Mannings formula for a rectangular channel can be written as Q = 1 nm (B H)5/3 (B +

Chapter 14, Problem 14.34

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Mannings formula for a rectangular channel can be written as Q = 1 nm (B H)5/3 (B + 2H)2/3 S where Q = flow (m3 /s), nm = a roughness coefficient, B = width (m), H = depth (m), and S = slope. You are applying this formula to a stream where you know that the width = 20 m and the depth = 0.3 m. Unfortunately, you know the roughness and the slope to only a 10% precision. That is, you know that the roughness is about 0.03 with a range from 0.027 to 0.033 and the slope is 0.0003 with a range from 0.00027 to 0.00033. Assuming uniform distributions, use a Monte Carlo analysis with n = 10,000 to estimate the distribution of flow.