AP Physics 1 - Unit 8: Fluids Review

Introduction

• States of Matter: Solid, liquid, and gas
  • Solid: Fixed shape and volume
  • Liquid: Fixed volume, no fixed shape
  • Gas: No fixed shape or volume
• Fluid Definition: Substance without fixed shape (includes liquids and gases)

Density

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

Pressure

• Definition: Pressure = Force (perpendicular) / Area
  • Scalar quantity (magnitude, no direction)
  • Units: Pascals (1 Pascal = 1 Newton/m²)
• Absolute Pressure in Fluids: Sum of surface pressure (P₀) and gauge pressure (ρgh)
  • Gauge pressure: Caused by fluid above a point, does not depend on cross-sectional area

Buoyant Force

• Definition: Upward force equal to the weight of the fluid displaced by an object
• Equation: Buoyant Force = ρ (density of fluid) × V (volume of fluid displaced) × g (gravitational field strength)
• Conditions:
  • If object density < fluid density: object accelerates upward when released
  • Floating object: Volume of fluid displaced < volume of object
  • Submerged object: Volume of fluid displaced = volume of object

Ideal Fluid Flow

• Conditions:
  • Nonviscous: No internal friction
  • Incompressible: Constant density
  • Steady (Laminar) Flow: Regular, consistent
  • Irrotational: Zero net angular velocity
• Volumetric Flow Rate: Cross-sectional area × Speed
  • Continuity Equation: A₁v₁ = A₂v₂ (Volumetric flow rate constant)

Bernoulli’s Equation and Principle

• Equation:
  • P₁ + 0.5ρv₁² + ρgh₁ = P₂ + 0.5ρv₂² + ρgh₂
  • Describes constant mechanical energy in ideal fluid flow
• Bernoulli’s Principle: Increase in fluid speed leads to a decrease in fluid pressure (assuming negligible height difference)

Torricelli’s Theorem

• Application: Speed of fluid exiting a large reservoir through a small hole
• Formula: Speed = √(2gh)

Conclusion

• Practical Applications: Understanding fluid dynamics principles is crucial for solving physics problems related to fluids.

Note: Ensure familiarity with deriving equations and applying principles to various scenarios in fluid mechanics.