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Introduction to Fluid Mechanics

Introduction to Fluid Mechanics. Chapter 6 Incompressible Inviscid Flow. Main Topics. Momentum Equation for Frictionless Flow: Euler’s Equation Euler’s Equation in Streamline Coordinates Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow

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Introduction to Fluid Mechanics

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  1. Introduction to Fluid Mechanics Chapter 6 IncompressibleInviscid Flow

  2. Main Topics • Momentum Equation for Frictionless Flow: Euler’s Equation • Euler’s Equation in Streamline Coordinates • Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow • The Bernoulli Equation Interpreted as an Energy Equation • Energy Grade Line and Hydraulic Grade Line

  3. Momentum Equation for Frictionless Flow: Euler’s Equation • Euler’s Equation • Continuity

  4. Momentum Equation for Frictionless Flow: Euler’s Equation • Rectangular Coordinates

  5. Momentum Equation for Frictionless Flow: Euler’s Equation • Cylindrical Coordinates

  6. Euler’s Equation inStreamline Coordinates • Along a Streamline(Steady Flow, ignoring body forces) • Normal to the Streamline(Steady Flow, ignoring body forces)

  7. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow • Euler’s Equation in Streamline Coordinates (assuming Steady Flow)

  8. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow • Integration Along s Coordinate

  9. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow • Bernoulli Equation • Steady Flow • No Friction • Flow Along a Streamline • Incompressible Flow

  10. Stagnation Dynamic Static Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow • Static, Stagnation, and Dynamic Pressures(Ignore Gravity)

  11. The Bernoulli Equation Interpreted as an Energy Equation

  12. The Bernoulli Equation Interpreted as an Energy Equation • Basic Equation • No Shaft Work • No Shear Force Work • No Other Work • Steady Flow • Uniform Flow and Properties

  13. The Bernoulli Equation Interpreted as an Energy Equation Hence Assumption 6: Incompressible Assumption 7:

  14. The Bernoulli Equation Interpreted as an Energy Equation • “Energy Equation” • No Shaft Work • No Shear Force Work • No Other Work • Steady Flow • Uniform Flow and Properties • Incompressible Flow • u2 – u1 – dQ/dm = 0

  15. Energy Grade Line and Hydraulic Grade Line • Energy Equation

  16. Energy Grade Line and Hydraulic Grade Line • Energy Grade Line (EGL) • Hydraulic Grade Line (HGL)

  17. Energy Grade Line and Hydraulic Grade Line

  18. Irrotational Flow • Irrotationality Condition

  19. Irrotational Flow • Velocity Potential

  20. Irrotational Flow • Velocity Potential automatically satisfies Irrotationality Condition

  21. Irrotational Flow • 2D Incompressible, Irrotational Flow

  22. Irrotational Flow • Elementary Plane Flows

  23. Irrotational Flow • Superposition

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