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Question 1
ప్రశ్న 1
Which statement best defines gradually varied flow in an open channel?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Gradually varied flow is a form of non-uniform open-channel flow. Its defining feature is that flow depth changes slowly with longitudinal distance. The vertical accelerations associated with the changing free surface are therefore relatively small. This permits the pressure distribution to be treated approximately as hydrostatic in standard GVF analysis. Therefore Option A is correct.
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Question 2
ప్రశ్న 2
Which set of assumptions is commonly used in the standard one-dimensional analysis of steady gradually varied flow in a prismatic channel?
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Explanation:
Standard GVF theory assumes that depth varies slowly enough for vertical accelerations to be neglected. The pressure distribution can then be approximated as hydrostatic. The channel is generally treated as prismatic with a relatively small bed slope. Friction slope is estimated using resistance relations such as Manning or Chezy at the local section. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
For steady gradually varied flow in a prismatic channel, with x measured positive downstream, kinetic-energy correction factor α taken as unity, and S0 defined positive for a bed falling downstream, which differential equation is the standard GVF equation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The total energy head may be written as bed elevation plus flow depth plus velocity head. Differentiating the energy equation along the channel introduces the bed slope S0 and friction slope Sf. For constant discharge in a prismatic section and with the kinetic-energy correction factor taken as unity, the velocity-head derivative produces the conventional Froude-number term. Under the stated sign convention the result is dy/dx = (S0 - Sf)/(1 - Fr²). Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
In the GVF equation dy/dx = (S0 - Sf)/(1 - Fr²), what does the numerator S0 - Sf primarily represent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The bed slope represents the gravitational contribution associated with the falling channel bed. The friction slope represents the rate of energy loss caused by boundary resistance. Their difference determines whether the available gravitational driving effect exceeds or falls short of the local frictional requirement. This difference forms the numerator of the standard GVF equation. Therefore Option A is correct.
వివరణ:
Question 5
ప్రశ్న 5
What is the hydraulic significance of the denominator 1 - Fr² in the standard GVF equation with α = 1?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For subcritical flow, Fr is less than one and 1 - Fr² is positive. For supercritical flow, Fr is greater than one and the denominator is negative. At critical flow, Fr equals one and the denominator becomes zero. Thus the denominator strongly influences the sign and mathematical behavior of a gradually varied profile. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
What is meant by normal depth yn in a prismatic open channel carrying a specified discharge?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Normal depth is associated with established uniform flow. At normal depth, the friction slope equals the bed slope for the specified discharge and channel. Its value therefore depends on discharge, channel geometry, roughness and bed slope. It is not generally identical to critical depth or to the actual depth in a GVF region. Therefore Option A is correct.
వివరణ:
Question 7
ప్రశ్న 7
What is meant by critical depth yc at a specified discharge and channel section?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Critical depth is fundamentally an energy and wave-propagation condition. For a specified discharge and channel geometry, it corresponds to minimum specific energy. At the critical state the Froude number is one under the conventional hydrostatic open-channel definition. Unlike normal depth, critical depth does not require the channel roughness or bed slope for its determination. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
Which statement correctly distinguishes actual depth y, normal depth yn and critical depth yc in a GVF analysis?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The actual depth y is the water depth present at the section being considered. Normal depth yn is a reference depth obtained from the uniform-flow resistance relation. Critical depth yc is another reference depth associated with minimum specific energy and Fr = 1. Comparing the actual depth with yn and yc helps classify the water-surface profile. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
For a prismatic channel carrying a specified discharge, which relationship distinguishes a mild slope from a steep slope?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Slope classification is conveniently expressed by comparing normal and critical depths for the stated discharge. On a mild slope, normal depth is greater than critical depth. On a steep slope, normal depth is less than critical depth. When normal and critical depths coincide, the channel is at the critical-slope condition. Therefore Option A is correct.
వివరణ:
Question 10
ప్రశ్న 10
In a mild-slope channel, an M1 profile has y > yn > yc. What is the sign of dy/dx in the downstream direction under ordinary GVF assumptions?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For y greater than yn, the local friction slope is less than the bed slope for the same discharge and channel. Hence S0 - Sf is positive. Since y is also greater than yc, the flow is subcritical and 1 - Fr² is positive. The ratio in the GVF equation is therefore positive, so the flow depth increases in the downstream direction. Therefore Option A is correct.
వివరణ:
Question 11
ప్రశ్న 11
In a mild-slope channel, an M2 profile satisfies yn > y > yc. What is the sign of dy/dx in the downstream direction?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Because y is below normal depth, the local friction slope exceeds the bed slope. Thus the numerator S0 - Sf is negative. Because y remains greater than critical depth, the flow is subcritical and the denominator is positive. Consequently dy/dx is negative and the depth decreases downstream. Therefore Option A is correct.
వివరణ:
Question 12
ప్రశ్న 12
In a mild-slope channel, an M3 profile satisfies y < yc < yn. What is the expected sign of dy/dx?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The actual depth is below normal depth, so the friction slope exceeds the bed slope and the numerator is negative. The depth is also below critical depth, so the flow is supercritical and 1 - Fr² is negative. A negative numerator divided by a negative denominator gives a positive depth gradient. Thus the depth increases in the downstream direction. Therefore Option A is correct.
వివరణ:
Question 13
ప్రశ్న 13
In a steep-slope channel, an S1 profile satisfies y > yc > yn. What is the sign of dy/dx?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Since the actual depth is greater than normal depth, the friction slope is less than the bed slope. The numerator S0 - Sf is therefore positive. Because the depth also exceeds critical depth, the flow is subcritical and the denominator is positive. The resulting value of dy/dx is positive. Therefore Option A is correct.
వివరణ:
Question 14
ప్రశ్న 14
In a steep-slope channel, an S2 profile satisfies yc > y > yn. What is the sign of dy/dx?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Here the actual depth exceeds normal depth, so the friction slope is lower than the bed slope and the numerator is positive. However, the actual depth is below critical depth, making the flow supercritical. Therefore 1 - Fr² is negative. The ratio is negative, meaning the flow depth decreases downstream. Therefore Option A is correct.
వివరణ:
Question 15
ప్రశ్న 15
In a steep-slope channel, an S3 profile satisfies y < yn < yc. What is the expected sign of dy/dx?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The depth is below normal depth, so the local friction slope exceeds the bed slope. Consequently S0 - Sf is negative. The depth is also below critical depth, so the flow is supercritical and the denominator is negative. The resulting quotient is positive and depth increases downstream. Therefore Option A is correct.
వివరణ:
Question 16
ప్రశ్న 16
Which statement about the hydraulic control of gradually varied profiles is generally correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In subcritical flow, surface disturbances can propagate upstream as well as downstream relative to the channel. A downstream boundary condition can therefore influence the upstream water-surface profile. In supercritical flow, disturbances cannot propagate upstream against the flow. Consequently supercritical profiles are ordinarily controlled from an upstream section. Therefore Option A is correct.
వివరణ:
Question 17
ప్రశ్న 17
What happens to dy/dx as the actual depth approaches normal depth, assuming the flow is not simultaneously critical?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At normal depth, the friction slope equals the bed slope. Therefore S0 - Sf approaches zero as the actual depth approaches yn. If the denominator 1 - Fr² remains finite, dy/dx consequently approaches zero. The depth profile therefore approaches the normal-depth condition asymptotically under the usual GVF description. Hence Option A is correct.
వివరణ:
Question 18
ప్రశ్న 18
What does the standard GVF equation predict as the flow approaches critical depth while S0 - Sf remains nonzero?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At critical flow, Fr approaches one. Consequently the denominator 1 - Fr² approaches zero. If the numerator remains nonzero, the magnitude of the computed depth gradient dy/dx becomes very large. This indicates a singularity of the simplified GVF differential equation near the critical condition and signals the limit of a smoothly varying profile description. Therefore Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
For a GVF reach, S0 = 0.0010, Sf = 0.0004 and Fr = 0.50. Using dy/dx = (S0 - Sf)/(1 - Fr²), what is dy/dx?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The numerator is 0.0010 - 0.0004 = 0.0006. The denominator is 1 - 0.50² = 0.75. Therefore dy/dx = 0.0006/0.75. The result is +0.0008, indicating increasing flow depth in the downstream direction. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
For a subcritical GVF reach, S0 = 0.0010, Sf = 0.0016 and Fr = 0.60. What is dy/dx approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The numerator is S0 - Sf = -0.0006. The denominator is 1 - 0.60² = 0.64. Therefore dy/dx = -0.0006/0.64. This gives approximately -0.0009375, or -0.000938. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
For a supercritical GVF reach, S0 = 0.0020, Sf = 0.0010 and Fr = 1.50. What is dy/dx?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The numerator is 0.0020 - 0.0010 = 0.0010. The denominator is 1 - 1.50² = 1 - 2.25 = -1.25. Thus dy/dx = 0.0010/(-1.25). The result is -0.0008, showing a downstream reduction in flow depth. Therefore Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
At a GVF section, dy/dx = +0.0010, bed slope S0 = 0.0015 and Fr = 0.50. What is the local friction slope Sf?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The GVF equation gives S0 - Sf = (dy/dx)(1 - Fr²). Here 1 - Fr² = 1 - 0.25 = 0.75. Thus S0 - Sf = 0.0010 × 0.75 = 0.00075. Therefore Sf = 0.00150 - 0.00075 = 0.00075. Hence Option B is correct.
వివరణ:
Question 23
ప్రశ్న 23
A wide rectangular channel carries a discharge per unit width q = 4.0 m²/s. What is the critical depth approximately? Take g = 9.81 m/s².
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Explanation:
For a rectangular channel, critical depth is yc = (q²/g)^(1/3). Substitution gives yc = (16/9.81)^(1/3). The quantity inside the cube root is approximately 1.631. Taking the cube root gives yc approximately 1.177 m. Therefore Option B is correct.
వివరణ:
Question 24
ప్రశ్న 24
A very wide rectangular channel carries q = 5.0 m²/s with Manning n = 0.020 and bed slope S0 = 0.001. Using R approximately equal to y for uniform flow, what are the normal depth and critical depth approximately, and how is the channel slope classified?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a very wide channel, Manning's equation per unit width gives q = (1/n)y^(5/3)S0^(1/2). Solving with the stated data gives yn approximately 1.995 m, or about 2.00 m. The critical depth is yc = (q²/g)^(1/3) = (25/9.81)^(1/3), which is approximately 1.366 m. Since yn is greater than yc, the channel is classified as mild for this discharge. Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about gradually varied flow: I. With x positive downstream and α = 1, dy/dx = (S0 - Sf)/(1 - Fr²). II. Normal depth corresponds to Sf = S0 in uniform flow. III. Critical depth corresponds to Fr = 1. IV. Subcritical GVF profiles are generally governed from downstream controls, while supercritical profiles are governed from upstream controls. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is the standard simplified differential equation for steady GVF under the stated sign convention and α = 1 assumption. Statement II correctly identifies the uniform-flow condition associated with normal depth. Statement III is the defining Froude-number condition for critical depth under the conventional formulation. Statement IV correctly reflects the different directions in which hydraulic information can influence subcritical and supercritical flows. 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 in which depth changes gradually with longitudinal distance over a relatively long reach సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: A. Hydrostatic pressure distribution, small bed slope, gradually changing depth and resistance evaluated with a uniform-flow formula సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. dy/dx = (S0 - Sf)/(1 - Fr²) సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: A. The imbalance between the gravitational bed-slope effect and frictional energy loss సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: A. Its sign distinguishes subcritical from supercritical flow and it becomes zero at critical flow సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: A. The depth at which uniform flow would occur for the given discharge, slope, geometry and resistance సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: A. The depth corresponding to minimum specific energy and Fr = 1 సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: A. y is the local water depth, yn is the corresponding uniform-flow depth, and yc is the critical-flow depth for the specified discharge సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: A. Mild slope: yn > yc; steep slope: yn < yc సమాధానం: A.
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Question 10 ప్రశ్న 10Answer: A. Positive సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: A. Negative సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: A. Positive సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: A. Positive సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: A. Negative సమాధానం: A.
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Question 15 ప్రశ్న 15Answer: A. Positive సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: A. Subcritical profiles are influenced by downstream controls, whereas supercritical profiles are influenced primarily by upstream controls సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: A. dy/dx approaches zero and the depth profile approaches the normal-depth line asymptotically సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: A. The denominator approaches zero and the computed magnitude of dy/dx becomes very large సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: A. +0.0008 సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: A. -0.000938 సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: A. -0.0008 సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: B. 0.00075 సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: B. 1.177 m సమాధానం: B.
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Question 24 ప్రశ్న 24Answer: A. yn = 2.00 m, yc = 1.37 m; mild slope సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.