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Introduction to Fluid Mechanics

Introduction to Fluid Mechanics. Chapter 8 Internal Incompressible Viscous Flow. Main Topics. Entrance Region Fully Developed Laminar Flow Between Infinite Parallel Plates Fully Developed Laminar Flow in a Pipe Turbulent Velocity Profiles in Fully Developed Pipe Flow

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Introduction to Fluid Mechanics

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  1. Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow

  2. Main Topics • Entrance Region • Fully Developed Laminar FlowBetween Infinite Parallel Plates • Fully Developed Laminar Flow in a Pipe • Turbulent Velocity Profiles inFully Developed Pipe Flow • Energy Considerations in Pipe Flow • Calculation of Head Loss • Solution of Pipe Flow Problems • Flow Measurement

  3. Entrance Region

  4. Fully Developed Laminar FlowBetween Infinite Parallel Plates • Both Plates Stationary

  5. Fully Developed Laminar FlowBetween Infinite Parallel Plates • Both Plates Stationary • Transformation of Coordinates

  6. Fully Developed Laminar FlowBetween Infinite Parallel Plates • Both Plates Stationary • Shear Stress Distribution • Volume Flow Rate

  7. Fully Developed Laminar FlowBetween Infinite Parallel Plates • Both Plates Stationary • Flow Rate as a Function of Pressure Drop • Average and Maximum Velocities

  8. Fully Developed Laminar FlowBetween Infinite Parallel Plates • Upper Plate Moving with Constant Speed, U

  9. Fully Developed Laminar Flowin a Pipe • Velocity Distribution • Shear Stress Distribution

  10. Fully Developed Laminar Flowin a Pipe • Volume Flow Rate • Flow Rate as a Function of Pressure Drop

  11. Fully Developed Laminar Flowin a Pipe • Average Velocity • Maximum Velocity

  12. Turbulent Velocity Profiles in Fully Developed Pipe Flow

  13. Turbulent Velocity Profiles in Fully Developed Pipe Flow

  14. Energy Considerations inPipe Flow • Energy Equation

  15. Energy Considerations inPipe Flow • Head Loss

  16. Calculation of Head Loss • Major Losses: Friction Factor

  17. Calculation of Head Loss • Laminar Friction Factor • Turbulent Friction Factor

  18. Calculation of Head Loss

  19. Calculation of Head Loss • Minor Losses • Examples: Inlets and Exits; Enlargements and Contractions; Pipe Bends; Valves and Fittings

  20. Calculation of Head Loss • Minor Loss: Loss Coefficient, K • Minor Loss: Equivalent Length, Le

  21. Calculation of Head Loss • Pumps, Fans, and Blowers

  22. Calculation of Head Loss • Noncircular Ducts Example: Rectangular Duct

  23. Solution of Pipe Flow Problems • Energy Equation

  24. Solution of Pipe Flow Problems • Major Losses

  25. Solution of Pipe Flow Problems • Minor Losses

  26. Solution of Pipe Flow Problems • Single Path • Find Dp for a given L, D, and Q • Use energy equation directly • Find L for a given Dp, D, and Q • Use energy equation directly

  27. Solution of Pipe Flow Problems • Single Path (Continued) • Find Q for a given Dp, L, and D • Manually iterate energy equation and friction factor formula to find V (or Q), or • Directly solve, simultaneously, energy equation and friction factor formula using (for example) Excel • Find D for a given Dp, L, and Q • Manually iterate energy equation and friction factor formula to find D, or • Directly solve, simultaneously, energy equation and friction factor formula using (for example) Excel

  28. Solution of Pipe Flow Problems • Multiple-Path Systems Example:

  29. Solution of Pipe Flow Problems • Multiple-Path Systems • Solve each branch as for single path • Two additional rules • The net flow out of any node (junction) is zero • Each node has a unique pressure head (HGL) • To complete solution of problem • Manually iterate energy equation and friction factor for each branch to satisfy all constraints, or • Directly solve, simultaneously, complete set of equations using (for example) Excel

  30. Flow Measurement • Direct Methods • Examples: Accumulation in a Container; Positive Displacement Flowmeter • Restriction Flow Meters for Internal Flows • Examples: Orifice Plate; Flow Nozzle; Venturi; Laminar Flow Element

  31. Flow Measurement • Linear Flow Meters • Examples: Float Meter (Rotameter); Turbine; Vortex; Electromagnetic; Magnetic; Ultrasonic

  32. Flow Measurement • Traversing Methods • Examples: Pitot (or Pitot Static) Tube; Laser Doppler Anemometer

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