### Design of a Concrete-Lined Drainage Channel**Problem Statement:**Design (Find \(y_n\), \(B\), \(T\), and \(F_b\)) a concrete-lined drainage channel (\(n = 0.015\)) to carry 150 m³/s with 1.5H:1V side slopes, \(B/y_n = 3\), and a longitudinal slope of 0.0005. Compute the velocity and Froude Number at design capacity.**Given:**- Discharge, \(Q = 150 \, \text{m}^3/\text{s}\)- Manning's Roughness Coefficient, \(n = 0.015\)- Side slopes, \(1.5H:1V\)- Ratio of bottom width to normal depth, \(B/y_n = 3\)- Longitudinal slope, \(S = 0.0005\)**Diagram Analysis:**The diagram provided is of a trapezoidal channel. Here is a breakdown of the key components:- **\(y_n\)**: Normal Depth- **\(B\)**: Bottom Width of the channel- **\(T\)**: Top Width of the water surface level at normal depth- **\(F_b\)**: Freeboard, which is the additional height above the normal depth to ensure safety against overflow.### Understanding the Channel Geometry:A trapezoidal channel is defined by its side slopes, bottom width, and normal depth. The area (\(A\)) and the wetted perimeter (\(P\)) are calculated using the following equations:\[ A = B y_n + s y_n^2 \]\[ P = B + 2y_n\sqrt{1 + s^2} \]Where,- \(s\) is the side slope (horizontal component), here \(s = 1.5\)### Computations:#### Step 1: Determining Normal Depth (\(y_n\)):Given \(B/y_n = 3\),\[ B = 3 y_n \]Using Manning's Equation:\[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \]Where,\[ R = \frac{A}{P} \] (Hydraulic Radius)Substitute \(A\), \(P\), and rearrange the

Manning's coefficient, n=0.015Discharge, Q=150 m3/sSlope = 1.5 H:1VB/y1=3Longitudinal slope,…

Design (Find y₁, B, T and Fb) a concrete-lined drainage channel (n = 0.015) to carry 150 m³/s with 1.5H:1V side slopes, B/y = 3, and a longitudinal slope of 0.0005. Compute the velocity and Froude Number at design capacity. Note: rectangular channel ss-0 triangular channel B-0 Freeboard (a) Trapezoidal channel A-By+ssy² P=B+2√√1+²

Design (Find y₁, B, T and Fb) a concrete-lined drainage channel (n = 0.015) to carry 150 m³/s with 1.5H:1V side slopes, B/y = 3, and a longitudinal slope of 0.0005. Compute the velocity and Froude Number at design capacity. Note: rectangular channel ss-0 triangular channel B-0 Freeboard (a) Trapezoidal channel A-By+ssy² P=B+2√√1+²

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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