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Physics Unit 8: Fluids

Fluids are liquids and gases. Pressure grows with depth, buoyancy pushes objects up, and faster-moving fluid has lower pressure.

Covers: Density, pressure, pressure with depth, buoyancy and Archimedes' principle, continuity and Bernoulli's principle

Study guide

Fluids (liquids and gases) flow and take the shape of their containers. Density is mass per volume, ρ = m/V; water's density is 1.0 g/cm³ or 1,000 kg/m³. Density determines whether something floats.

Pressure is force per unit area, P = F/A, measured in pascals (1 Pa = 1 N/m²). The same force spread over a larger area produces less pressure, which is why snowshoes work and needles pierce. Atmospheric pressure at sea level is about 101,000 Pa.

Pressure in a fluid increases with depth: P = P₀ + ρgh, where the gauge pressure ρgh comes from the weight of the fluid above. It depends only on depth and density, not on the container's shape. Pascal's principle says pressure applied to an enclosed fluid is transmitted equally throughout it, which is how hydraulic lifts multiply force: F₁/A₁ = F₂/A₂.

Archimedes' principle says a fluid exerts an upward buoyant force equal to the weight of the fluid displaced: F_b = ρ_fluid·V_displaced·g. An object floats if it's less dense than the fluid, and then it sinks just enough to displace its own weight. A denser object sinks but still weighs less in the fluid.

For moving fluids, the continuity equation A₁v₁ = A₂v₂ says the flow rate is constant, so fluid speeds up where a pipe narrows (like putting your thumb over a hose). Bernoulli's principle says that where a fluid moves faster, its pressure is lower. It helps explain airplane lift, curving balls and the way a shower curtain is pulled inward.

Bernoulli's equation is P + ½ρv² + ρgh = constant along a streamline. It's conservation of energy per unit volume, so faster flow or greater height means lower pressure. Use it together with A₁v₁ = A₂v₂ to solve for unknown speeds or pressures. Water leaving a small hole at depth h below the open surface of a tank exits at v = √(2gh), the same speed as an object falling from height h. After leaving the tank, the stream follows projectile motion.

A floating object's submerged fraction equals its density divided by the fluid's density, so ice (0.92 g/cm³) floats about 92% underwater. Absolute pressure includes the atmosphere, P = P₀ + ρgh. Gauge pressure is only the part above atmospheric pressure, ρgh.

Key ideas

• Density ρ = m/V.
• Pressure P = F/A; in a fluid, P = P₀ + ρgh.
• Buoyant force equals the weight of fluid displaced (Archimedes).
• An object floats if its density is less than the fluid's.
• Continuity: A₁v₁ = A₂v₂, so fluid speeds up in narrow pipes; Bernoulli: faster fluid has lower pressure.

Formulas and rules

Common mistakes

• Using the object's density instead of the fluid's for buoyant force.
• Thinking pressure depends on the container's shape. It depends on depth.

Words to know

Density

Mass ÷ volume.

Pressure

Force ÷ area.

Archimedes' principle

Buoyant force = weight of fluid displaced.

Buoyancy

Upward fluid force; an object floats if it's less dense than the fluid.

Continuity equation

A₁v₁ = A₂v₂

Fluid

A substance that flows: a liquid or gas.

Pascal (Pa)

The unit of pressure: 1 N/m².

Atmospheric pressure

About 101,000 Pa at sea level.

Pressure with depth

P = P₀ + ρgh

Pascal's principle

Pressure on an enclosed fluid is transmitted equally throughout.

Hydraulic lift

F₁/A₁ = F₂/A₂ multiplies force.

Buoyant force

F_b = ρ_fluid·V_displaced·g

Bernoulli's principle

Faster-moving fluid has lower pressure.

Sample practice questions

19 more questions like these, from level 1 to 5, are in the practice set.