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Question 1
ప్రశ్న 1
In open-channel flow, taking the velocity-distribution coefficient as unity, what is meant by specific energy at a section?
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Explanation:
Specific energy is the mechanical energy per unit weight measured relative to the local channel bed. With hydrostatic pressure distribution and velocity-distribution coefficient taken as unity, it consists of flow depth plus velocity head. Thus E = y + V²/(2g). It is different from total energy referred to an arbitrary common elevation datum because the local bed is used as the reference. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
For a rectangular channel carrying discharge per unit width q at depth y, and taking the velocity-distribution coefficient as unity, which expression gives the specific energy?
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Explanation:
For a rectangular channel, mean velocity is V = q/y because q is discharge per unit width. Specific energy is E = y + V²/(2g). Substituting V = q/y gives E = y + q²/(2gy²). The first term represents depth and the second represents velocity head. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
For a rectangular channel carrying a fixed discharge per unit width, what does the minimum point of the specific-energy versus depth curve represent?
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Explanation:
At fixed discharge, specific energy varies with flow depth. The specific-energy curve has a minimum at a particular depth known as critical depth. At this state the flow is critical and the Froude number is one. Depths on either side of this minimum correspond to different flow regimes when the same discharge can be maintained. Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
For a given discharge in a rectangular channel, a specific energy greater than the minimum specific energy ordinarily corresponds to which situation?
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Explanation:
The rectangular-channel specific-energy curve has two branches separated by the critical point. For a specific energy greater than the minimum, a horizontal line through the energy curve generally intersects it at two positive depths. The shallower alternate depth is on the supercritical branch. The deeper alternate depth is on the subcritical branch. Therefore Option A is correct.
వివరణ:
Question 5
ప్రశ్న 5
For a given channel cross-section and fixed specific energy, the discharge reaches its maximum value at which condition?
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Explanation:
Critical flow may be interpreted in two equivalent ways in the standard specific-energy analysis. For a fixed discharge, critical depth gives the minimum possible specific energy. Conversely, for a fixed specific energy, the maximum discharge occurs at the critical state. At that condition the appropriate Froude number is unity. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
For a general open-channel section with flow area A and top width T, taking the kinetic-energy correction factor as unity, which condition represents critical flow?
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Explanation:
For a general section, critical flow occurs when the derivative of specific energy with respect to depth vanishes at constant discharge. This leads to the condition Q²T/(gA³) = 1 when the correction factor is taken as unity. Since hydraulic depth is D = A/T, the same condition corresponds to V²/(gD) = 1. Thus the Froude number is one at critical flow. Therefore Option A is correct.
వివరణ:
Question 7
ప్రశ్న 7
For a rectangular channel carrying discharge per unit width q, which expression gives the critical depth yc?
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Explanation:
For a rectangular channel, area per unit width is y and the mean velocity is q/y. Applying the critical-flow condition gives q² = gyc³. Solving for critical depth gives yc = (q²/g)^(1/3). This result depends on discharge per unit width and gravity, not directly on Manning roughness or bed slope. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
For a rectangular channel at critical flow, what is the relationship between minimum specific energy Emin and critical depth yc?
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Explanation:
At critical flow in a rectangular channel, Vc² = gyc. The critical velocity head is therefore Vc²/(2g) = yc/2. Specific energy is depth plus velocity head, giving Emin = yc + yc/2. Hence Emin = 3yc/2. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
Which pair of relationships is correct for critical flow in a rectangular channel?
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Explanation:
For a rectangular channel, Fr = V/√(gy). Critical flow occurs at Fr = 1. Therefore Vc = √(gyc). This relationship is also consistent with q² = gyc³ because q = Vcyc. Hence Option A is correct.
వివరణ:
Question 10
ప్రశ్న 10
For a rectangular channel, which expression correctly gives the Froude number when V is the mean velocity and y is flow depth?
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Explanation:
The general open-channel Froude number is Fr = V/√(gD), where D is hydraulic depth. For a rectangular channel, hydraulic depth equals the actual flow depth y. Therefore Fr = V/√(gy). Values below, equal to and above one correspond respectively to subcritical, critical and supercritical flow. Therefore Option A is correct.
వివరణ:
Question 11
ప్రశ్న 11
A rectangular channel 3.0 m wide carries 9.0 m³/s of water at a depth of 1.5 m. Taking the velocity-distribution coefficient as unity, what is the specific energy approximately? Take g = 9.81 m/s².
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Explanation:
The flow area is A = 3.0 × 1.5 = 4.5 m². The mean velocity is V = Q/A = 9/4.5 = 2.0 m/s. Therefore E = y + V²/(2g) = 1.5 + 4/(19.62). This gives approximately 1.704 m. Hence Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
For the 3.0 m wide rectangular channel carrying 9.0 m³/s, what are the critical depth and minimum specific energy approximately? Take g = 9.81 m/s².
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Explanation:
The discharge per unit width is q = 9/3 = 3.0 m²/s. Critical depth is yc = (q²/g)^(1/3) = (9/9.81)^(1/3). This gives approximately 0.972 m. Minimum specific energy is 1.5yc, which is approximately 1.458 m. Therefore Option B is correct.
వివరణ:
Question 13
ప్రశ్న 13
For the same rectangular flow with depth 1.5 m and mean velocity 2.0 m/s, what is the Froude number and flow regime approximately?
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Explanation:
For a rectangular channel, Fr = V/√(gy). Substitution gives Fr = 2/√(9.81 × 1.5). The denominator is approximately 3.836 m/s, giving Fr approximately 0.521. Since this value is less than one, the flow is subcritical. Therefore Option A is correct.
వివరణ:
Question 14
ప్రశ్న 14
A rectangular channel is to have a critical depth of 0.80 m. What discharge per unit width is required approximately? Take g = 9.81 m/s².
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Explanation:
For critical flow in a rectangular channel, q² = gyc³. Therefore q = √(gyc³). Substituting yc = 0.80 m gives q = √(9.81 × 0.80³). The result is approximately 2.241 m²/s. Therefore Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
A 4.0 m wide rectangular channel is required to carry critical flow at a depth of 1.20 m. What discharge corresponds to this condition approximately? Take g = 9.81 m/s².
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Explanation:
At critical flow, discharge per unit width is q = √(gyc³). For yc = 1.20 m, q is approximately 4.117 m²/s. The total discharge is Q = bq = 4 × 4.117. This gives approximately 16.47 m³/s. Therefore Option C is correct.
వివరణ:
Question 16
ప్రశ్న 16
The minimum specific energy in a rectangular channel is 1.80 m. What is the corresponding critical depth?
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Explanation:
For a rectangular channel, Emin = 3yc/2. Rearranging gives yc = 2Emin/3. Substituting Emin = 1.80 m gives yc = 1.20 m. This result follows directly from the rectangular critical-flow energy relationship. Therefore Option B is correct.
వివరణ:
Question 17
ప్రశ్న 17
A rectangular channel carries q = 2.801 m²/s per unit width with specific energy E = 2.10 m. If one possible depth is approximately 0.50 m, what is the other positive alternate depth approximately? Take g = 9.81 m/s².
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Explanation:
For a rectangular channel, E = y + q²/(2gy²). With q approximately 2.801 m²/s, the constant q²/(2g) is approximately 0.400 m³. At y = 0.50 m, E is 0.50 + 0.400/0.25 = 2.10 m. Substitution of y = 2.00 m gives E = 2.00 + 0.400/4 = 2.10 m as well. Therefore 2.00 m is the alternate depth and Option D is correct.
వివరణ:
Question 18
ప్రశ్న 18
For the alternate-depth case with q = 2.801 m²/s, the critical depth is approximately 0.928 m. How should the two alternate depths 0.50 m and 2.00 m be classified?
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Explanation:
For a rectangular channel at a fixed discharge, depths smaller than the critical depth lie on the supercritical branch of the specific-energy curve. Depths greater than critical lie on the subcritical branch. Here 0.50 m is less than the critical depth of about 0.928 m. The 2.00 m depth is greater than the critical depth. Therefore Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
A wide rectangular channel carries q = 3.0 m²/s at an upstream depth of 2.0 m. A smooth hump is introduced with negligible energy loss. What is the maximum hump height that can be installed without requiring the upstream specific energy to increase? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The upstream velocity is V = q/y = 3/2 = 1.5 m/s. The upstream specific energy is therefore E1 = 2 + 1.5²/(2 × 9.81) = approximately 2.115 m. For q = 3.0 m²/s, the critical depth is approximately 0.972 m and Emin is approximately 1.458 m. The maximum bed rise before the crest reaches the critical condition is E1 - Emin = approximately 0.657 m. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
In an ideal smooth upward bed transition with negligible energy loss, what ordinarily happens to an initially subcritical rectangular flow as the bed rises but before choking occurs?
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Explanation:
Raising the bed reduces the specific energy available relative to the local bed when total head is otherwise conserved. On the subcritical branch, moving toward the minimum-energy point requires a reduction in depth. Continuity then requires the velocity to increase for a constant-width channel and constant discharge. If the available specific energy falls to the minimum value, critical flow occurs at the control. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
A smooth rectangular contraction carries Q = 6.0 m³/s with an available specific energy of 2.0 m at the contracted section, and transition losses are neglected. What is the minimum channel width that can pass this discharge without requiring more specific energy? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At the limiting contraction, the contracted section is critical because the available specific energy is just the minimum energy. For a rectangle, yc = 2E/3 = 2(2.0)/3 = 1.333 m. The critical unit discharge is q = √(gyc³), which is approximately 4.822 m²/s. Thus the minimum width is b = Q/q = 6/4.822 = approximately 1.244 m. Therefore Option B is correct.
వివరణ:
Question 22
ప్రశ్న 22
A rectangular channel has depth y = 1.50 m and Froude number Fr = 0.80. What is the mean velocity approximately? Take g = 9.81 m/s².
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Explanation:
For a rectangular channel, Fr = V/√(gy). Rearranging gives V = Fr√(gy). Substitution gives V = 0.80√(9.81 × 1.50). The result is approximately 3.07 m/s. Since Fr is less than one, the stated flow is subcritical. Therefore Option C is correct.
వివరణ:
Question 23
ప్రశ్న 23
Water flows in a rectangular channel at a depth of 0.60 m with mean velocity 4.0 m/s. What is the Froude number and basic flow regime approximately? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Froude number for a rectangular channel is Fr = V/√(gy). Substituting V = 4.0 m/s and y = 0.60 m gives 4/√(9.81 × 0.60). This evaluates to approximately 1.649. Since the value exceeds one, the flow is supercritical. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
At a fixed depth in a rectangular channel, the discharge per unit width is doubled. By what factor does the velocity-head component q²/(2gy²) of specific energy change?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At a fixed depth, the velocity-head term in the rectangular specific-energy equation is q²/(2gy²). This term is proportional to the square of discharge per unit width. Doubling q therefore multiplies q² by four. The depth and gravitational acceleration are unchanged in the comparison. Therefore Option B is correct.
వివరణ:
Question 25
ప్రశ్న 25
Which statement correctly distinguishes critical depth from normal depth in a prismatic open channel?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Critical depth corresponds to minimum specific energy for a specified discharge and channel geometry. In a rectangular channel it can be determined from q and g without using Manning roughness or bed slope. Normal depth is the depth associated with established uniform flow and depends on discharge, channel geometry, roughness and slope. Critical and normal depths may coincide for a particular critical-slope condition, but they are not generally equal. Therefore Option A is correct.
వివరణ:
Question 26
ప్రశ్న 26
Consider the following statements about rectangular open-channel flow: I. Specific energy is E = y + V²/(2g) when the velocity-distribution coefficient is unity. II. At critical flow, Fr = 1. III. For fixed discharge, minimum specific energy occurs at critical depth. IV. For a specific energy greater than the minimum, the two alternate positive depths lie on opposite sides of the critical depth. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is the standard specific-energy expression under the stated velocity-distribution assumption. Statement II is the defining Froude-number condition for critical flow. Statement III describes the minimum point of the specific-energy curve at a fixed discharge. Statement IV is also correct because the shallow alternate depth is supercritical and the deeper alternate depth is subcritical. 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. The energy per unit weight measured relative to the channel bed at that section సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: A. E = y + q²/(2gy²) సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. Critical flow సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: A. Two positive alternate depths, one shallow and one deep సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: A. Critical flow సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: A. Q²T/(gA³) = 1 సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: A. yc = (q²/g)^(1/3) సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: A. Emin = 3yc/2 సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: A. Fr = 1 and Vc = √(gyc) సమాధానం: A.
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Question 10 ప్రశ్న 10Answer: A. Fr = V/√(gy) సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: C. 1.704 m సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: B. yc = 0.972 m and Emin = 1.458 m సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: A. Fr = 0.521; subcritical సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: B. 2.241 m²/s సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: C. 16.47 m³/s సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: B. 1.20 m సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: D. 2.00 m సమాధానం: D.
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Question 18 ప్రశ్న 18Answer: A. 0.50 m is supercritical and 2.00 m is subcritical సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: B. 0.657 m సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: A. The depth decreases and the velocity increases toward the critical condition సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: B. 1.244 m సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: C. 3.07 m/s సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: C. Fr = 1.649; supercritical సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: B. It becomes four times as large సమాధానం: B.
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Question 25 ప్రశ్న 25Answer: A. Critical depth is an energy and Froude-number condition determined by discharge and section geometry, whereas normal depth is a uniform-flow condition that also depends on resistance and bed slope సమాధానం: A.
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Question 26 ప్రశ్న 26Answer: D. I, II, III and IV సమాధానం: D.