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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Correct Answer : Cd=\(\frac {D_f+D_P+D_i}{Sq_∞}\)
Explaination : For wing, the total drag comprises of viscous drag plus the induced drag. The coefficient of total drag is given by Cd=\(\frac {D_f+D_P+D_i}{Sq_∞}\), which is nothing but Cd=\(\frac {D_f+D_P}{Sq_∞}+\frac {D_i}{Sq_∞}\) i.e. Cd=cd+Cdi.
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.
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.
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).
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.
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.
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.
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
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).
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.
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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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Correct Answer : CD,i=\(\frac {C_l^2}{\pi AR}\)
Explaination : 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.
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).
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.
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.
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.
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.
