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Engineering

Stress, fluids, circuits and structures

Stress

Basic
σ=FA\sigma = \frac{F}{A}

Internal force per unit area in a material.

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Strain

Basic
ε=ΔLL0\varepsilon = \frac{\Delta L}{L_0}

Relative deformation of a material.

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Young's Modulus

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

Stiffness of a material (stress over strain).

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Bernoulli's Equation

Advanced
P+12ρv2+ρgh=constP + \frac{1}{2}\rho v^2 + \rho g h = \text{const}

Conservation of energy in fluid flow.

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Reynolds Number

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

Predicts laminar vs turbulent flow.

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Electrical Power

Basic
P=VIP = VI

Power in an electrical circuit.

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Second Moment of Area (Rect.)

Advanced
I=bh312I = \frac{bh^3}{12}

Resistance of a rectangular section to bending.

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Bending Stress

Advanced
σ=MyI\sigma = \frac{My}{I}

Stress in a beam due to bending.

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Linear Thermal Expansion

Intermediate
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T

Change in length due to temperature change.

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Efficiency

Basic
η=PoutPin×100%\eta = \frac{P_{out}}{P_{in}} \times 100\%

Ratio of useful output to input power.

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Torque

Intermediate
τ=rFsinθ\tau = r F \sin\theta

Rotational force about a pivot.

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Resistors in Series

Basic
Req=R1+R2+R_{eq} = R_1 + R_2 + \cdots

Total resistance of resistors in series.

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Resistors in Parallel

Intermediate
1Req=1R1+1R2+\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots

Total resistance of resistors in parallel.

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Factor of Safety

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

Ratio of ultimate strength to allowable stress.

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Electrical Power (3-phase)

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

Real power in a balanced three-phase system.

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Power from Torque

Intermediate
P=τωP = \tau\omega

Mechanical power from torque and angular speed.

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Gear Ratio

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

Ratio of teeth (or speeds) between gears.

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Mechanical Advantage

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

Force amplification of a machine.

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Efficiency

Basic
η=PoutPin×100\eta = \frac{P_{out}}{P_{in}}\times 100

Ratio of useful output to input power.

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Conductive Heat Transfer

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

Heat conducted through a material.

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Strain Energy

Intermediate
U=12FδU = \frac{1}{2}F\delta

Energy stored in an elastically deformed body.

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Volumetric Flow Rate

Basic
Q=AvQ = Av

Volume of fluid passing per unit time.

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Continuity Equation

Intermediate
A1v1=A2v2A_1 v_1 = A_2 v_2

Conservation of mass in incompressible flow.

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Power Factor

Intermediate
PF=PSPF = \frac{P}{S}

Ratio of real power to apparent power.

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Transformer Ratio

Intermediate
VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}

Voltage ratio equals the turns ratio.

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Factor of Safety

Basic
FoS=failure loadworking loadFoS = \frac{\text{failure load}}{\text{working load}}

Ratio of failure capacity to actual load.

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RC Time Constant

Intermediate
τ=RC\tau = RC

Charging time constant of a resistor-capacitor circuit.

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Synchronous Speed

Advanced
ns=120fPn_s = \frac{120 f}{P}

Rotational speed of an AC motor field.

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