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Question 1
ప్రశ్న 1
Which statement best describes a hydraulic jump in an open channel?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A hydraulic jump is a rapidly varied open-channel flow phenomenon. It normally converts a shallow, high-velocity supercritical stream into a deeper, lower-velocity subcritical stream. Strong turbulence, surface rollers and mixing occur within the jump. A significant amount of mechanical energy is dissipated, principally through turbulence. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
Which conservation principle is used primarily to relate the upstream and downstream depths of an idealized hydraulic jump in a short horizontal rectangular channel?
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Explanation:
A hydraulic jump involves substantial irreversible energy dissipation, so mechanical energy is not conserved across it. The jump occurs over a comparatively short distance, making a momentum balance particularly useful. Hydrostatic pressure forces at sections before and after the jump are combined with the change in momentum flux. This produces the conjugate-depth or sequent-depth relation. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
Which set of assumptions is appropriate for deriving the classical sequent-depth relation for a hydraulic jump in a horizontal rectangular channel?
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Explanation:
The classical derivation selects sections sufficiently far from the turbulent roller for pressure to be treated approximately as hydrostatic. The jump is short enough that boundary shear over the control volume is commonly neglected relative to the major pressure and momentum terms. The channel is taken as horizontal and rectangular for the standard closed-form relation. Flow is treated as steady through the control volume. Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
For a rectangular channel, which expression gives the momentum function per unit width when the momentum correction factor is taken as unity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a rectangular channel, the hydrostatic pressure contribution to the momentum function per unit width is y²/2. The momentum-flux contribution is q²/(gy), where q is discharge per unit width. Their sum gives M = y²/2 + q²/(gy). Conjugate depths of an ideal hydraulic jump have the same value of this momentum function. Therefore Option A is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which statement correctly defines conjugate or sequent depths in a rectangular hydraulic jump?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Conjugate or sequent depths are the upstream and downstream depths connected by the momentum balance across a hydraulic jump. For the idealized horizontal rectangular case, their momentum functions are equal. Their specific energies are not equal because energy is dissipated within the jump. This distinction separates conjugate depths from alternate depths obtained from a specific-energy diagram. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
For a hydraulic jump in a horizontal rectangular channel, which relation gives the sequent-depth ratio in terms of the upstream Froude number Fr1?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Applying the pressure-momentum equation to a horizontal rectangular jump yields the standard sequent-depth relationship. The ratio is y2/y1 = 0.5[√(1 + 8Fr1²) - 1]. It shows that the downstream depth becomes increasingly larger than the upstream depth as the incoming Froude number increases. The equation applies to the stated idealized rectangular-channel assumptions. Therefore Option A is correct.
వివరణ:
Question 7
ప్రశ్న 7
Which Froude-number condition is characteristic of an ordinary hydraulic jump?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The incoming stream of a hydraulic jump is shallow and rapid. Its Froude number is therefore greater than one, indicating supercritical flow. The jump produces a deeper and slower downstream stream. That downstream state is subcritical and has a Froude number less than one. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
A horizontal rectangular channel is 4.0 m wide and carries Q = 8.0 m³/s at an upstream depth y1 = 0.50 m. What is the upstream Froude number approximately? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The flow area upstream is A1 = 4.0 × 0.50 = 2.0 m². Thus V1 = Q/A1 = 8/2 = 4.0 m/s. For a rectangular channel, Fr1 = V1/√(gy1). Substitution gives 4/√(9.81 × 0.50) = approximately 1.806. Therefore Option B is correct.
వివరణ:
Question 9
ప్రశ్న 9
A horizontal rectangular channel is 4.0 m wide and carries Q = 8.0 m³/s at upstream depth y1 = 0.50 m. What is the conjugate downstream depth approximately? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The upstream velocity is 4.0 m/s, giving Fr1 approximately 1.806. The depth ratio is 0.5[√(1 + 8Fr1²) - 1]. This gives y2/y1 approximately 2.1027. Therefore y2 = 2.1027 × 0.50 = approximately 1.051 m. Hence Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
A horizontal rectangular channel is 4.0 m wide and carries Q = 8.0 m³/s. If a hydraulic jump changes the depth from y1 = 0.50 m to its conjugate depth y2 ≈ 1.051 m, what is the downstream Froude number approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The downstream area is approximately 4 × 1.051 = 4.205 m². The corresponding velocity is about 8/4.205 = 1.902 m/s. For a rectangular channel, Fr2 = V2/√(gy2). Substitution gives approximately 0.592. The value is below one, confirming that the downstream flow is subcritical, so Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
For an ideal hydraulic jump in a horizontal rectangular channel with conjugate depths y1 and y2, which expression gives the specific-energy loss?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The difference between upstream and downstream specific energies can be simplified using the conjugate-depth momentum relationship. For a horizontal rectangular jump, the result is ΔE = (y2 - y1)³/(4y1y2). The expression is always positive when y2 exceeds y1. It demonstrates that stronger jumps with larger depth differences dissipate substantially more energy. Therefore Option A is correct.
వివరణ:
Question 12
ప్రశ్న 12
In a horizontal rectangular hydraulic jump, y1 = 0.50 m and y2 = 1.051 m. What is the specific-energy loss approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The energy-loss relation is ΔE = (y2 - y1)³/(4y1y2). Using the more precise conjugate depth y2 ≈ 1.05134 m gives a depth difference of approximately 0.55134 m. Substitution gives ΔE approximately 0.0797 m. This is about 0.080 m to the precision of the options. Therefore Option C is correct.
వివరణ:
Question 13
ప్రశ్న 13
A hydraulic jump dissipates 0.0797 m of head while carrying Q = 8.0 m³/s of water. What is the rate of mechanical-energy dissipation approximately? Take ρ = 1000 kg/m³ and g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The hydraulic power dissipated is P = ρgQΔE. Substitution gives P = 1000 × 9.81 × 8.0 × 0.0797 W. This is approximately 6255 W. Converting to kilowatts gives about 6.26 kW. Therefore Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
A hydraulic jump occurs in a horizontal rectangular channel with upstream depth y1 = 0.40 m and upstream Froude number Fr1 = 3.0. What is the conjugate downstream depth approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The depth ratio is y2/y1 = 0.5[√(1 + 8Fr1²) - 1]. With Fr1 = 3, the ratio is approximately 3.772. Multiplying by the upstream depth 0.40 m gives y2 approximately 1.509 m. The downstream depth is therefore considerably larger than the approach depth. Hence Option C is correct.
వివరణ:
Question 15
ప్రశ్న 15
A rectangular hydraulic jump has conjugate depths y1 = 0.30 m and y2 = 1.20 m. What is the upstream Froude number approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Let the sequent-depth ratio be r = y2/y1 = 1.20/0.30 = 4. From the rectangular jump relation, Fr1² = r(r + 1)/2. Thus Fr1² = 4 × 5/2 = 10. Taking the square root gives Fr1 approximately 3.162. Therefore Option C is correct.
వివరణ:
Question 16
ప్రశ్న 16
A rectangular hydraulic jump has conjugate depths y1 = 0.30 m and y2 = 1.20 m. What discharge per unit width q is required approximately? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For rectangular conjugate depths, equality of the momentum function gives q²/g = y1y2(y1 + y2)/2. Substituting y1 = 0.30 m and y2 = 1.20 m gives q²/g = 0.27 m³. Therefore q = √(9.81 × 0.27). This evaluates to approximately 1.627 m²/s. Hence Option B is correct.
వివరణ:
Question 17
ప్రశ్న 17
A rectangular hydraulic jump has y1 = 0.50 m and y2 = 2.00 m. What is the specific-energy loss across the jump?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The energy loss is ΔE = (y2 - y1)³/(4y1y2). The depth difference is 1.50 m, whose cube is 3.375 m³. The denominator is 4 × 0.50 × 2.00 = 4.0 m². Therefore ΔE = 3.375/4 = 0.84375 m, so Option B is correct.
వివరణ:
Question 18
ప్రశ్న 18
Which statement correctly distinguishes conjugate depths from alternate depths in open-channel flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Conjugate or sequent depths arise from the momentum balance across a hydraulic jump. Because energy is dissipated, the two conjugate states do not possess equal specific energy. Alternate depths, by contrast, are the two depths associated with the same discharge and specific energy on an energy-depth diagram. Their momentum functions generally differ. Therefore Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
Which statement about energy and momentum across an idealized hydraulic jump is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mass is conserved through the jump, and the linear momentum equation is used together with the pressure forces acting on the control volume. Mechanical energy is not conserved because strong turbulence converts organized flow energy into internal energy and smaller-scale motions. Consequently the downstream specific energy is smaller than the upstream specific energy. The momentum function, however, is equal for the ideal horizontal rectangular conjugate states under the standard approximations. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
For a free hydraulic jump in a horizontal rectangular stilling basin, what tailwater condition is required approximately to maintain the jump at the intended location?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a given incoming supercritical condition, the momentum relationship determines the conjugate downstream depth needed for a free jump. If the available tailwater is approximately equal to this depth, the jump can be maintained near the intended location. Excessive tailwater tends to submerge or drown the jump. Insufficient tailwater can cause the jump to shift downstream or sweep out of the intended basin. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
Which statement about the length of a hydraulic jump is most accurate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The momentum equation determines the ideal relationship between the approach and downstream conjugate depths. It does not uniquely specify the physical length of the turbulent roller and transition region. Jump length depends on factors such as incoming Froude number, geometry and basin configuration. Experimental observations and empirical correlations are therefore normally used in design. Hence Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
Which is an important engineering use of a hydraulic jump?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
High-velocity flows downstream of spillways, gates and outlets can cause severe erosion and scour. A properly controlled hydraulic jump converts part of that kinetic energy into turbulent dissipation. Stilling basins are designed to contain this process in a protected reach. Hydraulic jumps can also provide strong mixing and aeration, but their principal structural use is energy dissipation. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
According to the conventional USBR characterization of hydraulic-jump forms, an incoming Froude number of about 5 lies in which range?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
USBR observations distinguish characteristic jump behavior using ranges of the incoming Froude number. The approximate range from 4.5 to 9 is associated with well-developed and comparatively well-balanced hydraulic jumps. An upstream Froude number of 5 lies within this range. The precise limits are empirical and can overlap somewhat depending on local conditions. Therefore Option A is correct.
వివరణ:
Question 24
ప్రశ్న 24
As the upstream Froude number of a rectangular hydraulic jump approaches 1 from above, what happens to the sequent-depth ratio and energy loss?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The sequent-depth relation gives y2/y1 = 0.5[√(1 + 8Fr1²) - 1]. As Fr1 approaches one, this ratio approaches one. The two depths therefore become nearly equal and the jump becomes very weak. Since the energy-loss formula contains the cube of y2 - y1, the loss approaches zero rapidly. Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about a hydraulic jump in a horizontal rectangular channel: I. The incoming flow is supercritical and the outgoing flow is subcritical. II. Conjugate depths are related primarily through a momentum balance. III. Specific mechanical energy decreases through the jump. IV. The jump can be deliberately used in a stilling basin for energy dissipation. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I correctly describes the flow-regime transition produced by an ordinary hydraulic jump. Statement II is correct because the classical conjugate-depth relation follows from the momentum equation. Statement III is correct because the turbulent jump dissipates mechanical energy. Statement IV is also correct because stilling basins intentionally use hydraulic jumps to control damaging high-velocity flow. 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 rapid transition from supercritical shallow flow to subcritical deeper flow with substantial energy dissipation సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: A. Linear momentum principle సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. Steady flow, hydrostatic pressure at the approach and downstream sections, negligible boundary shear over the short jump reach and a horizontal rectangular channel సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: A. M = y²/2 + q²/(gy) సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: A. They are the two depths before and after the jump that have the same momentum function for the same discharge సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: A. y2/y1 = 0.5[√(1 + 8Fr1²) - 1] సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: A. Fr1 > 1 before the jump and Fr2 < 1 after the jump సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: B. 1.806 సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: C. 1.051 m సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: B. 0.592 సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: A. ΔE = (y2 - y1)³/(4y1y2) సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: C. 0.080 m సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: B. 6.26 kW సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: C. 1.509 m సమాధానం: C.
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Question 15 ప్రశ్న 15Answer: C. 3.162 సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: B. 1.627 m²/s సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: B. 0.844 m సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: A. Conjugate depths have equal momentum function across a hydraulic jump, whereas alternate depths correspond to the same discharge and specific energy సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: A. The momentum balance is satisfied approximately while specific mechanical energy decreases సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: A. The available tailwater depth should be approximately equal to the required conjugate depth సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: A. Jump length is mainly obtained from empirical or experimental correlations and is not fixed by the sequent-depth momentum equation alone సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: A. Dissipating excess kinetic energy downstream of spillways, sluices and other hydraulic structures సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: A. A well-balanced or good-jump range, approximately Fr1 = 4.5 to 9 సమాధానం: A.
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Question 24 ప్రశ్న 24Answer: A. y2/y1 approaches 1 and the energy loss approaches zero సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.