Unit 8 · Fluids

Fluid ● (core concept) — A substance with no fixed shape — liquids and gases.

Density ● (core concept) — Mass per unit volume: ρ = m/V, used to characterize fluids.

Ideal fluid ● (core concept) — A model fluid that is incompressible — its density stays constant regardless of pressure — and has no viscosity.

Microscopic structure of matter ○ — The differences between solids, liquids, and gases come from the different interactions between their atoms and molecules.

Pressure ● (core concept) — The perpendicular force per unit area exerted on a surface: P = F_⊥/A. Pressure is a scalar.

Absolute and gauge pressure ● (core concept) — Absolute pressure is measured relative to vacuum: P_abs = P_0 + P_gauge. Gauge pressure is measured relative to a reference such as atmospheric pressure; for a fluid column, the gauge pressure is P_gauge = ρ·g·h.

Buoyant force ● (core concept) — The net upward force a fluid exerts on an immersed object, caused by the collective push of the fluid's particles. Its magnitude equals the weight of the fluid the object displaces.

Pressure-driven flow ● (core concept) — A pressure difference between two locations causes fluid to flow from the higher pressure to the lower pressure.

Volume flow rate ● (core concept) — The volume of fluid passing a point per unit time: Q = V/t = A·v. In a tube open at both ends, the inflow rate equals the outflow rate.

Continuity equation ● (core concept) — Conservation of mass for incompressible flow: A_1·v_1 = A_2·v_2 — fluid speeds up where the tube narrows and slows where it widens.

Bernoulli's equation ● (core concept) — Conservation of mechanical energy in fluid flow: P + ½·ρ·v² + ρ·g·h is constant along a streamline — faster flow or greater height means lower pressure.

Torricelli's theorem ● (core concept) — The speed of fluid exiting an opening follows from energy conservation: v = √(2·g·h), where h is the height difference between the opening and the fluid surface.