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If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections then the ratio of hydraulic radius of triangular section to that of rectangular section is.
- a)√2
- b)1/√2
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
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If water is flowing at the same depth in most hydraulically efficient ...
Hence, the correct option is (B).
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The hydraulic radius of a channel section is defined as the cross-sectional area divided by the wetted perimeter.
For a triangular section, the hydraulic radius can be calculated as:
R_triangular = (0.5 * base * height) / (base + 2 * height)
For a rectangular section, the hydraulic radius can be calculated as:
R_rectangular = (width * height) / (2 * width + 2 * height)
Let's assume that the base of the triangular section is equal to the width of the rectangular section, and the height of the triangular section is equal to the height of the rectangular section.
Therefore, the hydraulic radius ratio can be calculated as:
R_triangular / R_rectangular = [(0.5 * base * height) / (base + 2 * height)] / [(width * height) / (2 * width + 2 * height)]
Simplifying the expression:
R_triangular / R_rectangular = [(0.5 * base * height) * (2 * width + 2 * height)] / [(base + 2 * height) * (width * height)]
R_triangular / R_rectangular = (base * (2 * width + 2 * height)) / (base + 2 * height)
Since we assumed that the base of the triangular section is equal to the width of the rectangular section, and the height of the triangular section is equal to the height of the rectangular section, we can substitute these values into the expression:
R_triangular / R_rectangular = (width * (2 * width + 2 * height)) / (width + 2 * height)
Simplifying further:
R_triangular / R_rectangular = (2 * width^2 + 2 * width * height) / (width + 2 * height)
Therefore, the ratio of hydraulic radius of a triangular section to that of a rectangular section is (2 * width^2 + 2 * width * height) / (width + 2 * height).
For a triangular section, the hydraulic radius can be calculated as:
R_triangular = (0.5 * base * height) / (base + 2 * height)
For a rectangular section, the hydraulic radius can be calculated as:
R_rectangular = (width * height) / (2 * width + 2 * height)
Let's assume that the base of the triangular section is equal to the width of the rectangular section, and the height of the triangular section is equal to the height of the rectangular section.
Therefore, the hydraulic radius ratio can be calculated as:
R_triangular / R_rectangular = [(0.5 * base * height) / (base + 2 * height)] / [(width * height) / (2 * width + 2 * height)]
Simplifying the expression:
R_triangular / R_rectangular = [(0.5 * base * height) * (2 * width + 2 * height)] / [(base + 2 * height) * (width * height)]
R_triangular / R_rectangular = (base * (2 * width + 2 * height)) / (base + 2 * height)
Since we assumed that the base of the triangular section is equal to the width of the rectangular section, and the height of the triangular section is equal to the height of the rectangular section, we can substitute these values into the expression:
R_triangular / R_rectangular = (width * (2 * width + 2 * height)) / (width + 2 * height)
Simplifying further:
R_triangular / R_rectangular = (2 * width^2 + 2 * width * height) / (width + 2 * height)
Therefore, the ratio of hydraulic radius of a triangular section to that of a rectangular section is (2 * width^2 + 2 * width * height) / (width + 2 * height).
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If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections then the ratio of hydraulic radius of triangular section to that of rectangular section is.a)√2b)1/√2c)1d)2Correct answer is option 'B'. Can you explain this answer?
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