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A rectangular channel 22 feet wide carries a flow of 25,000 cfs on a slope of 0.01. Manning's n for the channel is 0.012. Find the depth of flow.

A rectangular channel 22 feet wide carries a flow of 25,000 cfs on a slope of 0.01. Manning's n for the channel is 0.012. Find the depth of flow.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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use minning equations 

**Problem Statement:** A rectangular channel 22 feet wide carries a flow of 25,000 cubic feet per second (cfs) on a slope of 0.01. Manning’s n for the channel is 0.012. Find the depth of flow. **Solution Explanation:** The problem involves determining the depth of flow in a rectangular open channel using the Manning’s equation. Key parameters given are the channel width (22 feet), flow rate (25,000 cfs), channel slope (0.01), and Manning’s coefficient (n = 0.012). The Manning’s equation is: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] where: - \( Q \) is the flow rate, - \( A \) is the cross-sectional area of flow, - \( R \) is the hydraulic radius (area/wetted perimeter), - \( S \) is the slope of the channel, - \( n \) is Manning’s roughness coefficient. To solve for the depth, iterative or computational methods would typically be used, as the equation involves both the area and the hydraulic radius, which are dependent on the unknown depth.
Transcribed Image Text:**Problem Statement:** A rectangular channel 22 feet wide carries a flow of 25,000 cubic feet per second (cfs) on a slope of 0.01. Manning’s n for the channel is 0.012. Find the depth of flow. **Solution Explanation:** The problem involves determining the depth of flow in a rectangular open channel using the Manning’s equation. Key parameters given are the channel width (22 feet), flow rate (25,000 cfs), channel slope (0.01), and Manning’s coefficient (n = 0.012). The Manning’s equation is: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] where: - \( Q \) is the flow rate, - \( A \) is the cross-sectional area of flow, - \( R \) is the hydraulic radius (area/wetted perimeter), - \( S \) is the slope of the channel, - \( n \) is Manning’s roughness coefficient. To solve for the depth, iterative or computational methods would typically be used, as the equation involves both the area and the hydraulic radius, which are dependent on the unknown depth.
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