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A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:
- a)b = 0.47 d
- b)b/d = 0.5
- c)b = 2d
- d)d2 b = 2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A trapezoidal section of an open channel has side slope 2H : 1V. If bo...
For most of the economical open channel Trapezoidal section,
Half of top width should be equal to length of the side slope (n:1=H:V)
Most Upvoted Answer
A trapezoidal section of an open channel has side slope 2H : 1V. If bo...
Let the trapezoidal section of the open channel have the following dimensions:
- Bottom width = b
- Side slope = 2H : 1V
- Depth of water = d
- Width of water surface = T
The cross-sectional area of the channel is given by:
A = (d + 2H)d + b(2H)
= d^2 + 2Hd + 2Hb
The wetted perimeter of the channel is given by:
P = T + 2d(1 + 4H^2)^(1/2)
The hydraulic radius of the channel is given by:
R = A/P
= (d^2 + 2Hd + 2Hb) / (T + 2d(1 + 4H^2)^(1/2))
The discharge through the channel can be calculated using the Manning's equation:
Q = (1/n)AR^(2/3)S^(1/2)
where:
- n is the Manning's roughness coefficient
- S is the slope of the channel bed
The slope of the channel bed can be calculated as:
S = (Z2 - Z1) / L
where:
- Z2 is the elevation of the downstream end of the channel
- Z1 is the elevation of the upstream end of the channel
- L is the length of the channel
Assuming that the channel is horizontal, Z2 = Z1 and S = 0.
Therefore, the discharge through the channel simplifies to:
Q = (1/n)AR^(2/3)
= (1/n)(d^2 + 2Hd + 2Hb)^(5/3) / (T + 2d(1 + 4H^2)^(1/2))^2/3
- Bottom width = b
- Side slope = 2H : 1V
- Depth of water = d
- Width of water surface = T
The cross-sectional area of the channel is given by:
A = (d + 2H)d + b(2H)
= d^2 + 2Hd + 2Hb
The wetted perimeter of the channel is given by:
P = T + 2d(1 + 4H^2)^(1/2)
The hydraulic radius of the channel is given by:
R = A/P
= (d^2 + 2Hd + 2Hb) / (T + 2d(1 + 4H^2)^(1/2))
The discharge through the channel can be calculated using the Manning's equation:
Q = (1/n)AR^(2/3)S^(1/2)
where:
- n is the Manning's roughness coefficient
- S is the slope of the channel bed
The slope of the channel bed can be calculated as:
S = (Z2 - Z1) / L
where:
- Z2 is the elevation of the downstream end of the channel
- Z1 is the elevation of the upstream end of the channel
- L is the length of the channel
Assuming that the channel is horizontal, Z2 = Z1 and S = 0.
Therefore, the discharge through the channel simplifies to:
Q = (1/n)AR^(2/3)
= (1/n)(d^2 + 2Hd + 2Hb)^(5/3) / (T + 2d(1 + 4H^2)^(1/2))^2/3
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Community Answer
A trapezoidal section of an open channel has side slope 2H : 1V. If bo...
For most economical trapezoidal section
half top width = side length
half top width= b +2nd/2 ( n=2)
= b+4d/2
side length = √(d^2 + (2d)^2
=√5d^2 = d√5
solving
b+4d/2= d√5
b+4d = 2d√5
b= 2d√5 - 4d
b= 0.472d
half top width = side length
half top width= b +2nd/2 ( n=2)
= b+4d/2
side length = √(d^2 + (2d)^2
=√5d^2 = d√5
solving
b+4d/2= d√5
b+4d = 2d√5
b= 2d√5 - 4d
b= 0.472d
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A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer?
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A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer?.
A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer?.
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A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A trapezoidal section of an open channel has side slope 2H : 1V. If bottom width is 'b’ and depth d’, the relation between b & d for most economical trapezoidal section of the channel is:a)b = 0.47 db)b/d = 0.5c)b = 2dd)d2b = 2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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