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Question 1
ప్రశ్న 1
What is meant by a hydraulically smooth surface in turbulent flow?
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Explanation:
Hydraulic smoothness is a flow-dependent concept rather than a statement that the surface is geometrically perfect. A physically rough surface may behave hydraulically smooth when its roughness elements remain effectively within the viscous near-wall region. Under this condition, the turbulent resistance behaves approximately like that of a smooth wall. Viscous effects shield the outer turbulent flow from the direct influence of the roughness elements. Therefore Option B is correct.
వివరణ:
Question 2
ప్రశ్న 2
Which statement correctly distinguishes geometrical smoothness from hydraulic smoothness?
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Explanation:
Geometrical roughness describes the physical size and character of surface irregularities. Hydraulic smoothness describes whether those irregularities significantly influence the resistance of a particular flow. The same physical surface may therefore behave hydraulically smooth under one flow condition and hydraulically rough under another. This occurs because the near-wall viscous scale changes with the flow and wall shear. Therefore Option B is correct.
వివరణ:
Question 3
ప్రశ్న 3
What is the principal role of the viscous sublayer in determining whether a turbulent wall behaves hydraulically smooth or rough?
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Explanation:
Very close to a turbulent wall, viscous effects remain important despite turbulent motion farther from the surface. If the roughness elements are small relative to this viscous near-wall scale, their direct effect on resistance is limited. As the roughness becomes increasingly exposed, it interacts more strongly with the turbulent flow. The wall then progresses from hydraulically smooth toward transitionally rough and eventually fully rough behavior. Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
Which description best represents transitionally rough turbulent flow?
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Explanation:
Transitionally rough behavior lies between the hydraulically smooth and fully rough regimes. The roughness elements are no longer completely shielded by the viscous near-wall region. At the same time, viscous effects have not become negligible in determining resistance. Consequently both Reynolds-number effects and surface roughness influence the wall resistance. Therefore Option C is correct.
వివరణ:
Question 5
ప్రశ్న 5
What characterizes fully rough turbulent wall behavior?
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Explanation:
In fully rough turbulent flow, roughness elements protrude sufficiently into the turbulent region to exert substantial pressure and form-drag effects. The resistance is then governed principally by the roughness geometry rather than by the viscous wall scale. For fully rough turbulent pipe flow, the Darcy friction factor becomes essentially independent of Reynolds number. It remains strongly dependent on relative roughness. Therefore Option B is correct.
వివరణ:
Question 6
ప్రశ్న 6
Why can increasing Reynolds number cause the same physically rough surface to change from hydraulically smooth toward rough behavior?
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Explanation:
The physical height of fixed wall roughness does not increase merely because the flow Reynolds number increases. However, the characteristic viscous length scale near the wall can become smaller relative to that roughness. Roughness elements that were effectively buried can then become increasingly exposed to turbulent motion. Their contribution to momentum transfer and form drag consequently becomes stronger. Therefore Option B is correct.
వివరణ:
Question 7
ప్రశ్న 7
A commonly used roughness Reynolds number is k_s+ = u_tau k_s/nu, where k_s is the equivalent sand-grain roughness height. What does u_tau represent?
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Explanation:
Friction velocity is a velocity scale constructed from the wall shear stress. It is defined as u_tau = sqrt(tau_w/rho), where tau_w is the wall shear stress and rho is fluid density. Although it has dimensions of velocity, it is not generally the actual fluid velocity at a particular point. It provides a natural scale for describing turbulent near-wall behavior. Therefore Option B is correct.
వివరణ:
Question 8
ప్రశ్న 8
Using a common engineering wall-unit classification, which condition most nearly represents a hydraulically smooth turbulent wall?
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Explanation:
The parameter k_s+ compares equivalent roughness height with the viscous wall scale. Values below approximately 5 are commonly associated with hydraulically smooth behavior. Intermediate values are generally classified as transitionally rough. Values sufficiently above roughly 70 are commonly associated with fully rough behavior. These boundaries are engineering guidelines and are not exact universal constants. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
Using commonly adopted wall-unit guidelines, a surface with k_s+ approximately 30 would most reasonably be classified as:
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Explanation:
A value of k_s+ near 30 lies between the commonly used smooth and fully rough limits. The roughness elements therefore influence the turbulent resistance appreciably. However, viscous effects remain important in the near-wall behavior. This places the wall in the transitionally rough regime under the stated engineering classification. Therefore Option B is correct.
వివరణ:
Question 10
ప్రశ్న 10
Water has rho = 1000 kg/m³ and nu = 1.0 × 10^-6 m²/s. If the wall shear stress is 4.0 Pa and equivalent sand-grain roughness height k_s = 0.05 mm, what is k_s+ approximately?
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Explanation:
The friction velocity is u_tau = sqrt(tau_w/rho) = sqrt(4/1000). This gives approximately 0.06325 m/s. The roughness height 0.05 mm equals 5.0 × 10^-5 m. Therefore k_s+ = 0.06325 × 5.0 × 10^-5/(1.0 × 10^-6) = approximately 3.16. Hence Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
Water has rho = 1000 kg/m³ and nu = 1.0 × 10^-6 m²/s. If the wall shear stress is 4.0 Pa and equivalent sand-grain roughness height k_s = 0.50 mm, what is k_s+ approximately?
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Explanation:
The friction velocity is u_tau = sqrt(4/1000) = approximately 0.06325 m/s. The roughness height 0.50 mm equals 5.0 × 10^-4 m. Therefore k_s+ = 0.06325 × 5.0 × 10^-4/(1.0 × 10^-6). The resulting value is approximately 31.6. This is within the commonly used transitionally rough range, so Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
Water has rho = 1000 kg/m³ and nu = 1.0 × 10^-6 m²/s. If the wall shear stress is 4.0 Pa and equivalent sand-grain roughness height k_s = 2.0 mm, what is k_s+ approximately?
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Explanation:
The friction velocity is approximately 0.06325 m/s. A roughness height of 2.0 mm equals 0.002 m. Thus k_s+ = 0.06325 × 0.002/(1.0 × 10^-6). This gives approximately 126.5. The value is well within the commonly used fully rough range, so Option D is correct.
వివరణ:
Question 13
ప్రశ్న 13
For turbulent flow in a circular pipe, which parameter is conventionally called relative roughness?
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Explanation:
The physical roughness height of a pipe is commonly represented by epsilon. Dividing this height by pipe diameter D produces the dimensionless relative roughness epsilon/D. Turbulent pipe-flow correlations such as the Colebrook equation use relative roughness together with Reynolds number. The ratio is natural for internal flow because pipe diameter provides the relevant geometric length scale. Therefore Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
A pipe has diameter D = 0.30 m and absolute roughness epsilon = 0.15 mm. What is its relative roughness epsilon/D?
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Explanation:
The absolute roughness 0.15 mm equals 0.00015 m. Relative roughness is epsilon/D. Thus epsilon/D = 0.00015/0.30. The result is 0.0005. Therefore Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
Which statement correctly describes the Darcy friction factor in fully developed laminar flow through a circular pipe?
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Explanation:
For fully developed laminar flow in a circular pipe, the Darcy friction factor follows the exact relation f = 64/Re. Ordinary surface roughness does not enter this classical laminar result. This differs fundamentally from turbulent pipe flow, in which wall roughness can strongly influence resistance. The distinction prevents turbulent roughness concepts from being incorrectly transferred to laminar pipe flow. Therefore Option A is correct.
వివరణ:
Question 16
ప్రశ్న 16
For turbulent pipe flow in the transitionally rough region, the Darcy friction factor principally depends on:
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In the transitionally rough turbulent regime, roughness elements influence the flow but viscous effects remain important. Reynolds number therefore continues to affect the resistance. At the same time, the relative roughness epsilon/D also influences the friction factor. The Colebrook relation incorporates both Reynolds-number and roughness effects. Therefore Option C is correct.
వివరణ:
Question 17
ప్రశ్న 17
In the fully rough turbulent region of pipe flow, which statement about the Darcy friction factor is correct?
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Explanation:
At sufficiently high roughness Reynolds number, the roughness elements dominate the wall-resistance behavior. The viscous contribution no longer controls the overall friction factor in the way it does for a hydraulically smooth turbulent pipe. The Darcy friction factor then approaches a value determined principally by epsilon/D. On the Moody diagram, fully rough curves approach nearly horizontal lines at sufficiently high Reynolds number. Therefore Option A is correct.
వివరణ:
Question 18
ప్రశ్న 18
Which expression is the fully rough limiting form of the Colebrook relation for the Darcy friction factor f in a circular pipe?
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Explanation:
The full Colebrook relation contains both a roughness term and a Reynolds-number-dependent viscous term. In the fully rough limit, the Reynolds-number-dependent term becomes negligible. The relation therefore reduces to 1/sqrt(f) = -2 log10[(epsilon/D)/3.7]. It shows explicitly that the limiting Darcy friction factor is controlled by relative roughness. Therefore Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
A fully rough turbulent pipe has relative roughness epsilon/D = 0.001. Using 1/sqrt(f) = -2 log10[(epsilon/D)/3.7], what is the Darcy friction factor approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Substitution gives 1/sqrt(f) = -2 log10(0.001/3.7). The resulting value of 1/sqrt(f) is approximately 7.136. Taking the reciprocal and squaring gives f approximately 0.01964. Rounded to the precision of the alternatives, this is 0.0196. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
If two fully rough pipes have the same absolute roughness epsilon but one pipe has a much larger diameter, what generally happens to its Darcy friction factor at otherwise comparable fully rough conditions?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Fully rough pipe resistance depends primarily on the relative roughness epsilon/D. For the same absolute roughness, increasing the pipe diameter decreases epsilon/D. A smaller relative roughness corresponds to a smaller fully rough Darcy friction factor. Thus the hydraulic significance of a fixed roughness height depends on the size of the pipe. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
Why is epsilon/D primarily a pipe-flow roughness parameter rather than a universal roughness parameter for an external boundary layer over a flat surface?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The ratio epsilon/D is natural for internal pipe flow because diameter is a fixed geometric scale of the conduit. A flat-plate boundary layer has no corresponding pipe diameter. Roughness in external turbulent boundary layers is therefore commonly described relative to wall units, equivalent sand-grain roughness scales or appropriate boundary-layer dimensions. This distinction prevents pipe-specific resistance parameters from being transferred blindly to external flows. Therefore Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
How can surface roughness influence transition of an external boundary layer over a plate?
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Explanation:
Transition of an external boundary layer is sensitive to disturbances. Surface roughness can generate perturbations and enhance the growth of instabilities within the layer. If the roughness is sufficiently significant relative to local boundary-layer scales, transition may occur earlier than on a smoother surface. The actual effect depends on roughness geometry, free-stream turbulence, pressure gradient and other conditions. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
For an already turbulent external boundary layer, what is the usual engineering effect of increasing dynamically significant surface roughness?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Exposed roughness elements interact strongly with turbulent flow near the wall. They alter near-wall momentum transfer and can generate additional pressure or form drag on the roughness elements. The overall wall resistance and drag therefore generally increase compared with a hydraulically smoother surface under comparable conditions. The no-slip condition continues to apply on the solid roughness surfaces. Therefore Option A is correct.
వివరణ:
Question 24
ప్రశ్న 24
Which statement about a hydraulically smooth turbulent pipe is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Hydraulically smooth does not mean frictionless. The no-slip condition and viscous effects remain present at the pipe wall. The term means that physical roughness elements are not large enough relative to the viscous wall scale to add a significant independent roughness penalty. A hydraulically smooth turbulent pipe therefore has a finite friction factor and measurable head loss. Therefore Option B is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about hydraulically smooth and rough boundaries: I. Hydraulic smoothness depends on roughness size relative to the near-wall viscous scale. II. A physically rough surface can behave hydraulically smooth. III. Fully rough turbulent pipe resistance becomes approximately independent of Reynolds number. IV. The pipe relative roughness epsilon/D should not automatically be used as the defining roughness parameter for an external flat-plate boundary layer. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I correctly expresses hydraulic roughness as a comparison between surface roughness and near-wall viscous scales. Statement II is correct because sufficiently small physical roughness can remain hydraulically submerged. Statement III describes the standard fully rough limiting behavior of turbulent pipe resistance. Statement IV correctly distinguishes the pipe-specific relative-roughness concept from roughness characterization in external boundary layers. 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: B. A surface whose roughness elements are sufficiently submerged within the viscous near-wall region that they do not significantly increase resistance సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: B. Hydraulic smoothness depends on both the surface roughness and the flow conditions సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: A. It determines whether surface roughness is effectively shielded from or exposed to the turbulent flow సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: C. The roughness elements influence the flow, but viscous effects are still significant, so resistance depends on both సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: B. The exposed roughness elements dominate the roughness-related resistance, and viscous scaling no longer controls the overall resistance in the same way as for a smooth wall సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: B. Because the viscous near-wall length scale becomes smaller relative to the fixed roughness elements సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: B. The friction velocity, u_tau = sqrt(tau_w/rho) సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: A. k_s+ less than about 5 సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: B. Transitionally rough సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: B. 3.16 సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: C. 31.6 సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: D. 126 సమాధానం: D.
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Question 13 ప్రశ్న 13Answer: B. epsilon/D సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: B. 0.0005 సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: A. It is f = 64/Re and is ordinarily independent of pipe-wall roughness సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: C. Both Reynolds number and relative roughness సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: A. It depends primarily on relative roughness and becomes essentially independent of Reynolds number సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: A. 1/sqrt(f) = -2 log10[(epsilon/D)/3.7] సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: B. 0.0196 సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: A. It generally decreases because epsilon/D becomes smaller సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: A. An external flat-plate boundary layer has no pipe diameter D, so roughness is more naturally compared with near-wall viscous scales or relevant boundary-layer scales సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: A. Sufficient roughness can introduce disturbances and promote earlier transition from laminar to turbulent flow సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: A. It tends to increase wall resistance and drag సమాధానం: A.
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Question 24 ప్రశ్న 24Answer: B. It still has frictional head loss because viscous wall effects remain present even though roughness does not significantly increase resistance సమాధానం: B.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.