A trapezoidal channel has a bottom width of 3.0 m and side slopes of 1 : 1. The bottom is of brick work (n = 0.02) and the sides are lined with concrete (n = 0.012). Flow takes place at a uniform depth equal to 1.2 m. Find the equivalent Manning's coefficient which can be adopted in the uniform

Question

A trapezoidal channel has a bottom width of 3.0 m and side slopes of 1 : 1. The bottom is of brick work (n = 0.02) and the sides are lined with concrete (n = 0.012). Flow takes place at a uniform depth equal to 1.2 m. Find the equivalent Manning's coefficient which can be adopted in the uniform flow computations of the channel.

Accepted Answer

For the bed, [latex]P_1[/latex] = 3.0 m and [latex]n_1[/latex] = 0.02

For the sides, [latex]P_2[/latex] = 2 × [latex]\sqrt2[/latex] × 1.2 = 3.39 m, and [latex]n_2[/latex] = 0.012, [latex]P = P_1 + P_2[/latex]

Therefore, from Eq. (11.46) the equivalent

[latex]n={\frac{(\sum P_{i}\,n_{i}^{3/2})^{2/3}}{P^{2/3}}}[/latex] (11.46)

[latex]n\,=\,\frac{\,(3.0 imes0.02^{3/2}+3.39 imes0.012^{3/2})^{2/3}}{\,(3.0+3.39)^{2/3}}=\frac{0.05528}{3.439}=0.016[/latex]

As [latex]P_1 ext{ and } P_2[/latex] are nearly the same in this example, the equivalent n worked out as the average of [latex]n_1 ext{ and } n_2[/latex]. This will not be the case, always.

Question 11.3: A trapezoidal channel has a bottom width of 3.0 m and side s......

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