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Analysis of Fluid Flow in a Horizontal Pipe Network: Flow Rates and Pressure Calculations

This problem focuses on a horizontal pipe network with specified parameters, including flow rates, pipe diameters, and pressure conditions. The task involves determining the flow rates and directions for all pipes as well as the pressures at specified points (B, C, and D) in the network. Using nodal and loop equations, the flow rates are calculated. Additionally, head loss is evaluated as a function of flow rate to understand its impact on system performance. The discussion highlights important assumptions regarding fluid properties, drawing parallels to biomedical applications such as blood flow in the human body.

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Analysis of Fluid Flow in a Horizontal Pipe Network: Flow Rates and Pressure Calculations

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  1. Problem 6.127Network Flow Scott Jewett BIEN 301 January 30, 2007

  2. Problem Diagram Horizontal Pipe Network 2 ft3/s D=8 in f = .025 PA= 120 psi T= 20°C D C 3000 ft D=6 in D=3 in D=9 in A B 2 ft3/s D=8 in 4000 ft

  3. Required • Determine the flow rate and direction in all the pipes • Determine the pressures at points B, C, and D.

  4. Assumptions • Liquid • Incompressible • Steady • Viscous

  5. Assumptions (cont.) • Flow directions • Loop directions Qcd C D L2 Qbc Qbd Qac L1 A B Qab

  6. Nodal Equations • Solve nodal equations Flow out - Flow in = 0 2ft3/s Qcd Node A: C D L2 Node C: Qbc Qbd Qac L1 Node B: A B 2ft3/s Qab

  7. Head loss • Use equation 6.10 to obtain head loss as a function of flow rate for each pipe

  8. Obtain five equations relating flow rate to head loss

  9. Loop Equations • Set up loop equations: Sum of head losses around loop = 0 Loop 1: Loop 2: Qcd C D If the flow is opposite the loop, then the head loss is negative. L2 Qcb Qbd Qac L1 A B Qab

  10. System of equations • Five equations, Five unknowns

  11. Solution • Solve using Mathcad or similar tool Qab = 1.187 ft3/s Qac = .813 ft3/s Qcb = .99 ft3/s Qcd = 1.803 ft3/s Qbd = .197 ft3/s

  12. Pressure Solution • Equation 6.8 relates pressure to head loss hf= (Pa-Pb)/(ρg)

  13. Pressure solution • Pb = Pa- ρghf(ab) Pb = 120 psi - ρg(19.116*(Qab)2) Pb = 108 psi • Pc = Pb - ρghf(cb) Pc = 102 psi • Pd = Pc - ρghf(cd) Pd = 74 psi

  14. Biomedical Application • Blood flow • Your body consists of blood vessels with varying: • Diameter • Friction • Height • All of these affect flow rate and pressure.

  15. Questions?

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