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Introduction to Fluid Mechanics

This chapter explores internal, incompressible viscous flow focusing on entrance regions, laminar and turbulent flow between parallel plates and in pipes. Topics include energy considerations, head loss calculation, flow measurement methods, friction factors, and resolving pipe flow problems. The chapter delves into fully developed laminar flow characteristics, velocity profiles, shear stress distribution, volume flow rates, pressure drops, and flow rates in both stationary and moving plate scenarios. Additionally, it covers energy equations, head loss calculations, friction factor computations, and various examples and solutions for pipe flow challenges.

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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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