Question:
The most economical trapezoidal channel section with 1:1 (horizontal:vertical) side slope is designed to carry a maximum of 40 cm depth of water at its full capacity. The bed slope of the channel is 1:2500 and the Manning's roughness coefficient of channel section is 0.01. The estimated discharge capacity of the channel in m\(^3\).s\(^{-1}\) is \(\underline{\hspace{1cm}}\) (round off to 2 decimal places).
The most economical trapezoidal channel section with 1:1 (horizontal:vertical) side slope is designed to carry a maximum of 40 cm depth of water at its full capacity. The bed slope of the channel is 1:2500 and the Manning's roughness coefficient of channel section is 0.01. The estimated discharge capacity of the channel in m\(^3\).s\(^{-1}\) is \(\underline{\hspace{1cm}}\) (round off to 2 decimal places).
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Use the Manning formula to calculate the discharge based on channel geometry and slope.
Updated On: Dec 22, 2025
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Correct Answer: 0.18
Solution and Explanation
Manning's formula for discharge:
\[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] Where: - \(n = 0.01\), - \(S = \frac{1}{2500}\), - depth = 0.4 m. For a trapezoidal section with 1:1 side slopes: \[ A = \text{cross-sectional area} = \frac{b \times h}{2} \text{(adjusting for channel shape)} \] Using the given formula, the estimated discharge is \( \boxed{0.19}\ \text{m}^3\text{s}^{-1} \).
\[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] Where: - \(n = 0.01\), - \(S = \frac{1}{2500}\), - depth = 0.4 m. For a trapezoidal section with 1:1 side slopes: \[ A = \text{cross-sectional area} = \frac{b \times h}{2} \text{(adjusting for channel shape)} \] Using the given formula, the estimated discharge is \( \boxed{0.19}\ \text{m}^3\text{s}^{-1} \).
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