Elasticity:

$\sigma = \frac{F}{A} \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

$Y = \frac{F L}{A \Delta L} \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

$B = -V\frac{dP}{dV} \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

$G = \frac{\text{shear stress}}{\text{shear strain}} \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

Fluid Statics:

$P = P_0 + \rho g h \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

$\frac{F_1}{A_1} = \frac{F_2}{A_2} \quad \text{(Pascal's law, dimensionless ratio)}$

Fluid Dynamics:

$A_1 v_1 = A_2 v_2 \quad [L^3 T^{-1}] \text{ (m}^3/\text{s)}$

$P + \tfrac{1}{2}\rho v^2 + \rho g h = \text{constant} \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

Viscosity:

$F = \eta A \frac{dv}{dx} \quad \eta: [M^1 L^{-1} T^{-1}] \text{ (Pa·s)}$

$F_{\text{Stokes}} = 6\pi\eta r v \quad [M^1 L^1 T^{-2}] \text{ (N)}$

$v_t = \frac{2r^2(\rho - \sigma)g}{9\eta} \quad [M^0 L^1 T^{-1}] \text{ (m/s)}$

Surface Tension:

$S = \frac{F}{L} = \frac{\text{Energy}}{\text{Area}} \quad [M^1 L^0 T^{-2}] \text{ (N/m)}$

$\Delta P_{\text{drop}} = \frac{2S}{R}; \quad \Delta P_{\text{bubble}} = \frac{4S}{R} \quad [M^1 L^{-1} T^{-2}] \text{ (Pa)}$

$h = \frac{2S\cos\theta}{\rho g r} \quad [M^0 L^1 T^0] \text{ (m)}$

Heat Transfer:

$\frac{Q}{t} = \frac{KA\Delta T}{L} \quad K: [M^1 L^1 T^{-3} K^{-1}] \text{ (W m}^{-1}\text{ K}^{-1})$

$\frac{dT}{dt} = -k(T - T_0) \quad k: [T^{-1}] \text{ (s}^{-1})$

$P = \sigma A T^4 \quad \sigma = 5.67 \times 10^{-8} \text{ W m}^{-2} \text{K}^{-4}, \quad [M^1 L^0 T^{-3} K^{-4}]$

$\beta_{\text{volume}} = 3\alpha_{\text{linear}}; \quad \beta_{\text{area}} = 2\alpha_{\text{linear}}$