AP Physics 1 Unit 8 Cheatsheet: Fluids

Density: ratio of mass to volume

ρ = m/V

• Units: kg/m³
• Constant for incompressible fluids

Ideal Fluid: incompressible (constant ρ and V) and frictionless (no viscosity)

Fluids vs. Solids: Fluids (liquids and gases) cannot sustain a static shear stress—any applied shear makes them flow and conform to their container's shape. Solids resist static shear, so they hold a fixed shape and only deform a finite amount under an applied shear. (The difference is about resistance to shear, not simply about whether the molecular bonding is 'strong' or 'weak'—liquid water, for example, has strong intermolecular forces.)

Mass Conservation: In incompressible flow, mass in = mass out at all cross-sections.

A₁v₁ = A₂v₂

• A = cross-sectional area
• v = flow speed
• Product Av = volume flow rate

Interpretation: Narrower pipe → faster flow; wider pipe → slower flow (same fluid, same mass rate).

Derived form: V/t = Av (volume per time)

Pressure Problems:

• Identify reference pressure (Patm, gauge, absolute)
• Use P = P₀ + ρgh for vertical columns
• Check units (Pa, atm, mmHg)

Buoyancy Problems:

• Draw free-body diagram (weight down, buoyancy up)
• Use Fb = ρVg (fluid density, displaced volume)
• Apply ΣF = ma for equilibrium or acceleration

Flow Problems:

• Continuity first (find unknown area or speed)
• Then Bernoulli (relate pressure, height, speed)
• Check energy conservation