h

b) V=Γ2h

c) V=Γ2πh

d) V=Γ4πh

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dExplanation: The velocity induced by a semi-infinite vortex filament with strength Γ at a point which is a perpendicular distance h, is given by the Biot-Savart law. The result is V=Γ4πh.

8 - 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

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aExplanation: 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.

9 - Question

A condition in which the wing has different values of α along the span is called as ______

a) Washout

b) Geometric twist

c) Aerodynamic twist

d) Washin

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bExplanation: Some wings are twisted i.e. they have different geometric angle of attack at different places along the span-called geometric twist. The other terms do not mean the same.

10 - Question

If the geometric angle of attack is higher at the tip than the root, it is called as ______

a) Washout

b) Geometric twist

c) Aerodynamic twist

d) Washin

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dExplanation: For a finite wing, the geometric angle of attack can be different at different locations along the span. If the geometric angle of attack is higher at the tip than the root it is called washin. Washout is the condition when angle of attack at the tip is lower than at the root is called washout.

11 - Question

Having a different zero angle of attack along span-wise locations is termed as______

a) Washout

b) Geometric twist

c) Aerodynamic twist

d) Washin

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cExplanation: For a finite wing, the zero lift angle of attack can vary along the span-wise direction for different airfoil sections. This condition is known as aerodynamic lift.

12 - Question

The lift distribution goes to zero at the tips for the finite wings.

a) False

b) True

c) Only true for elliptical wings

d) Only true for rectangular wing

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bExplanation: For a finite wing, there is pressure equilibrium from the bottom to the top of the wing, which makes the lift at the tips zero. This is true for all wing shapes.