Rucete ✏ AP Physics 2 In a Nutshell
6. Fluids
This chapter explores the properties of fluids at rest and in motion. Key topics include Pascal’s principle, fluid pressure at depth, buoyancy and Archimedes’ principle, laminar flow, and Bernoulli’s equation. It also covers applications such as hydraulic systems, barometers, and fluid flow through pipes.
Static Fluids
• Liquids are incompressible; gases are compressible.
• Fluids exert pressure due to their weight or motion.
• Pressure units: 1 pascal (Pa) = 1 N/m², 1 bar = 100,000 Pa.
• Atmospheric pressure is often expressed in millibars.
Pascal’s Principle
• External pressure applied to a confined fluid is transmitted equally in all directions.
• Hydraulic systems use this principle to amplify force:
F₂ = (A₂/A₁)·F₁
• Small force on small piston produces larger force on large piston proportionally to areas.
Static Pressure and Depth
• Pressure increases with depth:
P = P₀ + ρgh
• ρ = fluid density, g = gravitational acceleration, h = depth.
• Pressure depends only on depth, not container shape.
• In open containers, air pressure adds to the pressure from the liquid column.
Buoyancy and Archimedes’ Principle
• Buoyant force (FB) = weight of displaced fluid: FB = ρgVd
• An object floats if the buoyant force equals its weight.
• Specific gravity compares a substance’s density to that of water.
• Volume submerged = specific gravity × 100% (for floating objects).
Fluids in Motion
• Steady (laminar) flow: fluid moves smoothly in layers without mixing.
• Turbulent flow: chaotic, with mixing and eddies (occurs at high velocities).
• Ideal fluid assumptions: incompressible, non-viscous, steady flow, and no turbulence.
Continuity Equation
• For an incompressible fluid: A₁v₁ = A₂v₂
• Where A = cross-sectional area, v = speed of fluid.
• Fluids speed up in narrower regions and slow down in wider regions.
Bernoulli’s Equation
• Energy conservation for flowing fluids:
P + ½ρv² + ρgh = constant
• P = pressure energy, ½ρv² = kinetic energy per unit volume, ρgh = gravitational potential energy per unit volume.
• High velocity → low pressure; low velocity → high pressure.
• Explains lift on airplane wings (air moves faster over the top), atomizers, and curveballs.
Applications of Bernoulli’s Principle
• Airplane wings generate lift by creating a pressure difference.
• Carburetors and paint sprayers use low pressure to draw fluids upward.
• Blood flow through arteries follows principles of fluid continuity and pressure variations.
In a Nutshell
Fluids exert pressure based on depth and respond to applied forces according to Pascal’s principle. Moving fluids follow the continuity equation and Bernoulli’s principle, where conservation of energy governs changes in speed, pressure, and elevation. Mastery of these concepts explains everyday phenomena from hydraulic lifts to airplane flight and blood circulation.