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There is an underground pipe moving wet raw sludge down a hill at a 25° angle with an elevation difference of 200 ft. Pressure readings are P1 and P2 in psi. The inlet diameter is D1 ft and the outlet diameter is D2 ft and the flowrate through the pipe network is approximately Q cfs. The combined weight of the water and pipe is approximately 50 lbf. After a slope stability analysis, you determine the maximum vertical force that can applied onto the surrounding soil is 500lbf. Is the slope stable or will it collapse (i.e., is the vertical force required to keep the system in balance greater than 500 lbf)? State your assumptions. FYI, most wet raw sludges have a specific gravity ranging from about 1.01 to 1.03. P₂ J25° O R 7

There is an underground pipe moving wet raw sludge down a hill at a 25° angle with an elevation difference of 200 ft. Pressure readings are P1 and P2 in psi. The inlet diameter is D1 ft and the outlet diameter is D2 ft and the flowrate through the pipe network is approximately Q cfs. The combined weight of the water and pipe is approximately 50 lbf. After a slope stability analysis, you determine the maximum vertical force that can applied onto the surrounding soil is 500lbf. Is the slope stable or will it collapse (i.e., is the vertical force required to keep the system in balance greater than 500 lbf)? State your assumptions. FYI, most wet raw sludges have a specific gravity ranging from about 1.01 to 1.03. P₂ J25° O R 7

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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Please show all work including unit converstions and please make sure to show all units.

 

For P1=10+(6), so P1=16 psi

for P2=20+0, so P2=20 psi

for D1= 1ft

for D2=0.6ft

for Q=5.4 cubic ft per second

 

**Understanding Pipe Slope Stability in a Multiphase Flow System** In this example, we examine an underground pipe transporting wet raw sludge down a slope with a 25° inclination and an elevation difference of 200 ft. Key parameters to consider: - **Pressure readings:** - \( P_1 \) (initial pressure) and \( P_2 \) (final pressure), both measured in psi. - **Pipe dimensions:** - Inlet diameter: \( D_1 \) ft. - Outlet diameter: \( D_2 \) ft. - **Flow rate:** \( Q \) cfs (cubic feet per second). **Important facts:** 1. The combined weight of the water and the pipe is approximately 50 lbf. 2. Upon performing a slope stability analysis, the maximum vertical force that the surrounding soil can support is determined to be 500 lbf. 3. The specific gravity of most wet raw sludges ranges from 1.01 to 1.03. **Problem Statement:** - Determine whether the slope is stable or if it will collapse under the given conditions. This involves checking if the vertical force needed to maintain system balance exceeds 500 lbf. **Graphical Representation:** The diagram illustrates: - The pipe descending at a 25° angle. - Pressure readings \( P_1 \) and \( P_2 \) at different points along the pipe. - The figure also shows important factors like the elevations, forces in the direction of the slope, and diameters at the inlet and outlet. **Stability Analysis:** - Calculate the vertical force required using the given data and compare it against the 500 lbf threshold. **Assumptions to Consider:** - Consistent flow rate. - Steady pressure conditions. - The material properties of the sludge are uniform. Overall, the educational goal is to determine whether the slope stability is within safe bounds given the specific forces and environmental conditions described. **Conclusion:** For a stable slope, ensure the calculated force does not exceed 500 lbf. Otherwise, alternative measures must be considered to reinforce the slope or modify the flow conditions.
Transcribed Image Text:**Understanding Pipe Slope Stability in a Multiphase Flow System** In this example, we examine an underground pipe transporting wet raw sludge down a slope with a 25° inclination and an elevation difference of 200 ft. Key parameters to consider: - **Pressure readings:** - \( P_1 \) (initial pressure) and \( P_2 \) (final pressure), both measured in psi. - **Pipe dimensions:** - Inlet diameter: \( D_1 \) ft. - Outlet diameter: \( D_2 \) ft. - **Flow rate:** \( Q \) cfs (cubic feet per second). **Important facts:** 1. The combined weight of the water and the pipe is approximately 50 lbf. 2. Upon performing a slope stability analysis, the maximum vertical force that the surrounding soil can support is determined to be 500 lbf. 3. The specific gravity of most wet raw sludges ranges from 1.01 to 1.03. **Problem Statement:** - Determine whether the slope is stable or if it will collapse under the given conditions. This involves checking if the vertical force needed to maintain system balance exceeds 500 lbf. **Graphical Representation:** The diagram illustrates: - The pipe descending at a 25° angle. - Pressure readings \( P_1 \) and \( P_2 \) at different points along the pipe. - The figure also shows important factors like the elevations, forces in the direction of the slope, and diameters at the inlet and outlet. **Stability Analysis:** - Calculate the vertical force required using the given data and compare it against the 500 lbf threshold. **Assumptions to Consider:** - Consistent flow rate. - Steady pressure conditions. - The material properties of the sludge are uniform. Overall, the educational goal is to determine whether the slope stability is within safe bounds given the specific forces and environmental conditions described. **Conclusion:** For a stable slope, ensure the calculated force does not exceed 500 lbf. Otherwise, alternative measures must be considered to reinforce the slope or modify the flow conditions.
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