C14 - Fluid Mechanics

Pressure by depth

P = P₀ + ρ_fgh

F_buoyant

F_buoyant = ρgAh = ρgV

Archimedes’ principle

F_buoy = weight of displaced water

Surfaced floating object

Pascal’s Law

P₁ = P₂

• F₂ = (A₂/A₁)F₁

• F₁∆x₁ = F₂∆x₂

Flow

• Laminar: fluid follows orderly, smooth paths

• Turbulent: fluid paths are chaotic and cross over one another

  • Laminar becomes turbulent @ critical speeds

Ideal fluid flow rules

• ∑E_int = 0 (non-viscous)

• ∆v = 0 @ one point (steady flow)

• ρ = constant (incompressible)

• ω & L = 0 (irrotational)

Continuity for fluids

A₁v₁ = A₂v₂ = constant

Bernoulli’s equation