Question An open channel is to be designed to carry 5 (m^3/s) at a slope of 0.06. The channel material has an n value of 0.01. Find the most effcient cross section for a trapezoidal section?

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An open channel is to be designed to carry 5 (m^3/s) at a slope of 0.06. The channel material has an n value of 0.01. Find the most effcient cross section for a trapezoidal section?

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Sution\begin{array}{l}B=|.1547 y| \\ \text { Also } R=\frac{y}{2} \rightarrow \text { For most } \\ \text { Q } 1 \text { Eunomical lution } \\ \Rightarrow A=\frac{B+B+2 \times \frac{y}{\sqrt{3}}}{2} \times y=\left(B+\frac{y}{\sqrt{3}}\right) \times y \\ =1.732 y^{2} \\ \Rightarrow Q=\frac{1}{n} R^{2 / 3} s^{1 / 2} \times A \\ \Rightarrow \quad 5=\frac{1}{0.01} \times\left(\frac{y}{2}\right)^{2 / 3} \times 0.06^{1 / 2} \times 1.732 y^{2} \\ y=0.533 \mathrm{~m} \quad B=0.615 \mathrm{~m} \\\end{array} ...