Aerodynamics - Flow over Airfoils over Finite Wing Quiz(MCQ)

1 .

The airfoil data can also be called as_____

A)

Flight data

B)

Wing data

C)

Finite wing data

D)

Infinite wing data

Correct Answer : Infinite wing data

Explanation : An airfoil can be thought of as a wing with infinite wing span. Indeed, the airfoil data is generally called as infinite wing data.

2 .

Which is the incorrect statement with regards to the flow over an airfoil and a wing?

A)

Flow over airfoil is 2D

B)

Flow over airfoil is 3D

C)

Airfoils have a component of flow along span

D)

Wings have a component of flow along span

Correct Answer : Airfoils have a component of flow along span

Explanation : Wings (which by default means finite wings) have a component of flow along span, which gives them 3D characteristics. While airfoils, which are infinite wings, have a 2D flow as the span wise component is absent.

3 .

The 3D flow characteristic attributed to the wings is a by-product of_____

A)

Extra lift produced

B)

Thickness of the wing

C)

Pressure imbalance over top and bottom surfaces of the wing

D)

Pressure imbalance between leading and trailing edge of the airfoil

Correct Answer : Pressure imbalance over top and bottom surfaces of the wing

Explanation : Lift over an airfoil is produced by the pressure difference over top and bottom surfaces of airfoil. But for the finite wings, this creates a by-product in the form of span-wise flow, which gives a 3D flow. Thickness of the wing and extra lift produced are vague options.

4 .

For a finite wing, the local relative wind differs by the free-stream velocity by some angle. This angle is called as ____

A)

Twist angle

B)

Induced angle of attack

C)

Angle of attack

D)

Relative angle of attack

Correct Answer : Induced angle of attack

Explanation : For a wing, induced velocity in the downward direction is present apart from the free-stream velocity. The resultant of both (relative local wind) is inclined to the free-stream velocity by an angle, which is called the induced angle of attack.

5 .

The angle between the chord line and the direction of free-stream velocity is called the angle of attack.

A)

False

B)

True for wing only

C)

True for airfoil only

D)

True for airfoil and partially true for wings

Correct Answer : True for airfoil and partially true for wings

Explanation : For an airfoil, the angle between the chord line and the direction of free-stream velocity is called the angle of attack. For the wings, the precise name is geometric angle of attack. Hence the given statement is only partially true for a wing.

6 .

The downward velocity induced by the trailing vortex in the vicinity of the wing-tips is called as _____

A)

Downwash

B)

Wing velocity

C)

Effective velocity

D)

Local relative velocity

Correct Answer : Downwash

Explanation : The trailing vortices, in the vicinity of the wing-tips, drag along with them the surrounding air. This induces a small velocity component in the downward direction. This is called downwash. None of the other terms describe this induced velocity.

7 .

The trailing vortex is formed at each wing-tip as there is a circulatory motion established by the____

A)

Viscosity

B)

Air tornadoes

C)

Flowing wind

D)

Leaking flow at the wing- tips

Correct Answer : Leaking flow at the wing- tips

Explanation : The flow has a tendency to ‘leak’ around the wing-tips. This flow makes a circulatory motion that trails downstream of the finite weak, giving rise to trailing vortices. This flow is possible because of viscosity but it doesn’t happen because of viscosity.

8 .

The span-wise component of flow over the top surface of the wing flows______

A)

From wing-tip to root

B)

From root to wing-tip

C)

Along the free-stream direction

D)

Perpendicular to the wing upwards

Correct Answer : From wing-tip to root

Explanation : The pressure imbalance is such that there is a low pressure region on top and high pressure region at the bottom. This creates a flow from the bottom surface towards the top surface of the wing. Naturally, the flow moves from the wing-tips towards the wing root.

9 .

Which of the following is incorrect for a finite wing?

A)

Higher pressure region exists at the top surface

B)

Streamlines on the top surface bend towards the root

C)

Span-wise flow at the bottom surface is towards the tip

D)

Streamlines on the bottom surface bend towards the tip

Correct Answer : Higher pressure region exists at the top surface

Explanation : There is higher pressure region at the bottom and lower pressure at the top. Due to which the flow moves from the wing root at the bottom towards the wing-tips, turns upwards and moves towards the wing root at the top surface. Thus, streamlines on the bottom surface bend towards the tip and vice versa happens at the top surface.

10 .

For a finite wing, the local airfoil section sees the angle of attack which is called as ____

A)

Downwash angle

B)

Effective angle of attack

C)

Relative angle of attack

D)

Induced angle of attack

Correct Answer : Effective angle of attack

Explanation : The actual angle of attack seen by the local airfoil section is the effective angle of attack. This is the angle between the chord line and the local relative wind. Or in other words,
Effective angle of attack = Geometric angle of attack – induced angle of attack.

11 .

Induced drag is generated by a component of lift for a finite wing.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : The local lift vector is not aligned perpendicular to the free-stream velocity vector for a wing. Lift is perpendicular to local relative wind. This causes a component of local lift in the direction of drag, called induced drag.

12 .

Which is the correct statement with regards to the flow over a finite wing?

A)

Local lift is vertical

B)

Downward velocity increases lift

C)

Free-stream velocity causes all the drag

D)

Local lift is inclined to vertical by induced angle of attack

Correct Answer : Local lift is inclined to vertical by induced angle of attack

Explanation : Wings have the local lift aligned perpendicular to the local relative wind direction. Thus, it is aligned to the vertical by an angle (called induced angle of attack). The downwash causes this alignment and a component of lift generates what we call induced drag. Thus, lift is deceased.

13 .

The total drag coefficient for a wing is given by______

A)

C_d=\(\frac {D_f+D_P}{Sq_∞}\)

B)

C_d=\(\frac {D_f+D_P+D_i}{Sq_∞}\)

C)

C_d=\(\frac {D_f+D_P+D_i}{Sq_∞}\)

D)

C_d=\(\frac {D_f+D_P}{Sq_∞}\)+D_i

Correct Answer : C_d=\(\frac {D_f+D_P+D_i}{Sq_∞}\)

Explaination : For wing, the total drag comprises of viscous drag plus the induced drag. The coefficient of total drag is given by C_d=\(\frac {D_f+D_P+D_i}{Sq_∞}\), which is nothing but C_d=\(\frac {D_f+D_P}{Sq_∞}+\frac {D_i}{Sq_∞}\) i.e. C_d=c_d+C_di.

14 .

Identify the source which does not cause drag on a finite wing.

A)

Skin – friction

B)

Flow separation

C)

Trailing vortices

D)

Power provide by aircraft engine

Correct Answer : Power provide by aircraft engine

Explanation : The flow over a wing has drag which comes from viscosity (skin – friction drag and pressure drag) plus drag induced by the trailing vortices. The power by the aircraft engine is used to overcome the drag and not cause it.

15 .

Select the incorrect statement for a flow over wings.

A)

3D flow over wings cause induced drag

B)

Induced drag comes from pressure- drag

C)

Induced drag is a ‘type’ of pressure- drag

D)

Pressure imbalance makes D’Alembert’s paradox does not occur

Correct Answer : Induced drag comes from pressure- drag

Explanation : For a wing, 3D flow causes a pressure imbalance in the direction of free – stream velocity, which is the drag. Thus, induced drag is a type of pressure-drag. But it is not caused by pressure drag.

16 .

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

A)

Zero

B)

Constant

C)

Path-dependent

D)

Depends on the local strength

Correct Answer : Constant

Explanation : 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).

17 .

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

A)

Vorticity: Velocity

B)

Induced velocity: Magnetic induction

C)

Aerodynamics: Electromagnetism

D)

Vortex Filament: Current-carrying Wire

Correct Answer : Vorticity: Velocity

Explanation : 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.

18 .

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

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : 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.

19 .

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

A)

Washin

B)

Washout

C)

Geometric twist

D)

Aerodynamic twist

Correct Answer : Aerodynamic twist

Explanation : 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.

20 .

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

A)

Washout

B)

Washin

C)

Geometric twist

D)

Aerodynamic twist

Correct Answer : Washin

Explanation : 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

21 .

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

Correct Answer : Downwash is absent

Explanation : 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).

22 .

The incorrect statement regarding Helmholtz theorems is____

A)

Describes vortex behavior

B)

Valid for all inviscid flows

C)

Remains constant along vortex filament

D)

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

Correct Answer : Valid for all inviscid flows

Explanation : 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.

23 .

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

A)

Washin

B)

Washout

C)

Geometric twist

D)

Aerodynamic twist

Correct Answer : Geometric twist

Explaination : 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.

24 .

Is vortex filament is a very thin strip?

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

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.

25 .

Is weak external velocity, rolling up of the vortex filament?

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

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.

26 .

Is Helmholtz's theorems apply to inviscid flows?

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

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.

27 .

According to the reasoning given by Prandtl for his lifting line theory, finite wing is like a ________

A)

Free vortex

B)

Trailing vortex

C)

Horseshoe vortex

D)

Bound vortex

Correct Answer : Bound vortex

Explanation : Prandtl reasoned that the finite wing can be thought like a bound vortex, which is opposite to the free vortex. Since a vortex filament cannot end in the fluid, it is assumed that there are two trailing vortices which gives the appearance like that of a horseshoe vortex.

28 .

The downwash along the wing in the downward direction in Prandtl’s lifting line theory comes from______

A)

Free vortex

B)

Bound vortex

C)

Trailing vortices

D)

Horseshoe vortex

Correct Answer : Trailing vortices

Explanation : The bound vortex does not induce any velocity along itself. The downwash along the bound vortex (wing) comes from the two trailing vortices. Thus, horseshoe is also an incorrect option.

29 .

The incorrect statement regarding the downwash for a single horseshoe vortex in Prandtl’s lifting line theory is____

A)

Downwash becomes infinite at the tips

B)

Downwash has contribution from trailing vortices

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 vortex

Correct Answer : The contribution of two semi-infinite trailing vortices is same as an infinite vortex

Explaination : 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.

30 .

The circulation at the center for an elliptical wing distribution does not depend upon ________

A)

Lift distribution

B)

Total span length

C)

Free-stream velocity

D)

Density of fluid at center

Correct Answer : Density of fluid at center

Explanation : The circulation at the center for an elliptical wing distribution is dependent directly on the total lift which can be found from the lift distribution. Also, it depends upon the free-stream velocity, total span length and free-stream fluid density.

31 .

Which of the following is not implied by the elliptical lift distribution?

A)

Constant downwash along the span

B)

Chord length is constant along the span

C)

Downwash is zero for infinite wing span

D)

Induced angle of attack is zero for infinite wing span

Correct Answer : Chord length is constant along the span

Explanation : The elliptical lift distribution gives an elliptical chord length distribution along the span. The induced angle of attack and downwash becomes zero for infinite wing span, proving the infinite wing (airfoil) theory. The downwash is a constant value along the span.

32 .

Which is the wrong implication of the elliptical lift distribution for a wing?

A)

Lift is zero at the tips

B)

Maximum lift is at the center

C)

Span length does not affect circulation

D)

Circulation varies elliptically along span

Correct Answer : Span length does not affect circulation

Explanation : The elliptical lift distribution comes from the elliptical distribution of circulation along the span. The lift (or circulation) involves span length in the governing equations and hence the wrong statement. Lift is zero at the wing tips and maximum at the center.

33 .

Downwash for an elliptic wing circulation distribution is constant.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : For an elliptic distribution of lift over the span of a wing, downwash is a constant. This can be calculated from Biot-Savart law and using substitution to reveal that downwash is a constant along the span.

34 .

The lift coefficient for the airfoil section on a wing ______

A)

Is constant always

B)

Is same for the entire wing

C)

Is equal to the aerodynamic twist

D)

Depends on local lift slope for airfoil

Correct Answer : Depends on local lift slope for airfoil

Explanation : In wings, the lift coefficient for local airfoil section is equal to the local airfoil lift curve slope (2π for thin airfoils) into effective angle of attack minus zero lift angle of attack. Thus, it may or may not be same for the entire wing and is not equal to the aerodynamic twist.

35 .

For the case of infinite horseshoe vortices along the lifting line, a vortex sheet exists which_________

A)

Total strength is zero

B)

Equal and opposite trailing vortices

C)

Is perpendicular to free-stream velocity

D)

Is formed by continuous trailing vortices

Correct Answer : Is perpendicular to free-stream velocity

Explanation : The continuous trailing vortices gives a vortex sheet in the direction parallel to the free-stream velocity. The total strength of the vortex sheet is zero since it consists of trailing vortices with equal and opposite strength.

36 .

The infinite downwash at the wing tips for a single horseshoe vortex in Prandtls lifting line theory was a wrong result. Which of the following does not relate to the correction made?

A)

Lifting line along the span

B)

Trailing vortices only at the tip

C)

Different length of bound vortices

D)

Superimposition of horseshoe vortices

Correct Answer : Trailing vortices only at the tip

Explaination : The downwash due to a single horseshoe vortex in Prandtls lifting line theory gave a wrong result as infinite downwash at the wing tips. This was corrected by assuming a superimposition of many horseshoe vortices, each with different length of bound vortices lying along the span on a line, called lifting line. This gave many trailing vortices distributed along the span as well.

37 .

The induced angle of attack for an elliptical lift distribution increase when ______

A)

Lift decreased

B)

Aspect ratio decreased

C)

Increase in span length

D)

Decrease in planform area

Correct Answer : Aspect ratio decreased

Explanation : If we decrease the planform area or increase the span length, the aspect ratio increases. Since the induced angle of attack is indirectly proportional to the aspect ratio, these options are wrong. We need to decrease the aspect ratio to increase the induced angle of attack. Increasing the lift can also increase the induced angle of attack.

38 .

The incorrect statement for a finite wing with elliptical lift distribution out of the following is_____

A)

Induced drag coefficient is around 25%

B)

Induced drag coefficient ? coefficient of lift

C)

Induced drag coefficient increases rapidly with lift

D)

To reduce induced drag, we want wing with the lowest aspect ratio

Correct Answer : To reduce induced drag, we want wing with the lowest aspect ratio

Explanation : The induced drag coefficient varies directly with the square of lift coefficient. Thus, it increases rapidly with the lift. At high speeds, it is around 52% of total drag. For least induced drag, we want high aspect ratio for the wing.

39 .

The incorrect choice for the general lift distribution for a finite wing is ________

A)

0 ≤ θ ≤ 2π

B)

Circulation is assumed a Fourier series

C)

Coefficient of lift depends on aspect ratio directly

D)

Coordinate transformation is for spanwise direction to θ

Correct Answer : 0 ≤ θ ≤ 2π

Explaination : For a general lift distribution of a finite wing, the circulation is assumed a Fourier series from the expression obtained for elliptic lift distribution. The transformation involves spanwise coordinate transformed to θ, where 0 ≤ θ ≤ π. Using this the lift coefficient obtained depends directly on the aspect ratio.

40 .

Select the incorrect equation for the induced drag coefficient for a finite wing.

A)

C_D,i=\(\frac {C_l^2}{\pi eAR}\)

B)

C_D,i=\(\frac {C_l^2}{\pi AR}\)

C)

C_D,i=\(\frac {C_l^2s}{\pi eb^2 }\)

D)

C_D,i=\(\frac {C_l^2}{\pi AR}\)(1+δ)

Correct Answer : C_D,i=\(\frac {C_l^2}{\pi AR}\)

Explaination : The correct formula for induced drag coefficient for a general lift distribution is C_D,i=\(\frac {C_l^2}{\pi eAR}\) where e=\(\frac {1}{1+\delta}\) and AR=\(\frac {b^2}{S’}\) where δ is related to the Fourier coefficients and e is the span efficiency factor. Thus, the option C_D,i=\(\frac {C_l^2}{\pi AR}\) is wrong.

41 .

The incorrect difference between airfoil and wings is_______

A)

Lift slope of the wing is higher than of airfoil

B)

Difference in the lift-curve slope

C)

Presence of induced drag in wings

D)

Different effective angles of attack seen by

Correct Answer : Lift slope of the wing is higher than of airfoil

Explanation : The finite wing has a lower lift slope than infinite wing (airfoil). This is another difference than the presence of induced drag between wings and airfoil. Also, the effective angles of attack are different for both, being the same only when the lift is zero (at zero lift angle of attack).

42 .

Tapered wings are used more rather than elliptical wing planforms practically. The reason being______

A)

Tapered wing resembles elliptic wing highly

B)

Easy to manufacture than elliptic wings

C)

Tapered wing is another name for elliptic wing

D)

Aspect ratio more important for low induced drag

Correct Answer : Easy to manufacture than elliptic wings

Explanation : In reality, tapered wings are preferred over elliptic wings because they are easier to manufacture (they have straight edges). But the resemblance to elliptic wings (variation of δ) is secondary to reduce wing induced drag compared to the aspect ratio. Here we are only asked why tapered wings used; the answer is easy to manufacture.

43 .

Is prandtl lifting line theory is a mathematical model that predicts lift distribution over a three-dimensional wing?

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : The prandtl lifting line theory is a mathematical models that predicts lift distribution over a three dimensional wing based on its geometry. It is also known as the lanchester-prandtl wing theory. It was used to calculate lift on the wing.

44 .

Is it difficult to predict the analytically overall amount of lift?

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : It is difficult to predict analytically the overall amount of lift that a wing of given geometry will generate. The lifting line theory yields the lift distribution along the span wise direction based only on the wing geometry and flow conditions.

45 .

Is loading distribution is represented by the sum of finite number?

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : In the collocation solution of the basic integral equation, the loading distribution is represented by the sum of a finite number of known functions with unknown coefficient substituting the loading representation into their result.