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Right answer is (a) 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.

Correct ANSWER is (a) True

Explanation: The lifting surfaces antedates the achievements of powered FLIGHT, efforts have been focused largely on single, almost PLANE configuration in a STEADY motion. Since tractability has often been the criteria of the INTEREST.

The correct option is (a) True

The explanation: The downwash distribution on the PLATFORM is REGULAR if does not EXHIBIT discontinuities or infinities in value. THUS, referring to equation either the downwash MODES must be regular, or else the sum of the modes must be regular.

Correct answer is (a) False

The best I can EXPLAIN: On a three dimensional, finite wing, LIFT over each wing segment does not correspond SIMPLY to what two-dimensional analysis PREDICTS. Instead, this local amount of lift is strongly affected by the lift generated at neighboring wing section.

Right choice is (a) 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.

Correct choice is (a) True

Best explanation: The BASIC integral equation of subsonic lifting surface THEORY relates the normal velocity distribution to the pressure difference distribution on a THIN wing and may be written in the FORM of the lifting surface theory.

Correct option is (a) True

To elaborate: Plane FORMS with SMOOTH edge shapes with finite tip chord, suitable loading modes are readily defined of the leading and trailing edge respectively and the wing semi SPAN then to ensure that the DOWNWASH modes are regular.

Right answer is (b) True

Best 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.

Right answer is (C) Airfoils have a component of flow along span

For explanation I would say: 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.

The correct option is (b) True

Easiest explanation: VORTEX LINES leading from the wing TIPS, if the atmosphere has very HIGH humidity, you can sometimes see the vortex lines on an aircraft during landing as long thin clouds leaving the wing tips which CAUSES the down wash in the lower surface of the wing.

The correct option is (a) True

The best EXPLANATION: The lifting line THEORY applies the concept of CIRCULATION and the kutta-joukowski theorem so that instead of the lift distribution function, the unknown effectively becomes the distribution of circulation over the SPAN.

The correct option is (a) CHORD length is constant along the span

The BEST 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.

Correct answer is (b) False

Explanation: The filament can TAKE any shape, CURVED, straight, round etc. Hence, the GIVEN statement is false. In general, we assume a curved vortex filament.

Correct option is (b) True

To explain I WOULD say: In lifting line THEORY, the lifting line along the SPAN is a superimposition of many bound vortices with DIFFERENT lengths. This gives different strengths for each of the HORSESHOE vortex i.e. the circulation varies along the lifting line.

The correct choice is (d) Power provide by aircraft engine

The 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.

Correct CHOICE is (d) Effective angle of attack

The BEST 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.

Right option is (a) True

Easiest explanation: When the aircraft is rolling, an additional term can be ADDED that adds the wing STATION distance multiplied by the RATE of roll to give an additional angle of attack CHANGE, which introduces non-zero even coefficient in the EQUATION that must be an accounted for it.

The CORRECT ANSWER is (a) True

Explanation: When the lift is zero, there are no INDUCED effects i.e. induced DRAG and induced angle of attack are zero. Also, since the induced angle of attack is zero, the geometric angle of attack is the same as the effective angle of attack. This means zero lift angle of attack is the same for wing and airfoil.

Right answer is (d) To REDUCE induced drag, we want wing with the lowest aspect RATIO

The EXPLANATION is: 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.

Right option is (b) True

The explanation is: 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.

Right choice is (a) True

Best explanation: Induced drag is RELATED to the amount of induced downwash in the vicinity of the wing. The grey VERTICAL line labeled L is perpendicular to the free stream and INDICATES the ORIENTATION of the LIFT on the wing.

The correct option is (b) True

Easiest explanation: Lift is PRODUCED by the CHANGING direction of the flow around a wing. The change of direction results in a change of velocity, which is an acceleration, to charge the direction of flow REQUIRES that a force is applied to the fluid ACTING on the wing.

Correct answer is (a) MINIMUM induced drag

The best EXPLANATION: The coefficient of induced drag is CD,i=\(\FRAC {C_l^2}{\pi eAR}\). For an elliptic wing, E = 1 and/or δ = 0 i.e. the induced drag is minimum. The aspect ratio for the elliptic wing is not lowest. Moreover, we need a higher aspect ratio for lower induced drag.

Right answer is (a) True

Explanation: The lift distribution over a WING can be modeled with the CONCEPT of circulation. A vortex is shed downstream for every SPAN wise change in lift. Modeling the local lift with local circulation allows us to account for the influence of one section over its neighbors.

Correct option is (b) CD,i=\(\frac {C_l^2}{\pi AR}\)

For explanation: The correct formula for induced DRAG coefficient for a general lift distribution is CD,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 CD,i=\(\frac {C_l^2}{\pi AR}\) is wrong.

The correct choice is (a) False

Best explanation: The INDUCED drag coefficient for a finite wing is inversely dependent on the ASPECT ratio. Thus, the induced drag INCREASES with the decrease in aspect ratio and VICE versa for a finite wing with the same LIFT.

Right option is (d) INFINITE wing data

Best 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.

Right option is (b) True

The EXPLANATION is: For any GENERAL wing planform lift slope is GIVEN by a=\(\frac {a_0}{1+\frac {a_0}{\pi AR}(1+\tau)}\) where τ is a function of the Fourier coefficients used to describe the planform area. As aspect ratio becomes very large (i.e. AR tends to ∞), we find a becomes A0 i.e. for very high aspect ratio wings, lift slope for wing and airfoil is the same. Prandtl verified this through experiments ALSO.

Correct OPTION is (a) True

For 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.

Correct option is (b) 0 ≤ θ ≤ 2π

To elaborate: 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.

Correct answer is (c) Γ is known

To explain: The fundamental EQUATION of PRANDTLS lifting line theory simply states that the geometric angle of attack is the SUM of effective angle of attack and induced angle of attack. In mathematical form, it is an integro-differential equation where Γ is unknown and wing design, geometric AoA and free-stream VELOCITY is known.

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.

Right answer is (d) Washin

Easiest 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.

The correct option is (a) True

The 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.

The correct answer is (a) True

To elaborate: The chord distribution is ELLIPTICAL for an elliptical lift distribution. This is OBSERVED from the formula. Thus, the PLANFORM area is elliptical for an elliptical lift distribution for a FINITE wing.

Right choice is (a) Di’=L’sin sinαi

Easiest explanation: For a finite wing flat plate airfoil the induced DRAG is OBTAINED by the component of lift in the direction of free-stream VELOCITY i.e. Di’=L’sin sinαi. For a thin airfoil, we can make the SMALL angle approximation in sine but not for all general airfoils.

The correct answer is (c) AERODYNAMIC twist

For 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.

Correct answer is (b) 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.

The CORRECT ANSWER is (d) Trailing vortices

To explain I would say: 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.

Right choice is (a) True

To elaborate: The higher aspect ratio flat plates had higher lift and LOWER DRAG, a plane of fixed SIZE and WEIGHT would need LESS propulsive power the faster it flew, the counter-intuitive effect of induced drag will produce on the wing.

The correct choice is (B) Aspect RATIO decreased

The best 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.

Correct choice is (a) True

Easy EXPLANATION: The prandtl lifting-line theory is a mathematical MODEL that predicts lift distribution over a three dimensional wing based on its geometry. It is ALSO known as the lanchester-prandtl wing theory. The theory was expressed independently by Frederick W. lanchester in 1907.

The correct choice is (a) αi=\(\frac {w}{V_∞}\)

To elaborate: The induced angle of attack at an ARBITRARY POSITION ALONG SPAN, for a finite wing can be given as αi=\(\frac {w}{V_∞}\) where V∞ is the free-stream velocity and w is the DOWNWASH (modulus only).

Correct choice is (a) CD=\(\frac {D_f+D_P}{Sq_∞}\)

The explanation: The profile drag for a wing is the drag CAUSED by viscosity. For moderate ANGLES of attacks, it is same as that for AIRFOILS i.e. a combination of skin- friction drag and pressure drag. The correct formula is cd=\(\frac {D_f+D_P}{Sq_∞}\).

Correct answer is (b) True

The best explanation: There is HIGHER power required by the AIRCRAFT ENGINE to overcome the INDUCED drag, THUS leading to wastage of power. This power goes waste as it provides energy to the vortices, serving no useful purpose.