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CE 3372 water systems design

This lecture outlines head loss models in water systems design, including Hazen-Williams, Darcy-Weisbach, and Chezy-Manning. It covers frictional losses, pump curves, and minor (fitting) losses in pipeline systems. Examples and direct (Jain) equations are also discussed.

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CE 3372 water systems design

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  1. CE 3372 water systems design Lecture 8: head loss models

  2. outline • Head loss models • Hazen-Williams • Darcy-Weisbach • Chezy-Manning • Minor (Fitting) Losses

  3. Pipeline system 1 2 Head Loss Model Pump Curve

  4. Darcy-Weisbach loss model for pipe loss • Frictional loss proportional to • Length, Velocity^2 • Inversely proportional to • Cross sectional area • Loss coefficient (f) depends on • Reynolds number (fluid and flow properties) • Roughness height (pipe material properties)

  5. Moody Chart • Moody-Stanton chart is a tool to estimate the friction factor in the DW head loss model • Used for the pipe loss component of friction

  6. Examples • Three “classical” examples using Moody Chart • Head loss for given discharge, diameter, material • Discharge given head loss, diameter, material • Diameter given discharge, head loss, material

  7. Example 1 • Head loss for given discharge, diameter, material

  8. Example 1 • Head loss for given discharge, diameter, material

  9. Example 1 • Head loss for given discharge, diameter, material

  10. Example 1 • Head loss for given discharge, diameter, material

  11. Example 1 • Head loss for given discharge, diameter, material

  12. Example 2 • Discharge given head loss, diameter, material

  13. Example 2 • Discharge given head loss, diameter, material

  14. Example 3 • Diameter given discharge, head loss, material

  15. Example 3 • Diameter given discharge, head loss, material

  16. Direct (Jain) Equations • An alternative to the Moody chart are regression equations that allow direct computation of discharge, diameter, or friction factor.

  17. Jain equations • Build and Test the tool • Now need to testthe tool using known solutions:

  18. Jain equations • Link to On-Line Tool • A similar tool (to the spreadsheet just developed) is available online at: • http://theodores-pro.ttu.edu/mytoolbox-server/Hydraulics/QGivenHeadLoss/QGivenHeadLoss.html

  19. Hazen-Williams • Frictional loss proportional to • Length, Velocity^(1.8) • Inversely proportional to • Cross section area (as hydraulic radius) • Loss coefficient (Ch) depends on • Pipe material and finish • Turbulent flow only (Re>4000) • WATER ONLY!

  20. Hazen-Williams • HW Head Loss • Discharge Form

  21. Hazen-williams • Hazen-Williams C-factor

  22. Example using hazen-williams formula

  23. Hydraulic Radius • HW is often presented as a velocity equation using the hydraulic radius

  24. Hydraulic Radius • The hydraulic radius is the ratio of cross section flow area to wetted perimeter

  25. Hydraulic Radius • For circular pipe, full flow (no free surface) PERIMETER AREA D

  26. Chezy-Manning • Frictional loss proportional to • Length, Velocity^2 • Inversely proportional to • Cross section area (as hydraulic radius) • Loss coefficient depends on • Material, finish

  27. NEXT TIME • Fitting Losses • Darcy-Weisbach structure • Equivalent Lengths

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