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Stress

\sigma = \frac{F}{A}

Internal force per unit area in a material.

Strain

\varepsilon = \frac{\Delta L}{L_0}

Relative deformation of a material.

Young's Modulus

E = \frac{\sigma}{\varepsilon}

Stiffness of a material (stress over strain).

Bernoulli's Equation

P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}

Conservation of energy in fluid flow.

Reynolds Number

Re = \frac{\rho v L}{\mu}

Predicts laminar vs turbulent flow.

Electrical Power

P = VI

Power in an electrical circuit.

Second Moment of Area (Rect.)

I = \frac{bh^3}{12}

Resistance of a rectangular section to bending.

Bending Stress

\sigma = \frac{My}{I}

Stress in a beam due to bending.

Linear Thermal Expansion

\Delta L = \alpha L_0 \Delta T

Change in length due to temperature change.

Efficiency

\eta = \frac{P_{out}}{P_{in}} \times 100\%

Ratio of useful output to input power.

Torque

\tau = r F \sin\theta

Rotational force about a pivot.

Resistors in Series

R_{eq} = R_1 + R_2 + \cdots

Total resistance of resistors in series.

Resistors in Parallel

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots

Total resistance of resistors in parallel.

Factor of Safety

FoS = \frac{\sigma_{ult}}{\sigma_{allow}}

Ratio of ultimate strength to allowable stress.

Electrical Power (3-phase)

P = \sqrt{3}\,V I \cos\phi

Real power in a balanced three-phase system.

Power from Torque

P = \tau\omega

Mechanical power from torque and angular speed.

Gear Ratio

GR = \frac{N_{out}}{N_{in}}

Ratio of teeth (or speeds) between gears.

Mechanical Advantage

MA = \frac{F_{out}}{F_{in}}

Force amplification of a machine.

Efficiency

\eta = \frac{P_{out}}{P_{in}}\times 100

Ratio of useful output to input power.

Conductive Heat Transfer

Q = \frac{kA\Delta T}{d}

Heat conducted through a material.

Strain Energy

U = \frac{1}{2}F\delta

Energy stored in an elastically deformed body.

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Continuity Equation

A_1 v_1 = A_2 v_2

Conservation of mass in incompressible flow.

Power Factor

PF = \frac{P}{S}

Ratio of real power to apparent power.

Transformer Ratio

\frac{V_p}{V_s} = \frac{N_p}{N_s}

Voltage ratio equals the turns ratio.

Factor of Safety

FoS = \frac{\text{failure load}}{\text{working load}}

Ratio of failure capacity to actual load.

RC Time Constant

\tau = RC

Charging time constant of a resistor-capacitor circuit.