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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?
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...
Understanding Trapezoidal Channel Sections
In open channel hydraulics, trapezoidal sections are commonly analyzed for their efficiency in flow. The side slopes of 2H:1V indicate a slope of 2 horizontal units for every vertical unit.
Parameters of the Trapezoidal Section
- Bottom Width (b): The width of the channel at the bottom.
- Depth (d): The vertical distance from the bottom to the water surface.
Economical Trapezoidal Design
The relationship between the bottom width (b) and the depth (d) can be derived for the most economical design, which minimizes the surface area for a given cross-sectional flow area.
Deriving the Relationship
- For the trapezoidal section, the hydraulic radius and the cross-sectional area must be optimized.
- The formula for calculating the area (A) of the trapezoidal section is:
A = (b + 2d) * d / 2
- The wetted perimeter (P) is given by:
P = b + 2 * d * sqrt(1 + (2^2)) = b + 2 * d * sqrt(5)
Optimal Ratio Derivation
To minimize the area while maximizing the flow efficiency, the following ratio emerges:
- The most economical condition leads to the relationship:
b = 0.47 * d
This ratio ensures that the channel design minimizes energy loss and maximizes flow capacity.
Conclusion
Thus, the correct answer, representing the most economical trapezoidal section, is:
Option A: b = 0.47 d
In open channel hydraulics, trapezoidal sections are commonly analyzed for their efficiency in flow. The side slopes of 2H:1V indicate a slope of 2 horizontal units for every vertical unit.
Parameters of the Trapezoidal Section
- Bottom Width (b): The width of the channel at the bottom.
- Depth (d): The vertical distance from the bottom to the water surface.
Economical Trapezoidal Design
The relationship between the bottom width (b) and the depth (d) can be derived for the most economical design, which minimizes the surface area for a given cross-sectional flow area.
Deriving the Relationship
- For the trapezoidal section, the hydraulic radius and the cross-sectional area must be optimized.
- The formula for calculating the area (A) of the trapezoidal section is:
A = (b + 2d) * d / 2
- The wetted perimeter (P) is given by:
P = b + 2 * d * sqrt(1 + (2^2)) = b + 2 * d * sqrt(5)
Optimal Ratio Derivation
To minimize the area while maximizing the flow efficiency, the following ratio emerges:
- The most economical condition leads to the relationship:
b = 0.47 * d
This ratio ensures that the channel design minimizes energy loss and maximizes flow capacity.
Conclusion
Thus, the correct answer, representing the most economical trapezoidal section, is:
Option A: b = 0.47 d
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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 2025 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 2025 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 2025 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 2025 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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