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Question 1
ప్రశ్న 1
In Lacey's theory, what is meant by a channel being in regime?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Lacey used the term regime for an alluvial channel that has adjusted toward a stable condition. In such a condition, persistent aggradation and degradation are absent under the governing discharge and sediment regime. The bed, sides, depth, width and slope participate in establishing the equilibrium geometry. This differs from a rigid channel whose boundaries cannot adjust to the flow. Lacey's regime concept is empirical and represents an idealization of actual canal behavior. Therefore Option B is correct.
వివరణ:
Question 2
ప్రశ్న 2
Which combination most closely represents the conditions postulated for a true Lacey regime channel?
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Explanation:
Lacey's true-regime concept assumes conditions under which the mobile channel can adjust its geometry. Discharge and sediment load or grade are treated as essentially constant for the regime condition. The channel is assumed to flow through unlimited incoherent alluvium capable of erosion and deposition. The boundary material is also assumed to be broadly related to the sediment being transported. These ideal conditions are rarely satisfied perfectly in an actual irrigation canal. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
Which statement correctly distinguishes initial regime from final regime in Lacey's terminology?
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Explanation:
A canal constructed with dimensions different from its ultimate regime section may first establish a working equilibrium. Lacey referred to such a stage as initial regime, particularly when complete lateral adjustment is restricted. With sufficient mobility of the bed and sides, the channel can subsequently adjust its dimensions and slope. This more complete equilibrium is called final regime. If the sides are effectively non-erodible, full final-regime adjustment may not occur. Therefore Option C is correct.
వివరణ:
Question 4
ప్రశ్న 4
What is Lacey's silt factor f intended to represent?
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Explanation:
Lacey recognized that sediment size influences the equilibrium dimensions and velocity of an alluvial channel. He therefore introduced an empirical parameter known as the silt factor, denoted by f. The factor increases with the characteristic sediment size. It enters several Lacey regime equations for velocity, hydraulic radius and bed slope. It should not be confused with hydraulic roughness or channel side slope. Therefore Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which expression gives Lacey's silt factor when the representative sediment diameter d is expressed in millimetres?
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Explanation:
Lacey related the empirical silt factor to sediment size by f = 1.76 sqrt(d). The sediment diameter d is expressed in millimetres in this conventional relation. Because of the square-root dependence, f increases as sediment becomes coarser. The relationship is empirical rather than a first-principles sediment-transport law. Its use should therefore remain consistent with the regime-theory assumptions. Therefore Option C is correct.
వివరణ:
Question 6
ప్రశ్న 6
For sediment having representative diameter d = 0.25 mm, what is Lacey's silt factor?
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Explanation:
Lacey's relation is f = 1.76 sqrt(d), with d in millimetres. For d = 0.25 mm, sqrt(0.25) = 0.50. Thus f = 1.76 × 0.50 = 0.88. The result is dimensionless in its conventional empirical use. This value would then be used in the other regime equations for the channel. Therefore Option B is correct.
వివరణ:
Question 7
ప్రశ్న 7
If the representative sediment size increases while all other conceptual conditions are unchanged, what happens to Lacey's silt factor?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The empirical relation is f = 1.76 sqrt(d). An increase in sediment diameter therefore produces an increase in the silt factor. The increase is proportional to the square root of sediment size rather than directly proportional to it. The larger value of f subsequently changes the regime velocity, hydraulic radius and slope predicted by Lacey's equations. This is the principal mechanism by which sediment grade enters the theory. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
Which expression is commonly used for Lacey's regime mean velocity in terms of discharge Q and silt factor f?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A commonly used derived Lacey relation for mean regime velocity is V = (Qf^2/140)^(1/6). It expresses velocity as a weak function of discharge because Q appears to the one-sixth power. The influence of the silt factor is equivalent to approximately f^(1/3). This relationship is convenient in objective canal-design calculations because Q and f are normally known early in the design. It remains an empirical regime relationship rather than a universal sediment-transport formula. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
Using V = (Qf^2/140)^(1/6), what is the regime velocity for Q = 40 m³/s and f = 1.0?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The stated equation gives V = (40 × 1^2/140)^(1/6). The quantity inside the bracket is approximately 0.2857. Taking the sixth root gives approximately 0.8116 m/s. Rounded suitably, the regime velocity is about 0.812 m/s. This velocity can then be combined with continuity to determine the required regime flow area. Therefore Option B is correct.
వివరణ:
Question 10
ప్రశ్న 10
According to V = (Qf^2/140)^(1/6), which proportionality is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The equation can be written as V proportional to Q^(1/6)f^(2/6). Since 2/6 equals 1/3, the sediment-factor dependence is f^(1/3). The discharge exponent of one-sixth shows that regime velocity increases only slowly with increasing discharge. The silt factor also raises the predicted regime velocity when coarser sediment is represented by a larger f. These proportionalities follow directly from the empirical velocity equation. Therefore Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
What is Lacey's regime relationship for wetted perimeter P and discharge Q in SI units?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Lacey related the regime wetted perimeter directly to discharge. The conventional SI relation is P = 4.75 sqrt(Q). It predicts that larger-discharge regime channels require a larger wetted perimeter. The sediment factor does not appear explicitly in this particular equation. Combined with the area and hydraulic-radius relations, it helps determine the regime channel dimensions. Therefore Option B is correct.
వివరణ:
Question 12
ప్రశ్న 12
For a Lacey regime channel carrying Q = 64 m³/s, what wetted perimeter is given by P = 4.75 sqrt(Q)?
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Explanation:
The square root of 64 is 8. Lacey's perimeter relation therefore gives P = 4.75 × 8. This equals 38 m. The value represents the regime wetted perimeter predicted for the stated discharge. Actual channel dimensions must also satisfy the required flow area and selected cross-sectional geometry. Therefore Option C is correct.
వివరణ:
Question 13
ప్రశ్న 13
A regime channel has a wetted perimeter of 47.5 m. Using Lacey's relation P = 4.75 sqrt(Q), what discharge does this correspond to?
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Explanation:
The perimeter relation gives sqrt(Q) = P/4.75. Substituting P = 47.5 m gives sqrt(Q) = 10. Squaring this result gives Q = 100 m³/s. The calculation uses only the regime perimeter relation and does not yet define the complete channel geometry. Additional Lacey equations are required to establish the hydraulic radius, slope and section dimensions. Therefore Option C is correct.
వివరణ:
Question 14
ప్రశ్న 14
Which Lacey relationship connects regime velocity V, hydraulic radius R and silt factor f?
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Explanation:
One of Lacey's fundamental regime relations can be written as V = sqrt(2Rf/5). Squaring it gives V² = 2Rf/5. Rearranging also gives R = 5V²/(2f). This relation links the hydraulic size of the section with mean velocity and sediment grade. It is distinct from the separate perimeter-discharge and regime-slope equations. Therefore Option A is correct.
వివరణ:
Question 15
ప్రశ్న 15
If V = 0.90 m/s and f = 1.0, what hydraulic radius is obtained from R = 5V²/(2f)?
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Explanation:
The stated relation is R = 5V²/(2f). The square of 0.90 m/s is 0.81. Therefore R = 5 × 0.81/(2 × 1.0). This gives R = 4.05/2 = 2.025 m. The calculation is based on Lacey's regime relation for the stated velocity and silt factor. Therefore Option C is correct.
వివరణ:
Question 16
ప్రశ్న 16
Which approximate direct relationship for hydraulic radius is commonly used in Lacey regime design?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Combining Lacey's empirical regime relationships produces a convenient direct expression for hydraulic radius. A commonly used rounded SI form is R ≈ 0.48(Q/f)^(1/3). The hydraulic radius therefore increases with discharge and decreases as silt factor increases for a fixed discharge. Slightly different rounded constants may appear in textbooks because the underlying empirical coefficients themselves are rounded. The engineering interpretation remains the same. Therefore Option A is correct.
వివరణ:
Question 17
ప్రశ్న 17
Using R = 0.48(Q/f)^(1/3), what is the approximate hydraulic radius for Q = 64 m³/s and f = 1.0?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For Q = 64 m³/s and f = 1.0, the cube root of Q/f is the cube root of 64. This value is 4. Multiplying by 0.48 gives R = 1.92 m. The value is consistent with the rounded direct hydraulic-radius form used in Lacey regime calculations. Small differences can occur if alternative rounded versions of the underlying empirical constants are combined. Therefore Option C is correct.
వివరణ:
Question 18
ప్రశ్న 18
For fixed discharge Q, what happens to the hydraulic radius predicted by R ≈ 0.48(Q/f)^(1/3) when the silt factor f increases?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The direct Lacey relationship contains Q/f inside a cube root. At a fixed discharge, increasing f reduces the value of Q/f. The resulting hydraulic radius therefore decreases. Mathematically, R is proportional to f^(-1/3) for fixed Q. This illustrates how sediment grade influences the regime section predicted by Lacey's empirical theory. Therefore Option C is correct.
వివరణ:
Question 19
ప్రశ్న 19
Which expression gives the conventional Lacey regime bed slope S in terms of silt factor f and discharge Q?
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Explanation:
Lacey's theory provides a direct empirical relationship for the regime longitudinal slope. A commonly used form is S = f^(5/3)/(3340 Q^(1/6)). An equivalent rounded expression is approximately 0.0003f^(5/3)/Q^(1/6). The slope therefore increases strongly with silt factor and decreases mildly as discharge increases. Providing a direct slope relation is an important distinction between Lacey's method and Kennedy's original critical-velocity theory. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
For Q = 64 m³/s and f = 1.0, what regime bed slope is obtained from S = f^(5/3)/(3340 Q^(1/6))?
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Explanation:
The sixth root of 64 is 2. With f = 1.0, the numerator f^(5/3) is also 1. The denominator is therefore 3340 × 2 = 6680. Thus S = 1/6680, or approximately 0.0001497. The regime slope is consequently about 1 in 6680 for the stated values. Therefore Option C is correct.
వివరణ:
Question 21
ప్రశ్న 21
A Lacey regime channel carries Q = 40 m³/s with f = 1.0. Using V = (Qf²/140)^(1/6), what flow area A = Q/V is required?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For Q = 40 m³/s and f = 1.0, the Lacey velocity is approximately 0.8116 m/s. Continuity gives A = Q/V. Thus A = 40/0.8116, which is approximately 49.29 m². Rounded suitably, the required regime flow area is about 49.3 m². The area and wetted perimeter can subsequently be combined with an assumed practical cross-sectional form to determine channel dimensions. Therefore Option C is correct.
వివరణ:
Question 22
ప్రశ్న 22
For Q = 40 m³/s and f = 1.0, Lacey's equations give approximately A = 49.29 m² and P = 30.04 m. If a symmetrical trapezoidal section with side slope z = 0.5H:1V is adopted, using A = D(B + zD) and P = B + 2D sqrt(1 + z²), which trial dimensions satisfy both relations approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Lacey relations provide the required area and wetted perimeter but do not by themselves force a particular practical trapezoidal side slope. With z = 0.5, solving the two supplied section equations simultaneously gives D approximately 1.835 m. Substituting this depth into the perimeter equation gives B approximately 25.94 m. These dimensions reproduce both A ≈ 49.29 m² and P ≈ 30.04 m. The example illustrates how regime hydraulic quantities are converted into practical canal geometry. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
Which statement best describes the influence of discharge on Lacey's regime wetted perimeter?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Lacey's perimeter equation is P = 4.75 sqrt(Q). The wetted perimeter therefore increases when discharge increases. The dependence is through the square root, so doubling the discharge increases perimeter by a factor of sqrt(2), not by a factor of two. This relation reflects the empirical geometry of regime channels represented in Lacey's observations. It does not contain the silt factor explicitly. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
Which comparison between Kennedy's and Lacey's alluvial-canal theories is most accurate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Kennedy's classical method is centered on an empirical critical-velocity relationship involving depth and the critical velocity ratio. The canal slope must be obtained or checked using a separate resistance relationship because Kennedy did not give a direct regime-slope equation. Lacey explicitly introduced the silt factor to represent sediment-size effects. He also supplied relationships for wetted perimeter, hydraulic radius and longitudinal slope. Both approaches are empirical, but their formulation and design procedure are therefore substantially different. Therefore Option B is correct.
వివరణ:
Question 25
ప్రశ్న 25
Which statement identifies an important limitation of Lacey's regime theory?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Lacey developed the regime equations mainly from observations of stable alluvial channels. They are therefore empirical correlations rather than universal equations derived from fundamental sediment mechanics. Their predictions are most defensible for channels whose discharge, sediment and boundary conditions resemble those represented in the original regime data. Real canals can have variable discharge, cohesive banks, nonuniform sediment and changing sediment concentration. Such departures can reduce the accuracy of a purely regime-based design. Therefore Option B is correct.
వివరణ:
Question 26
ప్రశ్న 26
Why should Lacey's silt factor not be regarded as a complete description of sediment transport?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The silt factor provides a compact empirical representation of sediment-size influence. Actual sediment transport depends on many additional variables, including concentration, size distribution, settling velocity, turbulence, boundary shear and differences between bed and bank material. Real canal sediments can also change through sorting, deposition and abrasion. Lacey's equations do not explicitly resolve all of these mechanisms. The factor f is therefore useful for traditional regime design but should not be mistaken for a complete sediment-transport model. Therefore Option A is correct.
వివరణ:
Question 27
ప్రశ్న 27
Consider the following statements about Lacey's regime theory: I. The silt factor increases with representative sediment size. II. The wetted perimeter is proportional to sqrt(Q). III. Hydraulic radius may be expressed approximately as 0.48(Q/f)^(1/3). IV. Lacey provides an empirical relationship for regime bed slope. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is correct because f = 1.76 sqrt(d), so coarser representative sediment gives a larger silt factor. Statement II is correct because Lacey's regime perimeter relation is P = 4.75 sqrt(Q). Statement III is correct in the commonly rounded regime form R ≈ 0.48(Q/f)^(1/3). Statement IV is correct because Lacey also supplied an empirical longitudinal-slope relationship involving f and Q. These relations together allow the regime dimensions and slope to be estimated from the design discharge and sediment characteristics. 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. The channel is in a stable alluvial condition in which its section and slope are compatible with the discharge and sediment so that persistent silting or scouring does not occur సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: A. Constant discharge and sediment conditions, with the channel flowing in unlimited incoherent alluvium broadly similar to the transported material సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: C. In initial regime the canal may attain a working equilibrium mainly by slope adjustment, whereas in final regime its dimensions and slope have adjusted to the governing discharge and sediment conditions సమాధానం: C.
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Question 4 ప్రశ్న 4Answer: B. The effect of sediment size or grade on the regime characteristics of the alluvial channel సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: C. f = 1.76 sqrt(d) సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: B. 0.88 సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: A. It increases సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: A. V = (Qf^2/140)^(1/6) సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: B. Approximately 0.812 m/s సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: B. V is proportional to Q^(1/6) and f^(1/3) సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: B. P = 4.75 sqrt(Q) సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: C. 38 m సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: C. 100 m³/s సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: A. V² = 2Rf/5 సమాధానం: A.
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Question 15 ప్రశ్న 15Answer: C. 2.025 m సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: A. R ≈ 0.48(Q/f)^(1/3) సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: C. 1.92 m సమాధానం: C.
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Question 18 ప్రశ్న 18Answer: C. It decreases approximately as f^(-1/3) సమాధానం: C.
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Question 19 ప్రశ్న 19Answer: B. S = f^(5/3)/(3340 Q^(1/6)) సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: C. Approximately 1 in 6680 సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: C. Approximately 49.3 m² సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: A. D ≈ 1.84 m and B ≈ 25.94 m సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: C. P increases in proportion to the square root of discharge సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: B. Kennedy emphasizes a depth-based critical velocity and requires a separate resistance relation for slope, whereas Lacey introduces a silt factor and provides regime relationships for perimeter, hydraulic radius and slope సమాధానం: B.
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Question 25 ప్రశ్న 25Answer: B. Its regime equations are empirical and are most reliable for conditions broadly similar to the alluvial-channel data from which they were developed సమాధానం: B.
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Question 26 ప్రశ్న 26Answer: A. Because it represents sediment-size effects through a single empirical factor and does not explicitly describe all effects of sediment concentration, grading, bed-versus-bank properties and detailed transport mechanics సమాధానం: A.
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Question 27 ప్రశ్న 27Answer: D. I, II, III and IV సమాధానం: D.