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The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.
- a)0.012
- b)0.013
- c)0.014
- d)0.015
Correct answer is option 'B'. Can you explain this answer?
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The depth of a trapezoidal channel section is 2m, base width of 3m and...
Calculation of Manning's "n" for a Trapezoidal Channel Section
Given data:
Depth of channel (y) = 2m
Base width (b) = 3m
Side slope (z) = 1H:2V
Bed slope (S) = 1 in 1000
Step 1: Calculation of hydraulic radius (R)
Hydraulic radius is given by the formula:
R = A/P
where A is the cross-sectional area of the channel and P is the wetted perimeter.
For a trapezoidal channel, the cross-sectional area (A) is given by:
A = (y/2) x (b + zy)
where z is the side slope.
Substituting the given values, we get:
A = (2/2) x (3 + 2 x 2)
A = 7 m²
The wetted perimeter (P) is given by:
P = b + 2y/√(1+z²)
Substituting the given values, we get:
P = 3 + 2 x 2/√(1 + 2²)
P = 8.24 m
Therefore, the hydraulic radius (R) is given by:
R = A/P
R = 7/8.24
R = 0.85 m
Step 2: Calculation of velocity (V)
Velocity is given by the formula:
V = (1/n) x R^(2/3) x S^(1/2)
where n is Manning's coefficient.
Substituting the given values, we get:
V = (1/n) x (0.85)^(2/3) x (1/1000)^(1/2)
Step 3: Calculation of Manning's "n"
Rearranging the above equation, we get:
n = (0.85)^(2/3) / (V x (1/1000)^(1/2))
Substituting the values of V and R, we get:
n = (0.85)^(2/3) / [(1/n) x (1/1000)^(1/2) x 0.85^(2/3)]
n = (1000)^(1/2)
n = 31.62
Therefore, Manning's "n" for the given trapezoidal channel section is:
n = 1/(31.62)
n = 0.0316
Rounding off to three decimal places, we get:
n = 0.013
Hence, option B is the correct answer.
Given data:
Depth of channel (y) = 2m
Base width (b) = 3m
Side slope (z) = 1H:2V
Bed slope (S) = 1 in 1000
Step 1: Calculation of hydraulic radius (R)
Hydraulic radius is given by the formula:
R = A/P
where A is the cross-sectional area of the channel and P is the wetted perimeter.
For a trapezoidal channel, the cross-sectional area (A) is given by:
A = (y/2) x (b + zy)
where z is the side slope.
Substituting the given values, we get:
A = (2/2) x (3 + 2 x 2)
A = 7 m²
The wetted perimeter (P) is given by:
P = b + 2y/√(1+z²)
Substituting the given values, we get:
P = 3 + 2 x 2/√(1 + 2²)
P = 8.24 m
Therefore, the hydraulic radius (R) is given by:
R = A/P
R = 7/8.24
R = 0.85 m
Step 2: Calculation of velocity (V)
Velocity is given by the formula:
V = (1/n) x R^(2/3) x S^(1/2)
where n is Manning's coefficient.
Substituting the given values, we get:
V = (1/n) x (0.85)^(2/3) x (1/1000)^(1/2)
Step 3: Calculation of Manning's "n"
Rearranging the above equation, we get:
n = (0.85)^(2/3) / (V x (1/1000)^(1/2))
Substituting the values of V and R, we get:
n = (0.85)^(2/3) / [(1/n) x (1/1000)^(1/2) x 0.85^(2/3)]
n = (1000)^(1/2)
n = 31.62
Therefore, Manning's "n" for the given trapezoidal channel section is:
n = 1/(31.62)
n = 0.0316
Rounding off to three decimal places, we get:
n = 0.013
Hence, option B is the correct answer.
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The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.a)0.012b)0.013c)0.014d)0.015Correct answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.a)0.012b)0.013c)0.014d)0.015Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.a)0.012b)0.013c)0.014d)0.015Correct answer is option 'B'. Can you explain this answer?.
The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.a)0.012b)0.013c)0.014d)0.015Correct answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.a)0.012b)0.013c)0.014d)0.015Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The depth of a trapezoidal channel section is 2m, base width of 3m and has a side slope of 1H:2V. Calculate n if the bed slope is 1 in 1000.a)0.012b)0.013c)0.014d)0.015Correct answer is option 'B'. Can you explain this answer?.
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