The Falkner-Skan solutions extend the Blasius result to flows with
Answer: A
By taking the external velocity as a power of distance, Falkner and Skan obtained a family of similarity solutions covering accelerating and decelerating flows. The family includes the Blasius flat plate as the zero-gradient case and a separating profile at the adverse extreme.
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Skin-friction drag on a modern subsonic transport typically accounts for roughly
Answer: B
About half the cruise drag of a transport is skin friction, with most of the remainder being lift-induced. That split is why laminar flow control and riblets attract such sustained research attention despite the practical difficulties they present.
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Riblets, the fine streamwise grooves trialled on transport aircraft, reduce drag by
Answer: C
Grooves of the right size impede the lateral movement of the streamwise vortices that dominate the near-wall region, cutting turbulent momentum transport and with it the shear stress. Reductions of a few per cent have been measured, though keeping the surface clean and intact in service is the obstacle.
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A transport's cruise drag is \( 60 \) kN, of which half is skin friction. A riblet treatment cuts skin friction by \( 6 \) per cent. The saving in total drag is
Answer: D
The friction component is \( 30 \) kN and six per cent of that is \( 0.06 \times 30 = 1.8 \) kN, which is three per cent of the total. Small as it sounds, a three per cent fuel saving across a fleet is a large sum, which is why the idea keeps returning despite its practical difficulties.
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Assertion (A): The momentum integral equation can be solved without knowing the exact velocity profile.
Reason (R): It relates only integral quantities and the wall shear stress.
Select the correct answer from the options below.
Answer: A
Both are true and the second explains the first. Because the equation is written in terms of integrals across the layer, any reasonable assumed profile closes it, which is exactly what the Pohlhausen method does. The accuracy then depends on how good that assumption is.
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Assertion (A): Skin friction is a major target for drag reduction research on transport aircraft.
Reason (R): It accounts for roughly half the cruise drag of such an aircraft.
Select the correct answer from the options below.
Answer: B
Both statements are true and the second is the reason for the first. With half the drag attributable to friction, even a few per cent is worth pursuing, which is why riblets, laminar flow control and surface treatments continue to attract funding despite their in-service difficulties.
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Consider the following statements about the momentum integral equation:
1. It is derived by integrating the boundary-layer equations across the layer.
2. It requires an assumed velocity profile before it can be solved.
3. It applies only to laminar boundary layers.
Which of the statements given above is or are correct?
Answer: C
The first two are correct and describe both the derivation and the closure problem it leaves. The third is false: the integral form holds for turbulent layers too, and turbulent methods use it with an empirical skin-friction law in place of the laminar one.
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Consider the following statements about drag reduction on a transport aircraft:
1. Skin friction is roughly half the cruise drag.
2. Riblets act on the near-wall turbulent structures.
3. Laminar flow control is easy to maintain in airline service.
Which of the statements given above is or are correct?
Answer: D
The first two are correct. The third is emphatically false: insect contamination, rain, erosion and manufacturing waviness all destroy the laminar run, and keeping a leading edge in the required condition through a normal duty cycle has proved the central obstacle.
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Match each analysis method in List I with what characterises it in List II.
List I
A. Blasius solution
B. Falkner-Skan family
C. Momentum integral equation
D. Pohlhausen method
List II
1. Similarity solutions for wedge flows with a pressure gradient
2. The exact laminar flat-plate case with no pressure gradient
3. Closes the integral equation with an assumed quartic profile
4. Relates momentum thickness growth to wall shear and pressure gradient
Select the correct match.
Answer: A
The four form a natural progression from an exact special case, through a family of exact solutions, to an integral formulation and finally a practical way of closing it. Each buys generality at the cost of some exactness.
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The wake behind a bluff body is characterised by
Answer: B
Once the flow separates, the pressure in the wake cannot recover to the free-stream value and sits near the base pressure, leaving the front of the body pushed harder than the rear. Measuring the momentum deficit across the wake is in fact a standard way of determining the drag experimentally.
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