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 Equations of Fluid Statics
Body Force

4. The Basic Equations of Fluid Statics
Surface Force

5. The Basic Equations of Fluid Statics
Surface Force

6. The Basic Equations of Fluid Statics
Surface Force

7. The Basic Equations of Fluid Statics
Total Force

8. The Basic Equations of Fluid Statics
Newton’s Second Law

9. The Basic Equations of Fluid Statics
Pressure-Height Relation

10. Pressure
pgage = pabsolute – patm

11. Pressure Variation in a Static 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 a Static 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.
Stable Equilibrium:
Unstable 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: