Kuliah 4 Dan 5 Internal Incompressible Viscous Flow

8/18/2019 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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• Volume Flow Rate

Flow Rate as a Function of Pressure Drop

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• 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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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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• 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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Kuliah 4 Dan 5 Internal Incompressible Viscous Flow