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Introduction to Fluid Mechanics
Chapter 8
Internal Incompressible
Viscous Flow
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Main Topics
Entrance Region
Fully Developed Laminar FlowBetween Infinite Parallel Plates
Fully Developed Laminar Flow in a PipeTurbulent Velocity Profiles in
Fully Developed Pipe Flow
Energy Considerations in Pipe Flow
Calculation of Head Loss
Solution of Pipe Flow Problems
Flow Measurement
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Entrance Region
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Fully Developed Laminar Flow
Between Infinite Parallel PlatesBoth Plates Stationary
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Fully Developed Laminar Flow
Between Infinite Parallel PlatesBoth Plates Stationary
Transformation of Coordinates
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Fully Developed Laminar Flow
Between Infinite Parallel PlatesBoth Plates Stationary
Shear Stress Distribution
Volume Flow Rate
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Fully Developed Laminar Flow
Between Infinite Parallel PlatesBoth Plates Stationary
Flow Rate as a Function of Pressure Drop
Average and Maximum Velocities
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Fully Developed Laminar Flow
Between Infinite Parallel PlatesUpper Plate Moving with Constant Speed, U
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Fully Developed Laminar Flow
in a PipeVelocity Distribution
Shear Stress Distribution
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Fully Developed Laminar Flow
in a PipeVolume Flow Rate
Flow Rate as a Function of Pressure Drop
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Fully Developed Laminar Flow
in a PipeAverage Velocity
Maximum Velocity
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Turbulent Velocity Profiles in
Fully Developed Pipe Flow
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Turbulent Velocity Profiles in
Fully Developed Pipe Flow
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Energy Considerations in
Pipe FlowEnergy Equation
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Energy Considerations in
Pipe FlowHead Loss
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Calculation of Head Loss
Major Losses: Friction Factor
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Calculation of Head Loss
Laminar Friction Factor
Turbulent Friction Factor
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Calculation of Head Loss
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Calculation of Head Loss
Minor Losses Examples: Inlets and Exits; Enlargements and
Contractions; Pipe Bends; Valves and Fittings
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Calculation of Head Loss
Minor Loss: Loss Coefficient, K
Minor Loss: Equivalent Length, Le
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Calculation of Head Loss
Pumps, Fans, and Blowers
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Calculation of Head Loss
Noncircular Ducts
Example: Rectangular Duct
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Solution of Pipe Flow Problems
Energy Equation
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Solution of Pipe Flow Problems
Major Losses
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Solution of Pipe Flow Problems
Minor Losses
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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 QUse energy equation directly
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Solution of Pipe Flow Problems
Single Path (Continued) Find Q for a given Dp, L, and D
1. Manually iterate energy equation and friction factorformula to find V (orQ), or
2. Directly solve, simultaneously, energy equation andfriction factor formula using (for example) Excel
Find D for a given Dp, L, and Q1. Manually iterate energy equation and friction factorformula to find D, or
2. Directly solve, simultaneously, energy equation andfriction factor formula using (for example) Excel
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Solution of Pipe Flow Problems
Multiple-Path Systems
Example:
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Solution of Pipe Flow Problems
Multiple-Path Systems Solve each branch as for single path
Two additional rules1. The net flow out of any node (junction) is zero
2. Each node has a unique pressure head (HGL)
To complete solution of problem1. Manually iterate energy equation and friction factor
for each branch to satisfy all constraints, or
2. Directly solve, simultaneously, complete set ofequations using (for example) Excel
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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
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Flow Measurement
Linear Flow Meters Examples: Float Meter (Rotameter); Turbine;
Vortex; Electromagnetic; Magnetic; Ultrasonic
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Flow Measurement
Traversing Methods Examples: Pitot (or Pitot Static) Tube; Laser
Doppler Anemometer
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