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