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Question 1
ప్రశ్న 1
Which statement best describes steady uniform flow in a prismatic open channel?
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Explanation:
Uniformity refers to the absence of spatial variation of the principal flow variables along the channel reach. In steady uniform flow, depth, flow area and mean velocity remain constant with distance and time. A prismatic channel provides constant geometry, but uniform flow occurs only when the hydraulic conditions permit it. Boundary resistance balances the component of gravity driving the flow. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
In established steady uniform flow through a prismatic channel, which relationship between the relevant slopes is appropriate?
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Explanation:
In uniform flow, the flow depth remains constant along the channel. Consequently the bed and free-water surface are parallel over the uniform reach. The energy grade line is also parallel because the mean velocity does not vary longitudinally. Thus the bed slope, water-surface slope and friction or energy slope are equal in the standard uniform-flow model. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
Which expression is the Chezy equation for mean velocity in steady uniform open-channel flow?
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Explanation:
The Chezy resistance equation is V = C√(RS). Here V is mean velocity, C is the Chezy coefficient, R is hydraulic radius and S is the friction slope. In uniform flow, the friction slope equals the channel bed slope. The equation represents the balance between gravitational driving force and boundary resistance. Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
Which statement about the Chezy coefficient C is correct in SI units?
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Explanation:
From V = C√(RS), the quantity √(RS) has dimensions of the square root of length because slope is dimensionless. Therefore C has SI dimensions of m^(1/2)/s. A larger Chezy coefficient generally represents lower hydraulic resistance under comparable conditions. It is not the same coefficient as Manning's n, although the two can be related for a specified hydraulic radius. Therefore Option A is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which expression is Manning's equation for mean velocity in SI units?
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Explanation:
The SI form of Manning's equation is V = (1/n)R^(2/3)S^(1/2). The coefficient n is Manning's roughness coefficient. Hydraulic radius represents the effect of cross-sectional geometry, while S represents the friction slope. For established uniform flow, S may be taken equal to the channel bed slope. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
For the same hydraulic radius and slope, what is the effect of increasing Manning's roughness coefficient n?
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Explanation:
Manning's equation contains the factor 1/n. Therefore velocity is inversely proportional to the roughness coefficient when R and S remain fixed. Increasing n represents greater resistance to flow. Greater resistance produces a lower mean velocity for the same channel geometry and slope. Hence Option A is correct.
వివరణ:
Question 7
ప్రశ్న 7
Which geometric quantity must be used for R in the Chezy and Manning uniform-flow equations?
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Explanation:
The resistance equations use hydraulic radius rather than hydraulic depth. Hydraulic radius is defined as the flow area A divided by the wetted perimeter P. The free surface is not included in the wetted perimeter. Hydraulic depth A/T is important for Froude-number calculations but is a different quantity. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
A rectangular channel is 4 m wide and carries water 1.5 m deep. If the Chezy coefficient is C = 50 m^(1/2)/s and the uniform-flow slope is S = 0.0016, what is the mean velocity approximately?
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Explanation:
The area is A = 4 × 1.5 = 6 m² and the wetted perimeter is P = 4 + 2(1.5) = 7 m. Hence the hydraulic radius is R = 6/7 = 0.8571 m. Chezy's equation gives V = 50√(0.8571 × 0.0016). This evaluates to approximately 1.852 m/s. Therefore Option B is correct.
వివరణ:
Question 9
ప్రశ్న 9
A channel has mean velocity V = 2.4 m/s, hydraulic radius R = 0.64 m and uniform-flow slope S = 0.0025. What Chezy coefficient C is required?
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Explanation:
Chezy's equation is V = C√(RS). Rearranging gives C = V/√(RS). Here RS = 0.64 × 0.0025 = 0.0016, whose square root is 0.04. Therefore C = 2.4/0.04 = 60 m^(1/2)/s. Hence Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
A rectangular channel 4 m wide carries water 1.5 m deep. Using Manning's equation with n = 0.015 and S = 0.0016, what is the discharge approximately?
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Explanation:
The flow area is 6 m² and the wetted perimeter is 7 m, giving R = 6/7 = 0.8571 m. Manning's equation gives V = (1/0.015)(0.8571)^(2/3)(0.0016)^(1/2). The resulting mean velocity is approximately 2.406 m/s. Hence Q = AV = 6 × 2.406 = approximately 14.44 m³/s. Therefore Option C is correct.
వివరణ:
Question 11
ప్రశ్న 11
A channel must carry uniform flow at V = 2.0 m/s with hydraulic radius R = 0.90 m and Manning coefficient n = 0.015. What slope S is required approximately?
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Explanation:
Manning's equation can be rearranged as S = [Vn/R^(2/3)]². Substituting V = 2.0 m/s, n = 0.015 and R = 0.90 m gives the required slope. The calculated value is approximately 0.0010357. Rounded appropriately, this is 0.001036. Therefore Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
A channel has hydraulic radius R = 0.75 m, uniform-flow slope S = 0.0009 and mean velocity V = 1.8 m/s. What is Manning's roughness coefficient n approximately?
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Explanation:
Rearranging Manning's equation gives n = R^(2/3)S^(1/2)/V. The square root of 0.0009 is 0.03. Substituting R = 0.75 m and V = 1.8 m/s gives n approximately equal to 0.013758. Rounded suitably, n is 0.01376. Therefore Option B is correct.
వివరణ:
Question 13
ప్రశ్న 13
A uniform-flow channel has V = 2.0 m/s, Manning coefficient n = 0.016 and slope S = 0.0016. What hydraulic radius is required approximately?
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Explanation:
From Manning's equation, R^(2/3) = Vn/√S. Here √S = √0.0016 = 0.04. Thus R^(2/3) = 2.0 × 0.016/0.04 = 0.80. Raising both sides to the power 3/2 gives R = approximately 0.716 m. Therefore Option C is correct.
వివరణ:
Question 14
ప్రశ్న 14
A channel has Chezy coefficient C = 45 m^(1/2)/s and hydraulic radius R = 0.50 m. What uniform-flow slope is required to obtain V = 1.5 m/s?
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Explanation:
From Chezy's equation, S = (V/C)²/R. The ratio V/C is 1.5/45 = 1/30. Squaring gives approximately 0.001111. Dividing by R = 0.50 gives S approximately 0.002222. Therefore Option C is correct.
వివరణ:
Question 15
ప్రశ్న 15
For a given channel section with unchanged resistance coefficient, what happens to the uniform-flow velocity predicted by either the Chezy or Manning equation if the slope is increased to four times its original value?
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Explanation:
Both Chezy and Manning equations contain the square root of slope. Thus V is proportional to S^(1/2) when the other relevant quantities remain unchanged. Increasing slope by a factor of four increases velocity by √4. The resulting velocity ratio is 2. Therefore Option A is correct.
వివరణ:
Question 16
ప్రశ్న 16
For a fixed channel section and slope, Manning's n increases from 0.015 to 0.020. What is the ratio of the new mean velocity to the original mean velocity?
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Explanation:
For fixed R and S, Manning's equation gives V proportional to 1/n. Therefore V2/V1 = n1/n2. Substituting the values gives 0.015/0.020 = 0.75. Thus the rougher condition reduces the velocity to 75 percent of its original value. Therefore Option B is correct.
వివరణ:
Question 17
ప్రశ్న 17
According to the Chezy equation, if hydraulic radius doubles while C and S remain unchanged, by what factor does the mean velocity change?
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Explanation:
Chezy's equation gives V proportional to R^(1/2) when C and S are fixed. Doubling hydraulic radius therefore gives V2/V1 = √2. The numerical value of √2 is approximately 1.414. This comparison concerns velocity and assumes the stated resistance coefficient remains unchanged. Therefore Option B is correct.
వివరణ:
Question 18
ప్రశ్న 18
According to Manning's equation, if hydraulic radius doubles while n and S remain unchanged, by what factor does the mean velocity change?
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Explanation:
Manning's equation gives V proportional to R^(2/3) for fixed n and S. If R doubles, the velocity ratio becomes 2^(2/3). This evaluates to approximately 1.587. The dependence on hydraulic radius is therefore stronger than the explicit R^(1/2) dependence in the Chezy equation when the respective coefficients are held constant. Therefore Option C is correct.
వివరణ:
Question 19
ప్రశ్న 19
By equating the SI forms of the Chezy and Manning velocity equations for the same R and S, which relationship is obtained between C and n?
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Explanation:
Chezy's equation is V = C R^(1/2)S^(1/2). Manning's equation in SI units is V = (1/n)R^(2/3)S^(1/2). Equating the two expressions and cancelling the common slope factor gives C R^(1/2) = R^(2/3)/n. Hence C = R^(1/6)/n. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
For a channel with hydraulic radius R = 1.0 m and Manning coefficient n = 0.020, what equivalent Chezy coefficient follows from C = R^(1/6)/n?
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Explanation:
The stated conversion is C = R^(1/6)/n in SI form. Since R = 1.0 m, the numerical value of R^(1/6) is 1. Thus C = 1/0.020 = 50. In the Chezy equation its SI units are m^(1/2)/s. Therefore Option C is correct.
వివరణ:
Question 21
ప్రశ్న 21
A trapezoidal channel has bottom width 3 m, side slope 1 horizontal to 1 vertical, flow depth 1.5 m, Manning coefficient n = 0.018 and uniform-flow slope S = 0.001. What discharge does Manning's equation give approximately?
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Explanation:
For z = 1, the flow area is A = y(b + zy) = 1.5(3 + 1.5) = 6.75 m². The wetted perimeter is P = b + 2y√(1 + z²) = 3 + 3√2 = approximately 7.243 m. Thus R = A/P = approximately 0.932 m, and Manning's equation gives V approximately 1.676 m/s. Multiplying by the area gives Q = 6.75 × 1.676 = approximately 11.31 m³/s. Therefore Option C is correct.
వివరణ:
Question 22
ప్రశ్న 22
A symmetric triangular channel has side slope 1.5 horizontal to 1 vertical, water depth 1.2 m, Manning coefficient n = 0.020 and slope S = 0.0025. What is the uniform-flow discharge approximately?
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Explanation:
For a triangular section, A = zy² = 1.5 × 1.2² = 2.16 m². The wetted perimeter is P = 2y√(1 + z²) = 2.4√3.25 = approximately 4.327 m. Hence R = 2.16/4.327 = approximately 0.499 m, giving V approximately 1.573 m/s from Manning's equation. The discharge is Q = 2.16 × 1.573 = approximately 3.40 m³/s. Therefore Option C is correct.
వివరణ:
Question 23
ప్రశ్న 23
A very wide rectangular channel may be approximated by R = y. If Manning's n = 0.020, slope S = 0.0016 and discharge per unit width q = 3.93 m²/s, what is the normal depth approximately?
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Explanation:
For a very wide rectangular channel, R is approximately y and the area per unit width is y. Manning's equation therefore gives q = (1/n)y^(5/3)S^(1/2). Rearranging gives y = [qn/√S]^(3/5). Substituting q = 3.93 m²/s, n = 0.020 and S = 0.0016 gives approximately 1.50 m. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
A channel section has area A = 4.0 m² and hydraulic radius R = 0.80 m. It must carry Q = 8.0 m³/s with Manning coefficient n = 0.016. What uniform-flow slope is required approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The required mean velocity is V = Q/A = 8/4 = 2.0 m/s. Manning's equation can then be rearranged as S = [Vn/R^(2/3)]². Substituting V = 2.0 m/s, n = 0.016 and R = 0.80 m gives S approximately 0.0013788. Rounded appropriately, the required slope is 0.001379. Therefore Option C is correct.
వివరణ:
Question 25
ప్రశ్న 25
If the Chezy coefficient C and Manning coefficient n are each treated as fixed in their respective equations, which comparison of the explicit dependencies of velocity is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Chezy's equation is V = C R^(1/2)S^(1/2). Manning's equation is V = (1/n)R^(2/3)S^(1/2). Thus both equations contain the square root of slope when their resistance coefficients are treated as fixed. Their explicit hydraulic-radius exponents differ, being one-half for Chezy and two-thirds for Manning. Therefore Option A is correct.
వివరణ:
Question 26
ప్రశ్న 26
Consider the following statements about uniform open-channel flow: I. Chezy's equation may be written V = C√(RS). II. Manning's SI equation may be written V = (1/n)R^(2/3)S^(1/2). III. Increasing Manning's n decreases velocity when R and S are fixed. IV. In established uniform flow through a prismatic channel, the friction slope equals the bed slope. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is the standard Chezy velocity relationship. Statement II is the standard Manning velocity equation in SI form. Statement III follows from the inverse dependence of Manning velocity on the roughness coefficient n. Statement IV is a defining hydraulic feature of established uniform flow in a prismatic channel. 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. Flow depth and mean velocity remain constant with distance along the uniform reach and do not change with time సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: A. Bed slope = water-surface slope = friction or energy slope సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. V = C√(RS) సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: A. It represents channel resistance and has dimensions of length^(1/2) per time సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: A. V = (1/n)R^(2/3)S^(1/2) సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: A. Mean velocity decreases సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: A. Hydraulic radius R = A/P, where P is wetted perimeter సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: B. 1.852 m/s సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: C. 60 m^(1/2)/s సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: C. 14.44 m³/s సమాధానం: C.
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Question 11 ప్రశ్న 11Answer: C. 0.001036 సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: B. 0.01376 సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: C. 0.716 m సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: C. 0.002222 సమాధానం: C.
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Question 15 ప్రశ్న 15Answer: A. Velocity becomes twice the original value సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: B. 0.75 సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: B. 1.414 సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: C. 1.587 సమాధానం: C.
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Question 19 ప్రశ్న 19Answer: A. C = R^(1/6)/n సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: C. 50 m^(1/2)/s సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: C. 11.31 m³/s సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: C. 3.40 m³/s సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: C. 1.50 m సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: C. 0.001379 సమాధానం: C.
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Question 25 ప్రశ్న 25Answer: A. Both give V proportional to S^(1/2), while Chezy gives V proportional to R^(1/2) and Manning gives V proportional to R^(2/3) సమాధానం: A.
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Question 26 ప్రశ్న 26Answer: D. I, II, III and IV సమాధానం: D.