## Units | Name | Symbol | Equation | SI Units | Dimension | | ---------------------------------------------- | -------------- | ------------------------------------------------------- | --------------------------------- | --------------------------------------- | | Velocity | $v$ | $v =\dot{x}$ | ${} \mathrm{m / s} {}$ | ${} L / T {}$ | | Acceleration | $g$ | ${} a = \dot{v} {}$ | ${} \mathrm{m / s^{2}} {}$ | ${} \mathrm{L / T^{2}} {}$ | | Force | $F$ | ${} F = ma {}$ | ${} \mathrm{N} {}$ | ${} \mathrm{ML / T^{2}} {}$ | | Energy / Work | $W$ | ${} W = \int Fdx {}$ | ${} \mathrm{J} {}$ | $\mathrm{ML^{2} / T^{2}}$ | | Power | $P$ | ${} P = \dot{W} {}$ | ${} \mathrm{W} {}$ | ${} \mathrm{ML^{2} / T^{3}} {}$ | | Density | ${} \rho {}$ | ${} \rho = m /V {}$ | ${} \text{kg} / \text{m}^{3} {}$ | ${} \mathrm{M / L^{3}} {}$ | | Viscosity | $\mu$ | ${} \tau_{x}=\mu \frac{ \partial u }{ \partial x } {}$ | ${} \mathrm{Pa \cdot s} {}$ | ${} \mathrm{\frac{M}{LT}} {}$ | | Kinematic Viscosity / <br>Momentum diffusivity | $\nu$ | ${} \nu = \mu / \rho {}$ | ${} \mathrm{m^{2} / s} {}$ | $\mathrm{L^{2} / T}$ | | Thermal Diffusivity | ${} \alpha {}$ | ${} \alpha = k / \rho {}$ | ${} \mathrm{m^{2} / s} {}$ | $\mathrm{L^{2} / T}$ | | Heat Transfer Coefficient | $h$ | ${} R = \frac{1}{hA} {}$ | ${} \mathrm{\frac{W}{m^{2}K}} {}$ | ${} \mathrm{\frac{M}{T^{3}\theta}} {}$ | | Thermal Conductivity | $k$ | ${} R = \frac{L}{kA} {}$ | ${} \mathrm{\frac{W}{mK}} {}$ | ${} \mathrm{\frac{ML}{T^{3}\theta}} {}$ | | Specific Heat Capacity | $c$ | ${} \Delta U = mc\Delta T {}$ | ${} \mathrm{\frac{J}{kg~K}} {}$ | $\mathrm{\frac{L^{2}}{T^{2}\theta}}$ | ### Conversions Multiply imperial value by the conversion factor to get metric | Metric | | Conversion | Imperial | | ------ | --: | ---------: | -------- | | mm | = | 25.4 | in | | m/s | = | 0.45 | mph | | km | = | 1.61 | mi | | kg | = | 0.45 | lbm | | N | = | 4.5 | lbf | | GPa | = | 6.9 | ksi | | Nm | = | 0.11 | in-lb | | Nm | = | 1.4 | ft-lb | | °C | = | -32+0.56 | °F | | deg | = | 57.3 | rad |