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Introduction to Fluid Mechanics

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  1. Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion

  2. Main Topics • Conservation of Mass • Stream Function for Two-Dimensional Incompressible Flow • Motion of a Fluid Particle (Kinematics) • Momentum Equation

  3. Conservation of Mass • Basic Law for a System

  4. Conservation of Mass • Rectangular Coordinate System

  5. Conservation of Mass • Rectangular Coordinate System

  6. Conservation of Mass • Rectangular Coordinate System “Continuity Equation”

  7. Conservation of Mass • Rectangular Coordinate System “Del” Operator

  8. Conservation of Mass • Rectangular Coordinate System

  9. Conservation of Mass • Rectangular Coordinate System Incompressible Fluid: Steady Flow:

  10. Conservation of Mass • Cylindrical Coordinate System

  11. Conservation of Mass • Cylindrical Coordinate System

  12. Conservation of Mass • Cylindrical Coordinate System “Del” Operator

  13. Conservation of Mass • Cylindrical Coordinate System

  14. Conservation of Mass • Cylindrical Coordinate System Incompressible Fluid: Steady Flow:

  15. Stream Function forTwo-DimensionalIncompressible Flow • Two-Dimensional Flow • Stream Function y

  16. Stream Function forTwo-DimensionalIncompressible Flow • Cylindrical Coordinates • Stream Function y(r,q)

  17. Motion of a Fluid Particle (Kinematics) • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field • Fluid Rotation • Fluid Deformation • Angular Deformation • Linear Deformation

  18. Motion of a Fluid Particle (Kinematics)

  19. Motion of a Fluid Particle (Kinematics) • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field

  20. Motion of a Fluid Particle (Kinematics) • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field

  21. Motion of a Fluid Particle (Kinematics) • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field

  22. Motion of a Fluid Particle (Kinematics) • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field (Cylindrical)

  23. Motion of a Fluid Particle (Kinematics) • Fluid Rotation

  24. Motion of a Fluid Particle (Kinematics) • Fluid Rotation

  25. Motion of a Fluid Particle (Kinematics) • Fluid Rotation

  26. Motion of a Fluid Particle (Kinematics) • Fluid Deformation: • Angular Deformation

  27. Motion of a Fluid Particle (Kinematics) • Fluid Deformation: • Angular Deformation

  28. Motion of a Fluid Particle (Kinematics) • Fluid Deformation: • Linear Deformation

  29. Momentum Equation • Newton’s Second Law

  30. Momentum Equation • Forces Acting on a Fluid Particle

  31. Momentum Equation • Forces Acting on a Fluid Particle

  32. Momentum Equation • Differential Momentum Equation

  33. Momentum Equation • Newtonian Fluid: Navier-Stokes Equations

  34. Momentum Equation • Special Case: Euler’s Equation

  35. Computational Fluid Dynamics • Some Applications

  36. Computational Fluid Dynamics • Discretization