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 Surface Force

The Basic Equations of Fluid Statics Surface Force

The Basic Equations of Fluid Statics Surface Force

The Basic Equations of Fluid Statics Total Force

The Basic Equations of Fluid Statics Newton’s Second Law

The Basic Equations of Fluid Statics Pressure-Height Relation

Pressure pgage = pabsolute – patm

Pressure Variation in a Static Fluid Incompressible Fluid: Manometers

Manometer

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

Pressure Gages

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

Standard Atmosphere

Standard Atmosphere

Hydrostatic Force on Submerged Surfaces Plane Submerged Surface

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

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

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

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

Hydrostatic Force on Submerged Surfaces Curved Submerged Surface

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)

Buoyancy

Buoyancy For example, for a hot air balloon

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.

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”

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