AP Physics 1 - Unit 8: Fluids Review

States or Phases of Matter

• Three common states of matter:
  • Solid: Fixed shape and volume.
  • Liquid: Does not have a fixed shape, but has a fixed volume.
  • Gas: No fixed shape or volume.
• Fluids: Substances without a fixed shape, including liquids and gases.

Density

• Formula: Density (ρ) = Mass / Volume
• Symbol: Lowercase Greek letter rho (ρ)

Pressure

• Formula: Pressure = Force perpendicular / Area of surface
• Scalar: Has magnitude but no direction.
• Units: Pascals (Pa), where 1 Pa = 1 N/m².
• Absolute Pressure:
  • Formula: Absolute Pressure = P₀ + ρgh
  • Components:
    • P₀: Pressure at the top of the fluid
    • ρgh: Gauge pressure
    • ρ: Density of the fluid
    • g: Gravitational field strength
    • h: Depth of the fluid
• Importance: Gauge pressure doesn't depend on the cross-sectional area.

Understanding Pressure with Objects

• Pressure caused by an object's weight on a surface varies with contact area.
• Gauge pressure differs from pressure applied by solid objects on surfaces.

Buoyant Force

• Definition: Upward force by a fluid on an object.
• Formula: Buoyant Force = Density of fluid displaced × Volume displaced × Gravitational field strength
• Buoyant force equals the weight of the fluid displaced by the object.

Conditions for Ideal Fluid Flow

• Nonviscous: No internal friction, flows freely.
• Incompressible: Constant density.
• Steady flow (Laminar): Flow is regular and consistent.
• Irrotational: Zero net angular velocity.

Fluid Flow Mechanics

• Volumetric Flow Rate: Cross-sectional area × Speed
• Continuity Equation: A₁v₁ = A₂v₂ (Volumetric flow rate is constant)

Bernoulli’s Equation

• Describes mechanical energy conservation in fluid flow.
• Formula:
  • P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
  • P: Pressure, ρ: Density, v: Speed, g: Gravitational field strength, h: Height
• Bernoulli’s Principle: Higher speed leads to lower pressure if height difference is negligible.

Torricelli’s Theorem

• Gives speed of fluid exiting a reservoir through a small hole.
• Formula: v = √(2gh)
• Derived from Bernoulli’s equation.

Key Takeaways

• Understand derivations and application of formulas.
• Differentiate between concepts like gauge and object pressure.
• Recognize ideal fluid flow conditions and their implications.