PEC EPE Mechanical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Euler's formula

For any real angle θ, e^(iθ) = cos θ + i sin θ, linking exponential and trigonometric functions and enabling phasor representation of sinusoids.

Laplace derivative transform

The Laplace transform of f'(t) is sF(s) − f(0), where F(s) is the transform of f(t); repeated differentiation introduces higher powers of s and initial derivatives.

Newton-Raphson method

Iteration x_(n+1) = x_n − f(x_n)/f'(x_n) finds a root of f(x); convergence is quadratic near a simple root when f'(x) is nonzero.

Rank consistency criterion

A linear system Ax = b is consistent only when rank(A) equals rank([A|b]); if both equal the number of unknowns, the solution is unique.

Axial deformation formula

For a prismatic bar of length L, cross-sectional area A, and modulus E under axial load P, elongation is δ = PL/(AE), assuming linear elastic behavior.

Euler buckling load

The critical load for a slender column is P_cr = π²EI/(KL)², where K depends on end conditions and EI is the minimum flexural rigidity.

Von Mises plane stress

For plane stress, the von Mises equivalent stress is σ_vm = √(σ_x² − σ_xσ_y + σ_y² + 3τ_xy²), used to predict yielding of ductile metals.

Soderberg fatigue criterion

The Soderberg line predicts fatigue failure by σ_a/S_e + σ_m/S_y = 1/n, where σ_a is alternating stress, σ_m mean stress, S_e endurance limit, and n safety factor.

Carnot efficiency

The maximum thermal efficiency of a heat engine operating between hot and cold reservoirs at absolute temperatures T_H and T_C is η = 1 − T_C/T_H.

Fourier conduction law

One-dimensional steady conduction heat flux is q″ = −k dT/dx; for a plane wall of thickness L, q = kA(T_1 − T_2)/L.

Stefan-Boltzmann law

Net radiation exchange between a small gray surface and large surroundings is q = εσA(T_s⁴ − T_sur⁴), with σ = 5.67 × 10⁻⁸ W/(m²·K⁴).

Heat pump COP

A heat pump's coefficient of performance is COP_HP = Q_H/W_in, where Q_H is heat delivered to the hot space and W_in is work input; it exceeds refrigerator COP by one for reversible cycles.

Bernoulli equation

Along a steady, incompressible, inviscid streamline, p/(ρg) + V²/(2g) + z is constant, where p is pressure, V velocity, z elevation, ρ density, and g gravity.

Reynolds number

Re = ρVD/μ = VD/ν compares inertia to viscous forces; pipe flow is generally laminar below about 2300 and turbulent above about 4000.

Darcy-Weisbach equation

Major head loss in a pipe is h_f = f(L/D)(V²/(2g)), where f is the Darcy friction factor, L length, D diameter, and V average velocity.

Pump affinity laws

For geometrically similar pumps at constant impeller diameter, flow varies with speed N, head with N², and shaft power with N³; these laws guide speed changes.

Chvorinov's rule

Solidification time of a casting is t = C(V/A)², where V is volume, A heat-transfer surface area, and C a mold constant; thicker sections freeze more slowly.

Taylor tool life

Tool life in machining follows VT^n = C, where V is cutting speed, T tool life, and n, C are empirical constants; higher speed shortens tool life.

Thermoplastic vs thermoset

Thermoplastics soften and remelt when heated because their polymer chains are not cross-linked; thermosets have covalent cross-links and degrade rather than flow on reheating.

Heat-affected zone

The heat-affected zone is the base metal adjacent to a weld that is not melted but whose microstructure and properties change because of welding thermal cycles.

Little's law

Little's law states WIP = throughput × flow time, where WIP is work in process, throughput is output rate, and flow time is average time in the system.

EOQ formula

The economic order quantity is EOQ = √(2DS/H), where D is annual demand, S ordering cost per order, and H annual holding cost per unit.

Cp and Cpk

Cp = (USL − LSL)/(6σ) measures potential capability; Cpk = min(USL − μ, μ − LSL)/(3σ) measures actual capability relative to the mean.

PERT expected time

PERT expected activity time is t_e = (a + 4m + b)/6, where a is optimistic, m most likely, and b pessimistic; variance is ((b − a)/6)².

Critical path

The critical path is the longest path through a project network; its activities have zero total float, and any delay on them delays the project finish.

Cost performance index

CPI = EV/AC, where EV is earned value and AC actual cost; CPI below 1 means the project is over budget for work performed.

Total float formula

Total float = LS − ES = LF − EF, where LS late start, ES early start, LF late finish, and EF early finish; it is schedule slack before project delay.

RACI accountability rule

In a RACI matrix, each task should have exactly one accountable person; responsible people do the work, consulted provide input, and informed receive updates.

Paramount ethics obligation

Professional engineering ethics generally places the paramount obligation on protecting public health, safety, and welfare above client, employer, or personal interests.

Competence boundary

Engineers should accept assignments only when qualified by education or experience; when entering a new area, they must disclose limitations and obtain appropriate supervision or training.

Conflict of interest

A conflict of interest exists when personal, financial, or other interests could improperly influence professional judgment; it must be disclosed and avoided or managed.

Whistleblowing condition

Whistleblowing is ethically justified when a serious danger to public safety exists, internal reporting has failed, and disclosure to an appropriate authority is necessary and proportionate.