Ideal Fluids

Equation of continuity:  A₁v₁ = A₂v₂
Bernoulli's equation:  P₁ + ρgh₁ + ½ρv₁² = P₂ + ρgh₂ + ½ρv₂²
Surface tension, Laplace's law for a spherical membrane:  P_i - P_o = 2γ/r.
Capillary action:  h = 2γcosθ/(ρgr). 

Viscous fluids

Poiseuille's law: Q = π∆Pr⁴/(8ηL)
Stokes' law: F = 6πηrv
Reynolds number:  R = ρDv/η

Temperature and Heat

Ideal gas:  PV = (2/3)N(m<v²>/2) = (2/3)U,  PV = Nk_BT = nRT
k_B = 1.381*10^-23 J/K,  R = 8.31 J/(mol K)
Linear expansion:  ΔL = αLΔT
Thermal conductivity:  ΔQ/Δt = -kA ΔT/Δx
Stefan-Boltzmann Law:  Radiated power = emissivity * σ * T⁴ * Area
Wien Law:  λ_max(nm) = 3*10⁶/T(K)
Specific heat:  c = ΔQ/(m ΔT) 
Latent heat:  ΔQ = mL

Thermodynamics:

First law:  ΔU = ΔQ - ΔW
Second law:  Q_high/T_high = Q_low/T_low
Entropy:  S = k_B lnΩ,  ΔS = ΔQ/T

Oscillations and Waves:

Harmonic motion:
F = -kx.
x(t) = Acos(ωt + φ),  v(t) = -ωAsin(ωt + φ),   a(t) = -ω²Acos(ωt + φ) = -ω²x.
ω = sqrt(k/m) = 2πf =  2π/T.

Pendulum:  T = 2π(L/g)^1/2

Traveling waves:  y(x,t) = A sin(kx ± ωt + φ)
Waves on a string:  v = (F/μ)^1/2
Sound level:  β = 10 log₁₀(I/I₀)
Beat frequency:  |f₁ - f₂|

Standing sound waves:
tube of length L with two open ends:  L = nλ/2, n = 1, 2, 3, ...
tube of length L with one open end and one closed:  L = nλ/4, n = odd integer

Doppler effect:
f = f₀(v - v_obs)/(v - v_s)  (velocity components in the direction of v are positive)

Conversion:  

1 Cal = 1 kcal = 4186 J