Properties of Solids and Liquids: One-Page Formula Sheet

Properties of Solids and Liquids — formula sheet

Formulas

• Bernoulli: P + ½ρv² + ρgh = constant
• Stokes' law F = 6πηrv; terminal velocity v = 2r²(ρ−σ)g / 9η
• Capillary rise h = 2T cosθ / ρgr
• Heat conduction: dQ/dt = kAΔT / L

Key ideas

• Stress = F/A, strain = ΔL/L, Young's modulus Y = stress/strain
• Pressure at depth h: P₀ + ρgh
• Continuity: A₁v₁ = A₂v₂
• Excess pressure in a drop: 2T/r; in a soap bubble: 4T/r

Traps to avoid

• Using 2T/r for a soap bubble (two surfaces, so 4T/r)
• Forgetting buoyancy in terminal velocity
• Mixing linear and volume expansion coefficients (γ = 3α)

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