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Question 1
ప్రశ్న 1
Which statement best describes a surge in an open channel?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A surge is an unsteady open-channel disturbance produced by a relatively rapid change in hydraulic conditions. It involves changes in water depth and usually also in mean velocity and discharge. Gate operation, sudden inflow changes and flow-control actions can generate surges. Unlike gradually varied steady flow, a surge propagates through the channel with time. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
How are positive and negative surges distinguished?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The terms positive and negative describe the sign of the water-level change caused by the disturbance. A positive surge leaves a greater depth after it passes a fixed observer. A negative surge leaves a smaller depth. These terms do not by themselves specify the direction in which the wave travels. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
Which statement about surge direction and surge sign is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Surge sign describes whether water depth increases or decreases. Propagation direction is a separate characteristic determined by the origin of the disturbance and the underlying flow. For example, rapid downstream gate closure can produce an upstream-moving positive surge. Rapid opening of a gate separating two reaches can produce an upstream-moving negative disturbance and a downstream-moving positive disturbance. Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
For a small-amplitude long gravity wave in a rectangular open channel of depth y, what is the wave celerity relative to the water under the shallow-water approximation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a small-amplitude shallow-water gravity wave in a rectangular channel, the wave celerity relative to the local water is c = √(gy). This result follows from the linearized shallow-water equations. The depth y acts as the characteristic hydraulic depth for a rectangular section. The relation is also directly connected to the open-channel Froude number. Therefore Option A is correct.
వివరణ:
Question 5
ప్రశ్న 5
For a small-amplitude long wave in a general open-channel section, which expression gives the local wave celerity when D = A/T is the hydraulic depth?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a general channel section, hydraulic depth is D = A/T, where A is flow area and T is top width. The small-disturbance gravity-wave celerity is c = √(gD). For a rectangular channel, D equals the actual flow depth and the expression reduces to √(gy). Hydraulic radius is used primarily in resistance equations and is not the characteristic depth in this wave-speed expression. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
Water flows downstream at mean velocity V in a uniform channel, and a small-amplitude shallow-water wave has celerity c relative to the water. What are the two characteristic wave velocities relative to a stationary observer on the bank?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A small gravity disturbance travels at speed c relative to the moving water. The downstream-moving disturbance therefore has bank-frame velocity V + c. The disturbance attempting to propagate upstream has signed bank-frame velocity V - c when downstream is taken as positive. Whether this second velocity is actually upstream or downstream depends on the relative magnitudes of V and c. Therefore Option A is correct.
వివరణ:
Question 7
ప్రశ్న 7
Why can a small surface disturbance propagate upstream in subcritical open-channel flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Subcritical flow has Fr = V/c less than one. Therefore V is smaller than the shallow-water wave celerity c. The signed velocity V - c is consequently negative when downstream is positive. This allows a small disturbance to move physically upstream relative to a stationary observer. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
What happens to small disturbances in a supercritical open-channel flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Supercritical flow has a Froude number greater than one. Hence the mean velocity V exceeds the local shallow-water wave celerity c. Both V + c and V - c are then positive in a downstream-positive coordinate system. Thus even a disturbance propagating upstream relative to the water is swept downstream relative to the channel banks. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
At critical open-channel flow, what happens to an infinitesimal disturbance that attempts to propagate upstream relative to the water?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At critical flow, the Froude number equals one. Hence V = c for the small gravity-wave celerity. The upstream-running characteristic has bank-frame speed V - c = 0. It is therefore stationary relative to the channel in the idealized small-wave interpretation. Therefore Option A is correct.
వివరణ:
Question 10
ప్రశ్న 10
A rectangular channel has water depth y = 1.60 m. What is the small-amplitude shallow-water wave celerity relative to the water? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a rectangular channel, c = √(gy). Substituting y = 1.60 m gives c = √(9.81 × 1.60). The quantity inside the square root is 15.696 m²/s². Therefore c is approximately 3.962 m/s and Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
A rectangular channel carries water downstream at V = 1.50 m/s and depth y = 1.60 m. What are the approximate bank-frame speeds of small disturbances moving downstream and upstream? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At 1.60 m depth, the wave celerity is approximately 3.962 m/s. The downstream disturbance travels at V + c = 1.50 + 3.962 = approximately 5.462 m/s. The other characteristic has signed speed V - c = -2.462 m/s. Thus it moves physically upstream at a speed magnitude of approximately 2.46 m/s, so Option A is correct.
వివరణ:
Question 12
ప్రశ్న 12
A rectangular channel carries water downstream at V = 5.0 m/s and depth y = 0.90 m. What happens to a small disturbance that propagates upstream relative to the water? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The wave celerity is c = √(9.81 × 0.90) = approximately 2.971 m/s. The signed velocity of the upstream-running characteristic is V - c. This is 5.0 - 2.971 = approximately 2.029 m/s downstream. Thus the underlying flow is sufficiently rapid to sweep the disturbance downstream, and Option A is correct.
వివరణ:
Question 13
ప్రశ్న 13
At a nonrectangular channel section, the flow area is A = 6.0 m² and top width is T = 4.0 m. What is the small-amplitude gravity-wave celerity? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The hydraulic depth is D = A/T = 6/4 = 1.50 m. The small-wave celerity is c = √(gD). Thus c = √(9.81 × 1.50). This gives approximately 3.836 m/s, so Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
A small downstream-moving disturbance travels through a rectangular channel of depth 1.0 m in which the mean flow velocity is 1.2 m/s. Approximately how long will it take the disturbance to travel 800 m downstream? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The wave celerity relative to the water is √(9.81 × 1.0) = approximately 3.132 m/s. The downstream bank-frame wave speed is therefore V + c = 1.2 + 3.132 = 4.332 m/s. Travel time equals distance divided by speed. Hence t = 800/4.332 = approximately 184.7 s, making Option B correct.
వివరణ:
Question 15
ప్రశ్న 15
A gate at the downstream end of an open channel is closed rapidly, causing water to accumulate upstream of the gate. What disturbance is expected to propagate upstream from the gate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Rapid gate closure reduces the downstream discharge through the gate. Water consequently accumulates on the upstream side and its depth rises. That depth increase propagates away from the gate into the upstream channel. Because the disturbance produces an increase in depth, it is classified as a positive surge. Therefore Option A is correct.
వివరణ:
Question 16
ప్రశ్న 16
A sluice gate separating upstream and downstream channel reaches is opened rapidly from an initially more restrictive position. Which pair of disturbances is commonly produced?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Rapidly opening the gate increases the release from the upstream reach. The upstream water level therefore begins to fall, producing a negative disturbance that propagates into the upstream reach. The increased release into the downstream reach raises its flow depth and produces a positive disturbance propagating downstream. Thus surge sign and propagation direction must be identified separately. Therefore Option A is correct.
వివరణ:
Question 17
ప్రశ్న 17
Which statement best describes the nonlinear tendencies of positive and negative shallow-water disturbances?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Shallow-water gravity-wave celerity increases as water depth increases. Within a positive disturbance, deeper portions therefore tend to move faster than shallower portions, which can steepen the advancing front. In a negative disturbance, characteristics separate rather than crowd together. The falling-depth disturbance therefore tends to spread into a rarefaction fan rather than maintain a single sharp front. Therefore Option A is correct.
వివరణ:
Question 18
ప్రశ్న 18
A sharp positive surge moves downstream through a horizontal rectangular channel at bank-frame speed C, with C greater than the local flow velocities. State 1, with depth y1 and velocity V1, is ahead of the surge; state 2, with depth y2 and velocity V2, is behind the surge. Which moving-front continuity relation is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The surge can be made stationary by observing the flow from a reference frame moving downstream with speed C. In this frame, the magnitude of the relative approach velocity at state 1 is C - V1. The corresponding relative velocity at state 2 is C - V2. Conservation of mass per unit channel width therefore requires (C - V1)y1 = (C - V2)y2. Therefore Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
For a finite positive surge in a horizontal rectangular channel, why can the moving-surge problem be related to a hydraulic-jump momentum equation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The apparent unsteadiness of a moving surge results from the motion of its front relative to the channel. Choosing a frame that moves with the front makes the discontinuity stationary. Relative flow velocities can then be used in the continuity and linear-momentum equations. Under the usual short-front assumptions, the resulting depth relation has the same form as that for a stationary hydraulic jump. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
For a downstream-moving positive surge in a horizontal rectangular channel, assume hydrostatic pressure at the sections and negligible bed shear over the short surge front. The flow ahead of the surge has y1 = 1.0 m and V1 = 1.0 m/s, while the depth behind the surge is y2 = 1.5 m. What is the surge speed C approximately? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In the surge-fixed frame, the relative approach velocity is C - V1. The momentum relation for the two depths gives (C - V1)² = gy2(y1 + y2)/(2y1). Substitution gives C - V1 = √[9.81 × 1.5 × 2.5/(2 × 1.0)] = approximately 4.289 m/s. Therefore C = 1.0 + 4.289 = approximately 5.289 m/s. Hence Option C is correct.
వివరణ:
Question 21
ప్రశ్న 21
An upstream-moving positive surge occurs in a horizontal rectangular channel. The initial downstream flow ahead of the surge has y1 = 1.0 m and V1 = 3.0 m/s, and the depth behind the surge is y2 = 1.5 m. Under the standard short-surge momentum assumptions, what is the magnitude of the surge speed upstream approximately? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Let C denote the positive magnitude of the upstream surge speed. Since the surge moves against the downstream flow, the relative approach speed in the surge-fixed frame is V1 + C. The momentum relation gives V1 + C = √[gy2(y1 + y2)/(2y1)] = approximately 4.289 m/s. Hence C = 4.289 - 3.0 = approximately 1.289 m/s upstream. Therefore Option B is correct.
వివరణ:
Question 22
ప్రశ్న 22
A dynamically consistent downstream-moving positive surge in a horizontal rectangular channel has C = 5.289 m/s. Ahead of the surge, y1 = 1.0 m and V1 = 1.0 m/s; behind it, y2 = 1.5 m. Using moving-front continuity, what is V2 approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a downstream-moving front, continuity gives (C - V1)y1 = (C - V2)y2. Substitution gives (5.289 - 1.0)(1.0) = (5.289 - V2)(1.5). Thus 5.289 - V2 = 4.289/1.5 = approximately 2.859. Solving gives V2 approximately 2.430 m/s. The stated surge speed is also consistent with the momentum relation for y1 = 1.0 m and y2 = 1.5 m, so Option B is correct.
వివరణ:
Question 23
ప్రశ్న 23
Which statement correctly distinguishes a moving positive surge from a conventional hydraulic jump?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A positive surge and a hydraulic jump can both connect a shallower state to a deeper state through momentum effects. A conventional hydraulic jump is stationary or approximately stationary relative to the channel. A moving surge travels relative to the channel, so a fixed observer experiences time-varying depth and velocity. In a suitable moving reference frame, the momentum treatment of a finite positive surge has the same form as that of a stationary hydraulic jump. Therefore Option A is correct.
వివరణ:
Question 24
ప్రశ్న 24
Which statement about energy and momentum in the analysis of a finite steep positive surge is most appropriate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mass conservation remains fundamental even when the surge front moves. By using a frame attached to a steep surge front, a momentum balance can also be written across the disturbance. A finite positive surge may involve turbulence and irreversible mechanical-energy loss, particularly when it is bore-like. It is therefore incorrect to impose loss-free Bernoulli conservation across every finite surge. Hence Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about surges in open channels: I. A positive surge represents an increase in depth and a negative surge represents a decrease in depth. II. The small-wave celerity in a rectangular channel is approximately √(gy). III. In subcritical flow, an infinitesimal disturbance can propagate upstream relative to the channel. IV. A hydraulic jump can be regarded as a stationary special case of a positive surge. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I correctly classifies surge sign according to the change in flow depth. Statement II is the standard shallow-water celerity for a rectangular channel. Statement III follows because subcritical flow has V < c, allowing the upstream-running characteristic to have an upstream bank-frame velocity. Statement IV is consistent with the moving-reference-frame relationship between finite positive surges and stationary hydraulic jumps. 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 rapidly propagating unsteady disturbance associated with a change in flow depth and velocity సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: A. A positive surge produces a rise in water depth, whereas a negative surge produces a fall in water depth సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. Either a positive or a negative surge may propagate upstream or downstream depending on the hydraulic disturbance సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: A. c = √(gy) సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: A. c = √(gD) సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: A. V + c and V - c సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: A. Because V < c, so the upstream-running characteristic V - c is negative in a downstream-positive coordinate system సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: A. Both characteristic disturbances are carried downstream because V > c సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: A. It is stationary relative to the channel because V - c = 0 సమాధానం: A.
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Question 10 ప్రశ్న 10Answer: B. 3.96 m/s సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: A. 5.46 m/s downstream and 2.46 m/s upstream సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: A. It is still carried downstream at approximately 2.03 m/s సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: B. 3.84 m/s సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: B. 184.7 s సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: A. A positive surge సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: A. An upstream-moving negative surge and a downstream-moving positive surge సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: A. A positive disturbance tends to steepen because wave celerity increases with depth, whereas a negative disturbance tends to spread into a rarefaction fan సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: A. (C - V1)y1 = (C - V2)y2 సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: A. In a reference frame moving with the surge front, the front is stationary and continuity and momentum can be applied in the same form as to a stationary jump సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: C. 5.29 m/s సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: B. 1.29 m/s సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: B. 2.43 m/s సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: A. A hydraulic jump may be regarded as a stationary special case of a positive surge, whereas a surge generally moves relative to the channel and makes the bank-frame flow unsteady సమాధానం: A.
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Question 24 ప్రశ్న 24Answer: A. Continuity and momentum are used across the moving front, while mechanical energy need not be conserved because the front may be dissipative సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.