Introduction to Fluid Mechanics

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