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For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)
Correct answer is between '62,64'. Can you explain this answer?
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For a hydraulically efficient trapezoidal channel section carrying a d...
Concept:
For an efficient channel, the discharge should be maximum.
Parameters for the most efficient trapezoidal channel having depth 'y' are:
1) Depth = y
2) Top width = 
3) Area = 
4) Perimeter = 
5) Hydraulic Radius = y/2
Calculation:
⇒ y = 4.17 m
⇒ C = 62.82
Most Upvoted Answer
For a hydraulically efficient trapezoidal channel section carrying a d...
's roughness coefficient (n) is 0.025, the slope (S) is 0.001, and the channel bottom width (B) is 10 m, we can calculate the required depth (D) using the Manning's equation for open channel flow:
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q = discharge (m^3/s)
n = Manning's roughness coefficient
A = cross-sectional area of flow (m^2)
R = hydraulic radius (m)
S = slope of the channel
First, we need to calculate the hydraulic radius (R) using the trapezoidal channel section:
A = (B + D * Z) * D
P = B + 2D * sqrt(1 + Z^2)
R = A / P
where:
Z = side slope of the channel
Assuming Z = 2 (typical for trapezoidal channels), we can solve for D:
50 = (1/0.025) * [(10 + D * 2) * D] * [(10 + 2D * sqrt(1 + 4))]^(2/3) * 0.001^(1/2)
Simplifying the equation:
50 = 40 * D^2 * (10 + 2D * sqrt(5))^(2/3)
Dividing by 40:
1.25 = D^2 * (10 + 2D * sqrt(5))^(2/3)
Raising both sides to the power of 3/2:
(1.25)^(3/2) = D^3 * (10 + 2D * sqrt(5))
Simplifying further:
1.767766 = D^3 * (10 + 2D * sqrt(5))
Rearranging the equation:
D^3 * (10 + 2D * sqrt(5)) = 1.767766
Expanding the equation:
10D^3 + 2D^4 * sqrt(5) = 1.767766
Rearranging the equation:
2D^4 * sqrt(5) + 10D^3 - 1.767766 = 0
To solve this equation, we can use numerical methods such as Newton's method or the bisection method. The solution for D will be the required depth for the hydraulically efficient trapezoidal channel section carrying a discharge of 50 m^3/s.
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q = discharge (m^3/s)
n = Manning's roughness coefficient
A = cross-sectional area of flow (m^2)
R = hydraulic radius (m)
S = slope of the channel
First, we need to calculate the hydraulic radius (R) using the trapezoidal channel section:
A = (B + D * Z) * D
P = B + 2D * sqrt(1 + Z^2)
R = A / P
where:
Z = side slope of the channel
Assuming Z = 2 (typical for trapezoidal channels), we can solve for D:
50 = (1/0.025) * [(10 + D * 2) * D] * [(10 + 2D * sqrt(1 + 4))]^(2/3) * 0.001^(1/2)
Simplifying the equation:
50 = 40 * D^2 * (10 + 2D * sqrt(5))^(2/3)
Dividing by 40:
1.25 = D^2 * (10 + 2D * sqrt(5))^(2/3)
Raising both sides to the power of 3/2:
(1.25)^(3/2) = D^3 * (10 + 2D * sqrt(5))
Simplifying further:
1.767766 = D^3 * (10 + 2D * sqrt(5))
Rearranging the equation:
D^3 * (10 + 2D * sqrt(5)) = 1.767766
Expanding the equation:
10D^3 + 2D^4 * sqrt(5) = 1.767766
Rearranging the equation:
2D^4 * sqrt(5) + 10D^3 - 1.767766 = 0
To solve this equation, we can use numerical methods such as Newton's method or the bisection method. The solution for D will be the required depth for the hydraulically efficient trapezoidal channel section carrying a discharge of 50 m^3/s.
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For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. Can you explain this answer?
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For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. 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 For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. 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 For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. Can you explain this answer?.
For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. 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 For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. 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 For a hydraulically efficient trapezoidal channel section carrying a discharge of 50 m3/s. If Manning’s coefficient(n) is 0.018 then chezy’s coefficient C for the channel is _______ (Take Bed slope as 1 in 3000)Correct answer is between '62,64'. Can you explain this answer?.
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