The Manning equation can be written for a rectangular open channel as Q = S(B H)5/3 n(B
Chapter 6, Problem 6.25(choose chapter or problem)
The Manning equation can be written for a rectangular open channel as
\(Q=\frac{\sqrt{S}(B H)^{5 / 3}}{n(B+2 H)^{2 / 3}}\)
where \(Q=\text { flow }\left(\mathrm{m}^{3} / \mathrm{s}\right)\), S = slope (m/m), H = depth (m), and n = the Manning roughness coefficient. Develop a fixed-point iteration scheme to solve this equation for H given Q = 5, S = 0.0002, B = 20, and n = 0.03. Perform the computation until \(\varepsilon_{a}\) is less than \(\varepsilon_{s}\) = 0.05%. Prove that your scheme converges for all initial guesses greater than or equal to zero.
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