control equations

"Formula: Convection heat transfer rate (Q)"

"$Q = hA(T_2 - T_1)$"

"Formula: Gas Law (Pressure

Volume

"Formula: Linear thermal expansion (L2)"

"$L_2 = L_1 [1 + \alpha(T_2 - T_1)]$"

"Formula: Volumetric thermal expansion (V2)"

"$V_2 = V_1 [1 + \beta(T_2 - T_1)]$"

"Formula: Non-inverting op-amp gain"

"$V_{out} = (1 + \frac{R_2}{R_1})V_{in}$"

"Formula: Inverting op-amp gain"

"$V_{out} = -\frac{R_2}{R_1}V_{in}$"

"Formula: Voltage Follower output"

"$V_{out} = V_{in}$"

"Formula: Mathematical definition of Pressure"

"$\text{Pressure} = \frac{\text{force}}{\text{area}}$"

"Unit Conversion: 1 bar to kilopascals"

"$100 \text{ kPa}$"

"Unit Conversion: 1 Torr to mmHg"

"$1 \text{ mm Hg}$"

"Formula: Fluid pressure change with depth"

"$\Delta p = \gamma \Delta h$"

"Formula: Buoyancy force (B)"

"$B = \gamma \times \text{area} \times d$"

"Formula: Liquid level (d) from weight"

"$d = \frac{W_A - W_L}{\gamma \times \text{area}}$"

"Formula: Weight of material in container (W)"

"$W = \gamma V$"

"Formula: Kinematic Viscosity"

"Kinematic Viscosity = Dynamic Viscosity / Density"

"Unit: Dynamic Viscosity"

"poise or centipoise (10^-1 Pa s)"

"Unit: Kinematic Viscosity"

"stokes (10^-4 m^2/s) or centistokes"

"Formula: Flow Continuity Equation"

"Q = A1 * V1 = A2 * V2"

"Formula: Velocity from Head (Pitot/Venturi)"

"V = \sqrt{2 * g * \Delta h}"

"Formula: Reynolds Number (Laminar vs Turbulent)"

"R = (v * d * \rho) / \mu"

"Formula: RTD Resistance at Temperature T2"

"R_T2 = R_T1 * (1 + \alpha * [T2 - T1])"