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Introduction to Fluid Mechanics

Introduction to Fluid Mechanics. Chapter 3 Fluid Statics. Main Topics. The Basic Equations of Fluid Statics Pressure Variation in a Static Fluid Hydrostatic Force on Submerged Surfaces Buoyancy. The Basic Equations of Fluid Statics. Body Force. The Basic Equations of Fluid Statics.

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Introduction to Fluid Mechanics

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  1. Introduction to Fluid Mechanics Chapter 3 Fluid Statics

  2. Main Topics • The Basic Equations of Fluid Statics • Pressure Variation in a Static Fluid • Hydrostatic Force on Submerged Surfaces • Buoyancy

  3. The Basic Equationsof Fluid Statics • Body Force

  4. The Basic Equationsof Fluid Statics • Surface Force

  5. The Basic Equationsof Fluid Statics • Surface Force

  6. The Basic Equationsof Fluid Statics • Surface Force

  7. The Basic Equationsof Fluid Statics • Total Force

  8. The Basic Equationsof Fluid Statics • Newton’s Second Law

  9. The Basic Equationsof Fluid Statics • Pressure-Height Relation

  10. Pressure pgage = pabsolute – patm

  11. Pressure Variation in aStatic Fluid • Incompressible Fluid: Manometers

  12. Manometer

  13. Example • SGoil = 0.8, SGHg = 13.6 • Assumption: Static fluid, incompressible.

  14. Pressure Gages

  15. Pressure Variation in aStatic Fluid • Compressible Fluid: Ideal Gas Need additional information, e.g., T(z) for atmosphere

  16. Standard Atmosphere

  17. Standard Atmosphere

  18. Hydrostatic Force on Submerged Surfaces • Plane Submerged Surface

  19. Hydrostatic Force on Submerged Surfaces • Plane Submerged Surface We can find FR, and y´ and x´, by integrating, or …

  20. Hydrostatic Force on Submerged Surfaces • Plane Submerged Surface • Algebraic Equations – Total Pressure Force

  21. Hydrostatic Force on Submerged Surfaces • Plane Submerged Surface • Algebraic Equations – Net Pressure Force

  22. Hydrostatic Force on a Plane Surface: Geometric Properties Centroid Coordinates Areas Moments of Inertia

  23. Hydrostatic Force on Submerged Surfaces • Curved Submerged Surface

  24. Hydrostatic Force on Submerged Surfaces • Curved Submerged Surface • Horizontal Force = Equivalent Vertical Plane Force • Vertical Force = Weight of Fluid Directly Above(+ Free Surface Pressure Force)

  25. Buoyancy

  26. Buoyancy For example, for a hot air balloon

  27. Buoyancy and Flotation: Archimedes’ Principle We can apply the same principles to floating objects: If the fluid acting on the upper surfaces has very small specific weight (air), the centroid is simply that of the displaced volume, and the buoyant force is as before. If the specific weight varies in the fluid the buoyant force does not pass through the centroid of the displaced volume, but through the center of gravity of the displaced volume.

  28. Stability: Submerged Object Stable Equilibrium: if when displaced returns to equilibrium position. Unstable Equilibrium: if when displaced it returns to a new equilibrium position. Unstable Equilibrium: Stable Equilibrium: C > CG, “Higher” C < CG, “Lower”

  29. Buoyancy and Stability: Floating Object Slightly more complicated as the location of the center buoyancy can change:

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