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Question 1
ప్రశ్న 1
Which statement most accurately distinguishes laminar and turbulent boundary layers over a smooth surface?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In a laminar boundary layer, fluid motion is comparatively orderly and momentum transfer across the layer occurs mainly through molecular viscosity. In a turbulent boundary layer, velocity fluctuations create strong mixing in addition to viscous transport. This mixing transfers high-momentum fluid toward the wall more effectively. Consequently the mean velocity profile and skin-friction behavior differ substantially from those of a laminar layer. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
For incompressible flow with uniform external velocity U over a flat plate, what is the local Reynolds number at a distance x from the leading edge?
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Explanation:
The local flat-plate Reynolds number is based on the distance x measured from the leading edge. Using kinematic viscosity ν, it is defined as Reₓ = Ux/ν. The same quantity may be written as ρUx/μ when dynamic viscosity μ is used. It measures the relative importance of inertial and viscous effects at that streamwise location. Therefore Option B is correct.
వివరణ:
Question 3
ప్రశ్న 3
For a smooth flat plate in a reasonably quiet uniform external stream, which value is commonly used as an engineering estimate of the local Reynolds number at which transition may begin?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A commonly used engineering estimate for transition on a smooth flat plate is Reₓ of the order of 5 × 10⁵. This value is not a universal constant. Actual transition depends on free-stream turbulence, surface roughness, pressure gradient, leading-edge disturbances and other factors. Under very quiet conditions, laminar flow can persist to substantially higher Reynolds numbers. Therefore Option C is correct.
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Question 4
ప్రశ్న 4
Which factor can significantly alter the Reynolds number at which a flat-plate boundary layer transitions from laminar to turbulent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Boundary-layer transition is an instability process and is sensitive to disturbances. Surface roughness can introduce disturbances that promote earlier transition. Increased free-stream turbulence can also accelerate the growth of disturbances inside the boundary layer. Pressure gradients, surface curvature and leading-edge conditions can influence transition as well. Therefore Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which statement best describes the transition region of a flat-plate boundary layer?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Real transition does not usually occur instantaneously at one mathematical point. Disturbances begin to amplify and increasingly three-dimensional and irregular motions develop over a finite distance. Intermittent turbulent patches may appear and grow before fully turbulent behavior is established. The often-used critical Reynolds number is therefore an engineering indicator rather than an exact universal transition location. Hence Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
Compared with a laminar boundary layer under similar external conditions, how does a turbulent boundary-layer mean velocity profile generally appear when plotted as u/U against y/δ?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Turbulent mixing transports streamwise momentum efficiently across the boundary layer. This brings higher-momentum fluid from the outer region closer to the wall. The resulting mean velocity profile is commonly described as fuller than a laminar profile. Very near the wall, viscosity still remains essential and enforces the no-slip condition. Therefore Option A is correct.
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Question 7
ప్రశ్న 7
For comparable distance x, external velocity and fluid properties, which statement generally describes boundary-layer growth after a flat-plate boundary layer has become fully turbulent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Turbulent mixing enhances transverse momentum transport and causes the wall influence to extend farther into the flow. Consequently a turbulent boundary layer typically grows more rapidly downstream than a laminar one under comparable conditions. Standard smooth-flat-plate correlations reflect this different growth behavior. The exact comparison depends on how transition and thickness are defined, but the general engineering trend is robust. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
Why is turbulent skin friction generally higher than laminar skin friction under comparable flat-plate conditions?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Wall shear stress is directly related to the velocity gradient at the wall for a Newtonian fluid. Turbulent mixing continually transports relatively high streamwise momentum toward the near-wall region. This sustains a steeper near-wall mean velocity gradient than would generally occur in a comparable laminar layer. As a result, turbulent boundary layers usually produce greater skin-friction drag. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
Which expression defines the local skin-friction coefficient Cf,x for an incompressible external flow of density ρ and speed U?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The local skin-friction coefficient non-dimensionalizes the local wall shear stress using the dynamic pressure. Dynamic pressure is one-half ρU². Therefore Cf,x = τw/[(1/2)ρU²] = 2τw/(ρU²). This definition applies independently of which laminar or turbulent correlation is later used to estimate Cf,x. Hence Option B is correct.
వివరణ:
Question 10
ప్రశ్న 10
For a one-sided flat plate of length L and width b in uniform incompressible flow, which expression defines the average skin-friction coefficient over that wetted side?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The average skin-friction coefficient relates the total friction drag to the dynamic pressure acting over the wetted reference area. For one side of a rectangular plate, that area is bL. Thus Df = Cf,L(1/2)ρU²bL. Rearranging gives Cf,L = Df/[(1/2)ρU²bL]. Therefore Option A is correct.
వివరణ:
Question 11
ప్రశ్న 11
For a steady incompressible zero-pressure-gradient laminar boundary layer over a smooth flat plate, which approximation represents the conventional 99% boundary-layer thickness from the Blasius solution?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Blasius solution applies to a two-dimensional steady incompressible laminar boundary layer over a smooth flat plate with zero pressure gradient. Its conventional 99-percent thickness is commonly approximated as δ ≈ 5x/√Reₓ. This implies that δ grows approximately as the square root of x when U and ν remain constant. The relation should not be applied indiscriminately to turbulent or pressure-gradient boundary layers. Therefore Option A is correct.
వివరణ:
Question 12
ప్రశ్న 12
For the same Blasius laminar flat-plate boundary layer, what is the standard local skin-friction coefficient?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Blasius solution gives the local wall shear stress and hence a local skin-friction coefficient. The standard result is Cf,x = 0.664/√Reₓ. It decreases downstream because the local Reynolds number increases with x. The coefficient is specifically associated with the laminar zero-pressure-gradient smooth-flat-plate solution. Therefore Option B is correct.
వివరణ:
Question 13
ప్రశ్న 13
For a completely laminar Blasius boundary layer over a flat plate of length L, what is the average skin-friction coefficient from the leading edge to L?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The local laminar coefficient varies with x as Reₓ to the power minus one-half. Integrating the local shear stress over the plate from the leading edge to L gives the average coefficient. The resulting Blasius expression is Cf,L = 1.328/√ReL. This is twice the local coefficient evaluated at the trailing edge under the same assumptions. Therefore Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
For a completely laminar Blasius flat plate, how does the average skin-friction coefficient over 0 ≤ x ≤ L compare with the local coefficient at x = L?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At x = L, the Blasius local coefficient is 0.664/√ReL. The average coefficient over the full laminar plate is 1.328/√ReL. Dividing the latter by the former gives exactly two. The larger average reflects the very high local shear near the leading edge that contributes to the integral drag. Therefore Option C is correct.
వివరణ:
Question 15
ప్రశ్న 15
For a smooth flat plate treated as turbulent from the leading edge, which commonly used correlation estimates the turbulent boundary-layer thickness in the range where the one-fifth-power correlation is applicable?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A widely used engineering approximation for a turbulent smooth-flat-plate boundary layer is δ/x ≈ 0.37/Reₓ^(1/5). It corresponds to a boundary layer assumed turbulent from the leading edge and a zero-pressure-gradient type of treatment. The exponent differs from the laminar Blasius result, for which δ/x varies as Reₓ to the power minus one-half. The turbulent relation is empirical or semi-empirical rather than an exact similarity solution like Blasius flow. Therefore Option B is correct.
వివరణ:
Question 16
ప్రశ్న 16
For a smooth flat plate treated as turbulent from the leading edge in the usual one-fifth-power correlation range, which expression gives the local skin-friction coefficient?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A standard local correlation for a smooth turbulent flat-plate boundary layer is Cf,x ≈ 0.0592/Reₓ^(1/5). This expression is commonly quoted for a zero-pressure-gradient plate over an appropriate Reynolds-number range. It is a turbulent correlation and should not be confused with the Blasius laminar value 0.664/√Reₓ. The coefficient decreases downstream, but less rapidly with Reynolds number than the laminar local coefficient. Therefore Option C is correct.
వివరణ:
Question 17
ప్రశ్న 17
If a smooth flat plate is idealized as turbulent from its leading edge, which standard one-fifth-power correlation gives the average skin-friction coefficient over length L?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For the fully turbulent-from-the-leading-edge approximation, integration of the local one-fifth-power shear correlation gives an average coefficient of about 0.074/ReL^(1/5). The local coefficient at L uses the smaller constant 0.0592. This average turbulent expression does not account for an initial laminar portion before natural transition. When transition is important, a corrected mixed laminar-turbulent correlation should be used instead. Therefore Option A is correct.
వివరణ:
Question 18
ప్రశ్న 18
Air flows over a smooth flat plate at U = 10 m/s with kinematic viscosity ν = 1.0 × 10^-6 m²/s. If transition is estimated to begin at Reₓ = 5.0 × 10^5, how far from the leading edge is the estimated transition location?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The local Reynolds number is Reₓ = Ux/ν. Rearranging gives x = Reₓν/U. Substitution gives x = (5.0 × 10^5)(1.0 × 10^-6)/10. The result is 0.050 m. Therefore Option B is correct.
వివరణ:
Question 19
ప్రశ్న 19
A laminar boundary layer develops over a smooth flat plate with U = 2.0 m/s, ν = 1.0 × 10^-6 m²/s and x = 0.10 m. Using δ ≈ 5x/√Reₓ, what is the boundary-layer thickness approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The local Reynolds number is Reₓ = 2.0 × 0.10/(1.0 × 10^-6) = 2.0 × 10^5. Its square root is approximately 447.21. The Blasius thickness estimate is δ = 5(0.10)/447.21 m. This gives 0.001118 m, or approximately 1.12 mm. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
For a laminar smooth-flat-plate boundary layer at Reₓ = 2.5 × 10^5, what is the local skin-friction coefficient from the Blasius relation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The local Blasius coefficient is Cf,x = 0.664/√Reₓ. The square root of 2.5 × 10^5 is 500. Therefore Cf,x = 0.664/500. This equals 0.001328. Hence Option B is correct.
వివరణ:
Question 21
ప్రశ్న 21
A laminar flat-plate boundary layer in air has ρ = 1.2 kg/m³, U = 20 m/s and Reₓ = 4.0 × 10^5. Using the Blasius local coefficient, what is the local wall shear stress approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The local coefficient is Cf,x = 0.664/√(4.0 × 10^5) = approximately 0.0010499. Local wall shear is τw = Cf,x(1/2)ρU². The dynamic pressure is 0.5 × 1.2 × 20² = 240 Pa. Multiplication gives τw approximately 0.252 Pa. Therefore Option C is correct.
వివరణ:
Question 22
ప్రశ్న 22
Water with ρ = 1000 kg/m³ and ν = 1.0 × 10^-6 m²/s flows at U = 1.0 m/s over one side of a smooth flat plate 0.40 m long and 1.0 m wide. Assuming the boundary layer remains laminar over the entire plate, what is the friction drag approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The plate Reynolds number is ReL = UL/ν = 4.0 × 10^5, consistent with the stated laminar assumption for this exercise. The average Blasius coefficient is Cf,L = 1.328/√ReL = approximately 0.0020998. The wetted area is 1.0 × 0.40 = 0.40 m² and the dynamic pressure is 500 Pa. Thus Df = Cf,L(500)(0.40) = approximately 0.420 N. Therefore Option C is correct.
వివరణ:
Question 23
ప్రశ్న 23
For a smooth flat plate idealized as turbulent from the leading edge, x = 1.0 m and Reₓ = 1.0 × 10^6. Using δ/x ≈ 0.37/Reₓ^(1/5), what is δ approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The fifth root of 1.0 × 10^6 is approximately 15.849. Thus δ/x = 0.37/15.849 = approximately 0.02335. With x = 1.0 m, δ is therefore approximately 0.02335 m. Converting to millimeters gives about 23.3 mm. Hence Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
At Reₓ = 1.0 × 10^6, what local skin-friction coefficient is predicted by Cf,x ≈ 0.0592/Reₓ^(1/5) for a smooth turbulent flat-plate boundary layer?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For Reₓ = 10^6, Reₓ^(1/5) is approximately 15.849. Dividing 0.0592 by 15.849 gives approximately 0.003735. Rounding to the precision of the options gives 0.00374. This value is characteristic of the stated turbulent correlation, not the laminar Blasius relation. Therefore Option C is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements for smooth zero-pressure-gradient flat-plate boundary layers: I. The commonly used transition estimate Reₓ ≈ 5 × 10^5 is not universal. II. A turbulent mean velocity profile is generally fuller than a laminar profile. III. Turbulent skin friction is generally higher than laminar skin friction under comparable conditions. IV. The laminar local coefficient varies approximately as Reₓ^-1/2, whereas the standard one-fifth-power turbulent correlation varies as Reₓ^-1/5. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is correct because transition depends on disturbance environment, surface condition and pressure-gradient effects. Statement II is correct because turbulent mixing produces a fuller mean velocity profile. Statement III is correct because stronger near-wall momentum transport generally increases skin friction. Statement IV correctly distinguishes the Reynolds-number dependence of the standard laminar and turbulent flat-plate correlations used in this test. Therefore all four statements are correct and Option D is the valid answer.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: A. A laminar boundary layer has orderly fluid motion with relatively little transverse mixing, whereas a turbulent boundary layer contains strong fluctuations and mixing సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: B. Reₓ = Ux/ν సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: C. About 5 × 10⁵ సమాధానం: C.
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Question 4 ప్రశ్న 4Answer: B. Surface roughness and free-stream turbulence సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: A. It is generally a finite streamwise region in which laminar flow progressively changes into turbulent flow సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: A. It is fuller, with relatively high mean velocity extending closer to the wall సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: A. The turbulent boundary layer generally grows more rapidly and is thicker than the corresponding laminar boundary layer సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: A. Turbulence produces stronger momentum transport toward the wall and a larger mean velocity gradient in the near-wall region సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: B. Cf,x = 2τw/(ρU²) సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: A. Cf,L = Df/[(1/2)ρU² bL] సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: A. δ/x ≈ 5/√Reₓ సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: B. Cf,x = 0.664/√Reₓ సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: B. Cf,L = 1.328/√ReL సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: C. Cf,L = 2 Cf,x=L సమాధానం: C.
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Question 15 ప్రశ్న 15Answer: B. δ/x ≈ 0.37/Reₓ^(1/5) సమాధానం: B.
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Question 16 ప్రశ్న 16Answer: C. Cf,x ≈ 0.0592/Reₓ^(1/5) సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: A. Cf,L ≈ 0.074/ReL^(1/5) సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: B. 0.050 m సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: B. 1.12 mm సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: B. 0.001328 సమాధానం: B.
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Question 21 ప్రశ్న 21Answer: C. 0.252 Pa సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: C. 0.420 N సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: C. 23.3 mm సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: C. 0.00374 సమాధానం: C.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.