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Electrical
Cable & Conductor Sizing
AC Voltage Drop
Single-phase AC voltage drop from the tabulated mV/A/m method.
DC / Circuit Fundamentals
Ohm's Law
Solve for voltage, current or resistance from the other two.
Series Resistance
Total resistance of resistors connected in series.
Parallel Resistance
Equivalent resistance of resistors connected in parallel.
Wheatstone Bridge
Unknown resistance from a balanced Wheatstone bridge's known arms.
Delta-Wye Transformation
Converts a delta (Δ) resistor network to its equivalent wye (Y) network.
Voltage Divider
Output voltage of a two-resistor series voltage divider.
Capacitance — Series
Equivalent capacitance of capacitors connected in series.
Capacitance — Parallel
Equivalent capacitance of capacitors connected in parallel.
Wire Resistance from Resistivity
DC resistance of a uniform conductor from its resistivity, length and cross-sectional area.
Power & Energy
Single-Phase AC Power
Real, reactive and apparent power from voltage, current and power factor.
Three-Phase AC Power
Balanced three-phase real/reactive/apparent power from line values.
Power Factor Correction
Required capacitor kVAr to correct a load's power factor to a target value.
Motor Full Load Current
Full load current from motor output power, voltage, power factor and efficiency.
Transformer Turns Ratio
Ideal-transformer turns ratio and primary/secondary current from voltage and power.
Synchronous Motor Speed
Synchronous speed of an AC motor or generator from supply frequency and pole count.
Battery Runtime
Elementary discharge-runtime estimate for a battery under a constant discharge current.
AC Basics
AC RMS / Peak / Average
Peak, RMS, average and form/crest factor of a sinusoidal AC waveform.
Capacitive Reactance
Capacitive reactance Xc from frequency and capacitance, or solve for either.
Inductive Reactance
Inductive reactance XL from frequency and inductance, or solve for either.
RLC Series Impedance
Total impedance and phase angle of a series R-L-C circuit.
LC Resonant Frequency
Resonant frequency of an LC circuit where XL = XC.
Capacitor Energy Stored
Energy stored in the electric field of a charged capacitor.
Inductor Energy Stored
Energy stored in the magnetic field of a current-carrying inductor.
Mechanical
Solid Mechanics Basics
Direct Stress & Strain
Stress, strain and elongation of an axially loaded member (Hooke's law).
Simply Supported Beam — Point Load
Support reactions and maximum bending moment for a single point load.
Simply Supported Beam — UDL
Support reactions and maximum bending moment for a full-span UDL.
Torsion of a Circular Shaft
Polar second moment of area and maximum shear stress for a solid round shaft.
Section Properties
Area, second moment of area and section modulus for rectangular or circular sections.
Factor of Safety
Factor of safety and design margin from failure and working stress.
Linear Thermal Expansion
Change in length of a member due to a temperature change.
Euler Buckling Load
Critical elastic buckling load of a slender column for four end conditions.
Principal Stresses (2D)
Principal stresses, maximum shear stress and principal angle for a 2D stress state.
Cantilever Beam Deflection
Maximum deflection at the free end of a cantilever beam under a point load.
Projectile Motion (Range, Height & Time)
Range, maximum height and time of flight of a same-height projectile launch.
Power Transmission
Helical Spring Rate
Spring rate of a helical compression/extension spring from wire and coil geometry.
Gear Ratio, Speed & Torque
Gear ratio and ideal output speed/torque of a two-gear mesh.
Belt / Pulley Speed Ratio
Driven pulley speed from driver/driven pulley diameters and driver speed.
Flywheel Kinetic Energy
Rotational kinetic energy of a flywheel from its moment of inertia and rotational speed.
Shaft Power, Torque & Speed
Rotating-shaft power from torque and speed, or torque from power and speed.
Fluids & Piping
Thin-Wall Pressure Vessel Stress
Hoop and longitudinal stress in a thin-walled cylindrical pressure vessel.
Hydrostatic Pressure
Gauge pressure at depth in a static fluid.
Reynolds Number
Reynolds number and flow regime (laminar/transitional/turbulent) for pipe flow.
Hydraulic Cylinder Force
Extend (and optional retract) force of a hydraulic cylinder from pressure and bore/rod diameter.
Civil / Structural
General / Conversions
Length & Mass Unit Conversion
Length (m/ft/in) and mass (kg/lb) conversion using NIST-exact factors.
Area — Rectangular & Circular
Area of a rectangle or a circle from its dimensions.
Surveying
Horizontal Curve Geometry
Tangent length, arc length, long chord, external distance and mid-ordinate of a simple circular curve.
Traverse Latitude & Departure
Latitude and departure of a traverse leg from bearing and distance, and the resulting coordinate.
Vertical Curve (Parabolic)
Elevation at a point on an equal-tangent parabolic vertical curve, and its high/low point.
Hydrology & Drainage
Rational Method Peak Runoff
Peak stormwater runoff from runoff coefficient, rainfall intensity and catchment area.
Manning's Equation — Open Channel Flow
Flow velocity and rate in an open channel from Manning's roughness, hydraulic radius and slope.
Darcy-Weisbach Head Loss
Pipe friction head loss from the Darcy-Weisbach equation.
Hazen-Williams Head Loss
Pipe friction head loss for water flow using the Hazen-Williams empirical formula.
Rectangular Weir Flow
Flow rate over a rectangular sharp-crested weir.
Orifice Discharge Flow
Discharge velocity and flow rate through a submerged orifice.
Materials & Quantities
Concrete Mix Volume
Cement, sand and aggregate volumes for a nominal concrete mix by the dry-volume method.
Earthwork Volume (Average End Area)
Cut/fill earthwork volume between two cross-sections by the average end area method.