kuliah 4 dan 5 internal incompressible viscous flow
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INTERNAL INCOMPRESSIBLEINTERNAL INCOMPRESSIBLEVISCOUS FLOWVISCOUS FLOW
NazaruddinNazaruddin SinagaSinaga
Laboratorium Efisiensi dan Konservasi EnergiUniversitas Diponegoro
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Outline
2Flow Measurements
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Osborne Reynolds Experiment
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Laminar and Turbulent FlowLaminar and Turbulent Flow
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Entrance LengthEntrance Length
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Developing FlowDeveloping Flow
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Fully Developed Laminar FlowFully Developed Laminar Flowin a Pipein a Pipe
• Velocity Distribution
Shear Stress Distribution
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Fully Developed Laminar FlowFully Developed Laminar Flowin a Pipein a Pipe
• Volume Flow Rate
Flow Rate as a Function of Pressure Drop
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Fully Developed Laminar FlowFully Developed Laminar Flowin a Pipein a Pipe
• Average Velocity
Maximum Velocity
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Turbulent Velocity Profiles in FullyDeveloped Pipe Flow
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Head LossesHead Losses
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Head LossesHead Losses
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The momentum balance in the flow direction is thus given by
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Friction FactorFriction Factor
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Calculation of Minor Head LossCalculation of Minor Head Loss• Minor Losses
– Examples: Inlets and Exits; Enlargements and Contractions;Pipe Bends; Valves and Fittings
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C l l i f Mi H d LC l l i f Mi H d L
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Calculation of Minor Head LossCalculation of Minor Head Loss
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Solution of Pipe Flow ProblemsSolution of Pipe Flow Problems
• Single Path – Find p for a given L, D, and Q
Use energy equation directly
– Find L for a given p , D, and QUse energy equation directly
S l i f Pi Fl P blS l i f Pi Fl P bl
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Solution of Pipe Flow ProblemsSolution of Pipe Flow Problems
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Single Path (Continued) – Find Q for a given p , L, and D
1. Manually iterate energy equation and friction factorformula to find V (or Q ), or
2. Directly solve, simultaneously, energy equation andfriction factor formula using (for example) Excel
– Find D for a given p , L, and Q
1. Manually iterate energy equation and friction factorformula to find D, or2. Directly solve, simultaneously, energy equation and
friction factor formula using (for example) Excel
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Solution of Pipe Flow ProblemsSolution of Pipe Flow Problems•
Multiple-Path SystemsExample:
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Solution of Pipe Flow ProblemsSolution 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 zero2. Each node has a unique pressure head (HGL)
– To complete solution of problem
1. Manually iterate energy equation and friction factor for eachbranch to satisfy all constraints, or2. Directly solve, simultaneously, complete set of equations using
(for example) Excel
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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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The ndhe nd
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