Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow © Fox, Mc. Donald & Pritchard
Main Topics ü Entrance Region ü Fully Developed Laminar Flow Between Infinite Parallel Plates ü Fully Developed Laminar Flow in a Pipe ü Turbulent Velocity Profiles in Fully Developed Pipe Flow ü Energy Considerations in Pipe Flow ü Calculation of Head Loss ü Solution of Pipe Flow Problems ü Flow Measurement © Fox, Mc. Donald & Pritchard
Entrance Region © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow Between Infinite Parallel Plates ü Both Plates Stationary © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow Between Infinite Parallel Plates ü Both Plates Stationary • Transformation of Coordinates © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow Between Infinite Parallel Plates ü Both Plates Stationary • Shear Stress Distribution • Volume Flow Rate © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow Between Infinite Parallel Plates ü Both Plates Stationary • Flow Rate as a Function of Pressure Drop • Average and Maximum Velocities © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow Between Infinite Parallel Plates ü Upper Plate Moving with Constant Speed, U © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow in a Pipe ü Velocity Distribution ü Shear Stress Distribution © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow in a Pipe ü Volume Flow Rate ü Flow Rate as a Function of Pressure Drop © Fox, Mc. Donald & Pritchard
Fully Developed Laminar Flow in a Pipe ü Average Velocity ü Maximum Velocity © Fox, Mc. Donald & Pritchard
Turbulent Velocity Profiles in Fully Developed Pipe Flow © Fox, Mc. Donald & Pritchard
Turbulent Velocity Profiles in Fully Developed Pipe Flow © Fox, Mc. Donald & Pritchard
Energy Considerations in Pipe Flow üEnergy Equation © Fox, Mc. Donald & Pritchard
Energy Considerations in Pipe Flow üHead Loss © Fox, Mc. Donald & Pritchard
Calculation of Head Loss üMajor Losses: Friction Factor © Fox, Mc. Donald & Pritchard
Calculation of Head Loss üLaminar Friction Factor üTurbulent Friction Factor © Fox, Mc. Donald & Pritchard
Calculation of Head Loss © Fox, Mc. Donald & Pritchard
Calculation of Head Loss ü Minor Losses • Examples: Inlets and Exits; Enlargements and Contractions; Pipe Bends; Valves and Fittings © Fox, Mc. Donald & Pritchard
Calculation of Head Loss ü Minor Loss: Loss Coefficient, K ü Minor Loss: Equivalent Length, Le © Fox, Mc. Donald & Pritchard
Calculation of Head Loss üPumps, Fans, and Blowers © Fox, Mc. Donald & Pritchard
Calculation of Head Loss üNoncircular Ducts Example: Rectangular Duct © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems üEnergy Equation © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems üMajor Losses © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems üMinor Losses © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems ü 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 © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems ü Single Path (Continued) • Find Q for a given Dp, L, and D 1. Manually iterate energy equation and friction factor formula to find V (or Q), or 2. Directly solve, simultaneously, energy equation and friction factor formula using (for example) Excel • Find D for a given Dp, L, and Q 1. Manually iterate energy equation and friction factor formula to find D, or 2. Directly solve, simultaneously, energy equation and friction factor formula using (for example) Excel © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems ü Multiple-Path Systems Example: © Fox, Mc. Donald & Pritchard
Solution of Pipe Flow Problems ü Multiple-Path Systems • Solve each branch as for single path • Two additional rules 1. The net flow out of any node (junction) is zero 2. Each node has a unique pressure head (HGL) • To complete solution of problem 1. Manually iterate energy equation and friction factor for each branch to satisfy all constraints, or 2. Directly solve, simultaneously, complete set of equations using (for example) Excel © Fox, Mc. Donald & Pritchard
Flow Measurement ü Direct Methods • Examples: Accumulation in a Container; Positive Displacement Flowmeter ü Restriction Flow Meters for Internal Flows • Examples: Orifice Plate; Flow Nozzle; Venturi; Laminar Flow Element © Fox, Mc. Donald & Pritchard
Flow Measurement ü Linear Flow Meters • Examples: Float Meter (Rotameter); Turbine; Vortex; Electromagnetic; Magnetic; Ultrasonic © Fox, Mc. Donald & Pritchard
Flow Measurement ü Traversing Methods • Examples: Pitot (or Pitot Static) Tube; Laser Doppler Anemometer © Fox, Mc. Donald & Pritchard
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