Engineering

Stress, fluids, circuits and structures

The Engineering category brings together the key formulas behind stress, fluids, circuits, structures, and energy transfer. It’s designed to help students, exam candidates, and working engineers quickly find the relationships they need for calculations in mechanics, electrical systems, and materials. These formulas matter because they turn real-world design and problem-solving into clear, reliable answers.

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.

Synchronous Speed

n_s = \frac{120 f}{P}

Rotational speed of an AC motor field.