Answered: A rectangular concrete channel (n =…

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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$### Problem Statement: Hydraulics in Rectangular Channels **Channel Characteristics:** - **Type:** Rectangular concrete channel - **Width:** 10.5 feet - **Slope:** 0.006 - **Discharge Rate:** 200 cubic feet per second (cfs) - **Manning's Roughness Coefficient (n):** 0.015 **Tasks:** 1. **Compute the Normal Depth**: - Use the Manning's equation for open channel flow to determine the normal depth. 2. **Compute the Critical Depth**: - Use the appropriate formula to find the critical depth for the rectangular channel. 3. **Determine the Flow Condition**: - Given the depth of flow is 5.7 feet, evaluate if the flow is subcritical or supercritical by comparing it with the critical depth. 4. **Identify the Flow Profile Type**: - Based on the flow depth and the critical depth, determine the type of flow profile in the channel. ### Explanation of Concepts **Normal Depth (y_n):** - The depth of flow in a channel where the flow is uniform and steady. It's calculated using Manning's equation: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] Where: - $ Q $ is the discharge (200 cfs), - $ n $ is the Manning's roughness coefficient (0.015), - $ A $ is the cross-sectional area of flow, - $ R $ is the hydraulic radius, - $ S $ is the slope of the channel (0.006). **Critical Depth (y_c):** - The depth of flow where the specific energy is at a minimum for a given discharge. It's calculated using: \[ Q^2 = g A^3 / B \] Where: - $ g $ is the gravitational acceleration (32.2 ft/s²), - $ A $ is the cross-sectional area, - $ B $ is the top width of the flow. **Flow Conditions:** - **Subcritical Flow:** Occurs when the flow depth is greater than the critical depth ($ y > y_c $). - **Supercritical Flow:** Occurs when the flow depth is less than the critical depth ($ y < y_c $). **Flow Profile Types:**$

Transcribed Image Text:### Problem Statement: Hydraulics in Rectangular Channels **Channel Characteristics:** - **Type:** Rectangular concrete channel - **Width:** 10.5 feet - **Slope:** 0.006 - **Discharge Rate:** 200 cubic feet per second (cfs) - **Manning's Roughness Coefficient (n):** 0.015 **Tasks:** 1. **Compute the Normal Depth**: - Use the Manning's equation for open channel flow to determine the normal depth. 2. **Compute the Critical Depth**: - Use the appropriate formula to find the critical depth for the rectangular channel. 3. **Determine the Flow Condition**: - Given the depth of flow is 5.7 feet, evaluate if the flow is subcritical or supercritical by comparing it with the critical depth. 4. **Identify the Flow Profile Type**: - Based on the flow depth and the critical depth, determine the type of flow profile in the channel. ### Explanation of Concepts **Normal Depth (y_n):** - The depth of flow in a channel where the flow is uniform and steady. It's calculated using Manning's equation: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] Where: - $ Q $ is the discharge (200 cfs), - $ n $ is the Manning's roughness coefficient (0.015), - $ A $ is the cross-sectional area of flow, - $ R $ is the hydraulic radius, - $ S $ is the slope of the channel (0.006). **Critical Depth (y_c):** - The depth of flow where the specific energy is at a minimum for a given discharge. It's calculated using: \[ Q^2 = g A^3 / B \] Where: - $ g $ is the gravitational acceleration (32.2 ft/s²), - $ A $ is the cross-sectional area, - $ B $ is the top width of the flow. **Flow Conditions:** - **Subcritical Flow:** Occurs when the flow depth is greater than the critical depth ($ y > y_c $). - **Supercritical Flow:** Occurs when the flow depth is less than the critical depth ($ y < y_c $). **Flow Profile Types:**

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