1001 Solved Engineering Fundamentals Problems Review

Essential engineering concepts, principles, formulas, and vocabulary terms spanning mathematics, economics, fluids, thermodynamics, materials science, mechanics, dynamics, circuits, and physics from the FE Fundamentals review text.

Even Symmetry

The mathematical characteristic of a function where $f(t) = f(-t)$, meaning the curve is mirrored across the vertical axis.

Resultant

A vector that represents the vector sum of two or more constituent vectors.

Helix

A three-dimensional curve generated by a point undergoing uniform circular motion about an axis while simultaneously translating at a constant speed parallel to that axis.

Sample Space

In probability theory, the mathematical set containing all possible outcomes of an experiment.

Event

A specific possible outcome or subset of outcomes of a trial or experiment.

Annuity

A series of uniform financial amounts or payments occurring at regular intervals over a specified period of time.

Acid Test Ratio

A financial liquidity metric defined as the ratio of current assets (exclusive of inventory) to total current liabilities.

Economic Order Quantity (EOQ)

The order quantity that minimizes total inventory costs per unit time, given by the formula $\text{EOQ} = \sqrt{\frac{2aK}{h}}$, where $a$ is constant depletion rate, $K$ is fixed cost per order, and $h$ is storage cost.

Fluid

A substance that deforms continuously under the application of a shear stress and cannot sustain a shear force at rest.

Streamline

A curve that is everywhere tangent to the instantaneous local velocity vector of a fluid, across which no fluid flow can occur, and which remains fixed in space for steady flow.

Reynolds Number

A dimensionless ratio of inertial forces to viscous forces in a fluid flow, mathematically given as $\text{Re} = \frac{\rho v D}{\mu}$.

Intensive Property

A physical or thermodynamic property of a system that does not depend on the amount of material present, such as temperature, pressure, or composition.

Enthalpy

A thermodynamic state property defined as the sum of internal energy and flow energy: $h = u + pv$.

Vapor Quality ($x$)

The fraction of the total mass in a saturated liquid-vapor mixture that exists as saturated vapor.

Triple Point

The specific state of temperature and pressure at which the solid, liquid, and vapor phases of a substance coexist in equilibrium.

Carnot Cycle

An idealized, completely reversible thermodynamic power cycle consisting of two isothermal processes and two isentropic processes.

Otto Cycle

An ideal four-stroke engine power cycle composed of adiabatic (isentropic) compression, constant-volume heat addition, adiabatic (isentropic) expansion, and constant-volume heat rejection.

Molality

A concentration measure in chemistry defined as the number of moles of solute per $1000\,g$ ($1\,kg$) of solvent.

Oxidation

A chemical reaction or process in which a substance loses electrons, increasing its formal oxidation state.

Isomers

Chemical compounds that share the exact same molecular formula but have different physical arrangements or structural connections of their atoms.

Valence Electrons

Electrons occupying the outermost quantum shell of an atom, which primarily govern chemical bonding and material properties.

Van der Waals Forces

Weak, secondary attractive bonds or forces acting between neutral atoms or molecules.

Atomic Packing Factor (APF)

The ratio of the volume occupied by hard-sphere atoms in a unit cell to the total volume of that unit cell.

Creep

The progressive, time-dependent plastic deformation of a material subjected to continuous mechanical stress below its normal yield strength, commonly occurring under high temperatures.

Strain Hardening

The phenomenon whereby a metal becomes harder and more resistant to further deformation as plastic slip increases, requiring higher applied stress to continue deformation.

Normal Strain

The ratio of elongation or change in length to the original unstrained length of a specimen: $\epsilon = \frac{\delta}{L}$.

Poisson's Ratio

The negative ratio of transverse (lateral) strain to axial (longitudinal) strain for a material under uniaxial stress: $\nu = -\frac{\epsilon_y}{\epsilon_x}$.

Dilatation ($e$)

The total volumetric unit change or unit volume expansion of a material element, defined as the sum of normal strains in three orthogonal directions: $e = \epsilon_x + \epsilon_y + \epsilon_z$.

Euler Buckling Load

The critical compressive axial force at which a slender pinned-end column becomes unstable and buckles: $P_{\text{cr}} = \frac{\pi^2 E I}{L^2}$.

Instantaneous Velocity

The time rate of change of displacement, expressed mathematically as $v = \lim_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$.

Coefficient of Restitution

A dimensionless ratio of relative impulse or velocities during the restitution phase to the deformation phase of an impact, possessing a value strictly between $0$ and $1$.

Tesla

The standard SI unit of magnetic flux density ($B$), equivalent to one weber per square meter ($\text{Wb/m}^2$).

Electrical Time Constant ($\tau$)

The characteristic response time of an RC circuit, mathematically equal to the product of resistance and capacitance: $\tau = RC$.

Root-Mean-Square (RMS) Current

The effective value of a time-varying alternating current, evaluated as $I_{\text{rms}} = \sqrt{\frac{1}{T} \int_0^T I^2(t)\,dt}$, delivering the same heating power to a resistor as an equivalent DC current.

Critical Angle

The minimum angle of incidence inside an optically denser medium at which light refracts at an angle of $90^\circ$ along the boundary, beyond which total internal reflection takes place.

Little's Formula

A fundamental theorem in queueing theory defining steady-state behavior as $L = \lambda W$, where $L$ is the expected number of units in the system, $\lambda$ is the mean arrival rate, and $W$ is the average waiting time per unit.