For a trapezoidal channel with the horizontal dimension of the side slope is 3 (i.e Z=3), a normal depth 2.87 in ft, and a channel bed slope of 0.065. The channel is lined with concrete with a roughness coefficient of 0.013. The channel base width 4.5. Calculate the velocity (v) in fps.
For a trapezoidal channel with the horizontal dimension of the side slope is 3 (i.e Z=3), a normal depth 2.87 in ft, and a channel bed slope of 0.065. The channel is lined with concrete with a roughness coefficient of 0.013. The channel base width 4.5. Calculate the velocity (v) in fps.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Can you please show how to do this problem? I’m confused on this homework question and please box answer and pleas write clear thank you.
![**Problem Statement:**
For a trapezoidal channel with the horizontal dimension of the side slope is 3 (i.e Z=3), a normal depth of 2.87 ft, and a channel bed slope of 0.065. The channel is lined with concrete with a roughness coefficient of 0.013. The channel base width is 4.5 ft. Calculate the velocity (v) in feet per second (fps).
**Explanation:**
To solve this problem, you would typically use the Manning's equation for open channel flow, which is given by:
\[ v = \frac{1}{n} R^{2/3} S^{1/2} \]
where:
- \( v \) = velocity (fps)
- \( n \) = Manning’s roughness coefficient
- \( R \) = hydraulic radius (ft)
- \( S \) = slope of the channel bed
**Given Data:**
- Side slope \( Z \) = 3
- Normal depth \( y \) = 2.87 ft
- Channel bed slope \( S \) = 0.065
- Roughness coefficient \( n \) = 0.013
- Channel base width \( b \) = 4.5 ft
**Steps to Calculate Velocity:**
1. **Calculate the Area (A) of the trapezoidal section:**
\[ A = \left( b + Z \cdot y \right) \cdot y = \left( 4.5 + 3 \cdot 2.87 \right) \cdot 2.87 \]
2. **Calculate the Wetted Perimeter (P):**
\[ P = b + 2 \cdot y \sqrt{1 + Z^2} = 4.5 + 2 \cdot 2.87 \sqrt{1 + 3^2} \]
3. **Calculate the Hydraulic Radius (R):**
\[ R = \frac{A}{P} \]
4. **Apply Manning’s Equation to Find the Velocity (v):**
\[ v = \frac{1}{n} R^{2/3} S^{1/2} \]
By following these steps, you will be able to determine the velocity of the water flow in the trapezoidal channel.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b7dd8f1-dbab-4607-8b33-bde9974f18c9%2F186268d8-57d6-40e3-affb-549c7c814072%2Fgt3csio_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
For a trapezoidal channel with the horizontal dimension of the side slope is 3 (i.e Z=3), a normal depth of 2.87 ft, and a channel bed slope of 0.065. The channel is lined with concrete with a roughness coefficient of 0.013. The channel base width is 4.5 ft. Calculate the velocity (v) in feet per second (fps).
**Explanation:**
To solve this problem, you would typically use the Manning's equation for open channel flow, which is given by:
\[ v = \frac{1}{n} R^{2/3} S^{1/2} \]
where:
- \( v \) = velocity (fps)
- \( n \) = Manning’s roughness coefficient
- \( R \) = hydraulic radius (ft)
- \( S \) = slope of the channel bed
**Given Data:**
- Side slope \( Z \) = 3
- Normal depth \( y \) = 2.87 ft
- Channel bed slope \( S \) = 0.065
- Roughness coefficient \( n \) = 0.013
- Channel base width \( b \) = 4.5 ft
**Steps to Calculate Velocity:**
1. **Calculate the Area (A) of the trapezoidal section:**
\[ A = \left( b + Z \cdot y \right) \cdot y = \left( 4.5 + 3 \cdot 2.87 \right) \cdot 2.87 \]
2. **Calculate the Wetted Perimeter (P):**
\[ P = b + 2 \cdot y \sqrt{1 + Z^2} = 4.5 + 2 \cdot 2.87 \sqrt{1 + 3^2} \]
3. **Calculate the Hydraulic Radius (R):**
\[ R = \frac{A}{P} \]
4. **Apply Manning’s Equation to Find the Velocity (v):**
\[ v = \frac{1}{n} R^{2/3} S^{1/2} \]
By following these steps, you will be able to determine the velocity of the water flow in the trapezoidal channel.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning