Fluids

Whether something is a solid, liquid or gas depends on how strongly its atoms and molecules attract each other. Liquids and gases are fluids: they flow and take the shape of their container. You describe a fluid by its density, ρ = m/V (in kg/m³), and in AP Physics 1 you treat fluids as ideal: incompressible (the density never changes) and with no viscosity (no internal friction).

Pressure is the perpendicular force per unit area, P = F/A, measured in pascals (Pa), and it's a scalar. In a fluid, the absolute pressure at depth h is P = P₀ + ρgh, where P₀ is the pressure at the surface (often atmospheric pressure) and ρgh is the gauge pressure from the fluid above.

A fluid speeds up, slows down or turns only when the forces on it are unbalanced, just as Newton's laws predict. Because pressure grows with depth, the fluid pushes up on the bottom of a submerged object harder than it pushes down on its top. The difference is the upward buoyant force, which equals the weight of the fluid the object pushes aside: F_b = ρVg (Archimedes' principle), where ρ is the fluid's density and V is the submerged volume.

A difference in pressure is what makes a fluid flow. Because an ideal fluid can't be compressed, whatever flows into a full pipe each second must flow out, so A₁v₁ = A₂v₂ (the continuity equation): narrower sections mean faster flow. Bernoulli's equation, P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂², is conservation of energy for a flowing fluid; it gives Torricelli's theorem, v = √(2gh), for fluid leaving a hole a depth h below the surface of a large open tank.