Refer to the following channel cross section. Normal depth is 3.0 feet. (a) What is the cross-sectional area of flow? (b) What is the wetted perimeter? (c) What is the hydraulic radius?
Refer to the following channel cross section. Normal depth is 3.0 feet. (a) What is the cross-sectional area of flow? (b) What is the wetted perimeter? (c) What is the hydraulic radius?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Channel Cross Section Analysis
Refer to the following channel cross section. The normal depth is given as 3.0 feet. Examine the trapezoidal channel shape to answer the questions below:
#### Diagram Description:
- The channel cross section is trapezoidal.
- The top width of the trapezoid is comprised of two equal side lengths of 1.5 feet each, and a bottom width of 5.0 feet.
- The depth (vertical height) of the channel is 3.0 feet.
#### Questions:
(a) **What is the cross-sectional area of flow?**
(b) **What is the wetted perimeter?**
(c) **What is the hydraulic radius?**
To solve these, consider:
- **Cross-sectional Area:** Calculated using the formula for the area of a trapezoid:
\[
A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
- **Wetted Perimeter:** Sum of the bottom width and the lengths of the two sides of the trapezoid.
- **Hydraulic Radius:** The ratio of the cross-sectional area of flow to the wetted perimeter:
\[
R = \frac{A}{P}
\]
Use the provided dimensions to compute these values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f7667e6-d7e6-4d0a-9b2e-fc86c4bd82dc%2Fe8234fbd-b776-4077-8a0f-4c79e88ef632%2Fln2dw7g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Channel Cross Section Analysis
Refer to the following channel cross section. The normal depth is given as 3.0 feet. Examine the trapezoidal channel shape to answer the questions below:
#### Diagram Description:
- The channel cross section is trapezoidal.
- The top width of the trapezoid is comprised of two equal side lengths of 1.5 feet each, and a bottom width of 5.0 feet.
- The depth (vertical height) of the channel is 3.0 feet.
#### Questions:
(a) **What is the cross-sectional area of flow?**
(b) **What is the wetted perimeter?**
(c) **What is the hydraulic radius?**
To solve these, consider:
- **Cross-sectional Area:** Calculated using the formula for the area of a trapezoid:
\[
A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
- **Wetted Perimeter:** Sum of the bottom width and the lengths of the two sides of the trapezoid.
- **Hydraulic Radius:** The ratio of the cross-sectional area of flow to the wetted perimeter:
\[
R = \frac{A}{P}
\]
Use the provided dimensions to compute these values.
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