Question
Download Solution PDFWhat is the best side slope (n) for the most economic trapezoidal channel having depth d and base width b?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
For Trapezoidal channel section
\(\text{Condition for most economical trapezoidal section:} m = \frac{1}{\sqrt{3}}, B = \frac{2Y}{\sqrt{3}} \)
Side slope = 1 : m (m = horizontal and 1 = vertical)
Area of flow = A = (B + mY)Y
Hydraulic radius = R =Y/2
\({\rm{Wetted\;perimeter\;}} = {\rm{\;P\;}} = {\rm{\;\;B}} + 2Y\sqrt {1 + {{\rm{m}}^2}{\rm{}}} \)
For hydraulically efficient trapezoidal channel section,
The top width of the section = T = 2Y
Area of flow = Y2
Wetted perimeter = P = 2√2 Y
Hydraulic radius = R = Y/(2√2 )
Also Width of channel section = length of side slope = B
\(B = \frac{{2Y}}{{\sqrt 3 }}\)
Additional Information
A Trapezoidal channel will be most efficient if
- Length of sloping side = Half of top width
- i.e., \(d \sqrt{n^2 + 1 }= \frac{b + 2nd}{2}\)
- Hydraulic mean depth = Half of depth of flow
- i.e., m = d/2
- The three sides of the trapezoidal section are the tangential to the semi-circle described on the water-line.
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