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The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: - q₁ = K(P; — P;) qi q;= K(P; - P;) qj where q; and q; are fluid flow at nodes i and j, respectively; P; and P; are fluid pressure at nodes i and j, respectively; and K is K = πD4 128μL where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9×104 Pa's. a. Write the element matrix equation for the flow in the pipe element. b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero. What is the outflow rate for elements 4, 6, and 7? 1 1 (3) 3 (4) 4 Q2' (2) 2 5 ⑤ 6 7 Elem 1 2 3 4 5 6 7 D(mm) 40 40 50 25 40 25 25 L(m) 1 1 1 4 2 3 3 6 8

The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: - q₁ = K(P; — P;) qi q;= K(P; - P;) qj where q; and q; are fluid flow at nodes i and j, respectively; P; and P; are fluid pressure at nodes i and j, respectively; and K is K = πD4 128μL where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9×104 Pa's. a. Write the element matrix equation for the flow in the pipe element. b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero. What is the outflow rate for elements 4, 6, and 7? 1 1 (3) 3 (4) 4 Q2' (2) 2 5 ⑤ 6 7 Elem 1 2 3 4 5 6 7 D(mm) 40 40 50 25 40 25 25 L(m) 1 1 1 4 2 3 3 6 8

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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The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: - q₁ = K(P; — P;) qi q;= K(P; - P;) qj where q; and q; are fluid flow at nodes i and j, respectively; P; and P; are fluid pressure at nodes i and j, respectively; and K is K = πD4 128μL where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9×104 Pa's. a. Write the element matrix equation for the flow in the pipe element. b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero. What is the outflow rate for elements 4, 6, and 7? 1 1 (3) 3 (4) 4 Q2' (2) 2 5 ⑤ 6 7 Elem 1 2 3 4 5 6 7 D(mm) 40 40 50 25 40 25 25 L(m) 1 1 1 4 2 3 3 6 8
Transcribed Image Text:The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: - q₁ = K(P; — P;) qi q;= K(P; - P;) qj where q; and q; are fluid flow at nodes i and j, respectively; P; and P; are fluid pressure at nodes i and j, respectively; and K is K = πD4 128μL where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9×104 Pa's. a. Write the element matrix equation for the flow in the pipe element. b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero. What is the outflow rate for elements 4, 6, and 7? 1 1 (3) 3 (4) 4 Q2' (2) 2 5 ⑤ 6 7 Elem 1 2 3 4 5 6 7 D(mm) 40 40 50 25 40 25 25 L(m) 1 1 1 4 2 3 3 6 8
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