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Problem 6.127 Network Flow

Problem 6.127 Network Flow. Scott Jewett BIEN 301 January 30, 2007. Problem Diagram. Horizontal Pipe Network. 2 ft 3 /s. D=8 in. f = .025 P A = 120 psi T= 20 °C. D. C. 3000 ft. D=6 in. D=3 in. D=9 in. A. B. 2 ft 3 /s. D=8 in. 4000 ft. Required.

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Problem 6.127 Network Flow

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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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