Definitions

• Fluid: A substance that flows and takes the shape of its container (liquids and gases)
• Density (ρ): Mass per unit volume
  • ρ = m/V
• Pressure (P): Force per unit area
  • P = F/A
  • Pressure in a fluid at depth h: P = P₀ + ρgh

Archimedes' Principle and Buoyancy

An object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces:

• Fbuoyant = ρfluid × Vdisplaced × g

An object floats if its average density is less than the fluid's density.

Fluid Dynamics

Continuity Equation: For incompressible fluids in steady flow:

• A₁v₁ = A₂v₂

where A is cross-sectional area and v is flow velocity (volume flow rate is constant).

Bernoulli's Equation

For an ideal fluid (incompressible, non-viscous, steady flow), total energy per unit volume is constant:

• P + ½ρv² + ρgh = constant

This explains why faster-moving fluids have lower pressure (e.g., airplane wings).

Viscosity and Turbulence

• Viscosity: Internal friction in a fluid that resists flow. High viscosity fluids (honey) flow slowly; low viscosity fluids (water) flow easily.
• Laminar Flow: Smooth, orderly flow in parallel layers
• Turbulent Flow: Chaotic, irregular flow with eddies and vortices, typically occurring at high velocities