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A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certain section of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?
- a)M2
- b)M3
- c)S2
- d)S3
Correct answer is option 'C'. Can you explain this answer?
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A wide rectangular channel carries discharge of 6 m3/s per meter width...
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A wide rectangular channel carries discharge of 6 m3/s per meter width...
Given data:
Discharge, Q = 6 m3/s/m
Bed slope, S = 0.009
Manning's roughness coefficient, n = 0.015
Flow depth, y = 1.5 m
To determine the gradually varied flow profile at the given section of the channel, we need to use the standard step method. This involves dividing the channel into small segments and calculating the water surface elevation at the end of each segment using the energy equation.
Step 1: Determine the hydraulic radius
The hydraulic radius, R, can be calculated using the formula:
R = A/P
where A is the cross-sectional area of flow and P is the wetted perimeter. For a rectangular channel, we have:
A = yB
P = 2y + B
where B is the bottom width of the channel. Substituting the given values, we get:
A = 1.5B
P = 3B
R = (1.5B)/(3B) = 0.5
Step 2: Calculate the cross-sectional average velocity
The cross-sectional average velocity, V, can be calculated using the discharge equation:
Q = AV
where A is the cross-sectional area of flow. Substituting the given values, we get:
A = 1.5B
Q = 6 m3/s/m
V = Q/A = (6 m3/s/m)/(1.5B) = 4/B m/s
Step 3: Calculate the Froude number
The Froude number, Fr, is given by:
Fr = V/√(gR)
where g is the acceleration due to gravity. Substituting the given values, we get:
Fr = (4/B)/√(9.81*0.5) = (4/B)/2.22
Step 4: Determine the type of flow
Based on the Froude number, we can determine the type of flow:
- If Fr < 1,="" the="" flow="" is="" subcritical="" />
- If Fr > 1, the flow is supercritical (M)
- If Fr = 1, the flow is critical (C)
Substituting the value of Fr, we get:
Fr = (4/B)/2.22
- If B > 0.91 m, Fr < 1="" and="" the="" flow="" is="" subcritical="" />
- If 0.45 m < b="" />< 0.91="" m,="" fr="" ≈="" 1="" and="" the="" flow="" is="" critical="" />
- If B < 0.45="" m,="" fr="" /> 1 and the flow is supercritical (M3)
Since the flow depth is 1.5 m, we can assume that the channel is wide enough (B > 0.91 m) and the flow is subcritical (S2).
Therefore, the gradually varied flow profile at the given section of the channel is option (C) S2.
Discharge, Q = 6 m3/s/m
Bed slope, S = 0.009
Manning's roughness coefficient, n = 0.015
Flow depth, y = 1.5 m
To determine the gradually varied flow profile at the given section of the channel, we need to use the standard step method. This involves dividing the channel into small segments and calculating the water surface elevation at the end of each segment using the energy equation.
Step 1: Determine the hydraulic radius
The hydraulic radius, R, can be calculated using the formula:
R = A/P
where A is the cross-sectional area of flow and P is the wetted perimeter. For a rectangular channel, we have:
A = yB
P = 2y + B
where B is the bottom width of the channel. Substituting the given values, we get:
A = 1.5B
P = 3B
R = (1.5B)/(3B) = 0.5
Step 2: Calculate the cross-sectional average velocity
The cross-sectional average velocity, V, can be calculated using the discharge equation:
Q = AV
where A is the cross-sectional area of flow. Substituting the given values, we get:
A = 1.5B
Q = 6 m3/s/m
V = Q/A = (6 m3/s/m)/(1.5B) = 4/B m/s
Step 3: Calculate the Froude number
The Froude number, Fr, is given by:
Fr = V/√(gR)
where g is the acceleration due to gravity. Substituting the given values, we get:
Fr = (4/B)/√(9.81*0.5) = (4/B)/2.22
Step 4: Determine the type of flow
Based on the Froude number, we can determine the type of flow:
- If Fr < 1,="" the="" flow="" is="" subcritical="" />
- If Fr > 1, the flow is supercritical (M)
- If Fr = 1, the flow is critical (C)
Substituting the value of Fr, we get:
Fr = (4/B)/2.22
- If B > 0.91 m, Fr < 1="" and="" the="" flow="" is="" subcritical="" />
- If 0.45 m < b="" />< 0.91="" m,="" fr="" ≈="" 1="" and="" the="" flow="" is="" critical="" />
- If B < 0.45="" m,="" fr="" /> 1 and the flow is supercritical (M3)
Since the flow depth is 1.5 m, we can assume that the channel is wide enough (B > 0.91 m) and the flow is subcritical (S2).
Therefore, the gradually varied flow profile at the given section of the channel is option (C) S2.
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A wide rectangular channel carries discharge of 6 m3/s per meter width...
In a very long, wide rectangular channel the discharge intensity is 3 m3/s/m widths. The bed slope of the channel is 0.004 and Manning’s n=0.015. At a certain section in this channel the depth of flow is observed to be 0.9m. What type of GVF profile occurs in the neighborhood of this section?
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A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer?
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A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer?.
A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wide rectangular channel carries discharge of 6 m3/s per meter width. The channel has a bed slope of 0.009 and Manning's roughness coefficient, n = 0.015. At a certainsection of the channel, the flow depth is 1.5m. What gradually varied flow profile exist at this section ?a)M2b)M3c)S2d)S3Correct answer is option 'C'. Can you explain this answer?.
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