A turbulent boundary layer grows along a flat plate roughly in proportion to
Answer: B
The turbulent layer thickens far more quickly than the laminar half-power law, going roughly as distance to the four-fifths. The practical consequence is that a long surface with early transition carries a much thicker layer at its trailing edge than the laminar estimate would suggest.
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Laminar flow aerofoils achieve low drag by
Answer: C
Moving the point of maximum thickness aft keeps the flow accelerating over much of the surface, and that favourable gradient suppresses the instabilities that would otherwise trigger transition. The saving is real but fragile, since insects, rain or manufacturing waviness can destroy it.
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The drag bucket seen in the drag polar of a laminar-flow section is
Answer: D
Inside a limited band of lift coefficient the favourable gradient survives on both surfaces and the drag drops sharply, giving the characteristic bucket. Outside that band the stagnation point moves and transition jumps forward, so the advantage disappears abruptly.
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A body's drag coefficient is defined using which reference quantity in the denominator?
Answer: A
The coefficient normalises the drag force by the dynamic pressure and an agreed reference area, which makes it dimensionless and comparable between scales. The reference area must always be stated, since wing planform, frontal and wetted areas are all used in different contexts.
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Air at \( 1.225 \) kg/m\( ^3 \) and \( 1.8 \times 10^{-5} \) Pa s flows at \( 30 \) m/s over a plate \( 2 \) m long. The Reynolds number at the trailing edge is nearest to
Answer: B
Substituting into \( Re = \rho V L/\mu \) gives \( 1.225 \times 30 \times 2 / (1.8 \times 10^{-5}) = 73.5 / 1.8 \times 10^{5} = 4.08 \times 10^6 \). With transition near half a million, only the first quarter-metre or so of this plate carries a laminar layer.
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On a flat plate the laminar boundary layer thickness at a station where \( Re_x = 10^6 \) and \( x = 1 \) m is nearest to
Answer: C
The Blasius result is \( \delta = 5x/\sqrt{Re_x} \), so \( 5 \times 1 / 1000 = 0.005 \) m, that is 5 mm. The thinness is the whole point of Prandtl's hypothesis: viscous effects are confined to a layer a fraction of a per cent of the body length.
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For laminar flow at \( Re_x = 10^6 \), the local skin-friction coefficient is nearest to
Answer: D
The Blasius local coefficient is \( 0.664/\sqrt{Re_x} = 0.664/1000 = 6.64 \times 10^{-4} \). The distractor 0.00133 is the plate-averaged coefficient over the same length, which is exactly twice the local value at the trailing edge for laminar flow.
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What is the average skin-friction coefficient for a wholly laminar flat plate at \( Re_L = 10^6 \)?
Answer: A
The averaged Blasius result is \( 1.328/\sqrt{Re_L} = 1.328/1000 = 1.33 \times 10^{-3} \). It is twice the local value at the trailing edge, because the layer is thinnest and the friction highest near the leading edge.
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A flat plate at \( Re_L = 10^7 \) carries a fully turbulent layer. Its average skin-friction coefficient, from the one-fifth power law, is nearest to
Answer: B
Using \( C_F = 0.074/Re_L^{0.2} \) with \( (10^7)^{0.2} = 10^{1.4} = 25.1 \) gives \( 0.074/25.1 = 2.95 \times 10^{-3} \). Compare this with the laminar value at the same Reynolds number, which would be about ten times smaller: turbulence is expensive in friction.
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For the Blasius laminar profile, the shape factor is nearest to
Answer: C
With \( \delta^* = 1.721x/\sqrt{Re_x} \) and \( \theta = 0.664x/\sqrt{Re_x} \), the ratio is \( 1.721/0.664 = 2.59 \). A turbulent layer comes in nearer 1.4, and a laminar layer climbing past about 3.5 is on the point of separating.
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