FE Other Disciplines flashcards

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

Ideal gas constant R

R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K) = 10.73 psia·ft³/(lbmol·R). Use absolute temperature in PV = nRT; substituting gauge pressure or Celsius temperature gives wrong results.

Steady-flow energy equation

Q̇ − Ẇ = ṁ[(h₂ − h₁) + (V₂² − V₁²)/2 + g(z₂ − z₁)]. For adiabatic turbines and nozzles, work or kinetic energy is obtained directly from the enthalpy change of the stream.

Bernoulli equation

P/γ + V²/(2g) + z = constant along a streamline for steady, incompressible, frictionless flow. Pressure falls where velocity rises, which explains lift and carburetor action.

Reynolds number

Re = ρVD/μ = VD/ν. Below about 2300 pipe flow is laminar, above about 4000 it is turbulent, and between the two the regime is transitional and unpredictable.

Darcy–Weisbach head loss

h_f = f(L/D)(V²/2g), where f is the Darcy friction factor from the Moody chart or Colebrook equation. In laminar flow f = 64/Re, independent of pipe roughness.

Continuity for incompressible flow

A₁V₁ = A₂V₂ for steady flow of a constant-density fluid. Reducing a pipe diameter by half quadruples the velocity and raises the dynamic pressure by a factor of sixteen.

Pump power requirement

Ẇ_pump = ρgQH/η, where Q is volumetric flow, H is total head added, and η is pump efficiency. Required driver power is larger than fluid power by 1/η.

Heat conduction through a wall

q = kAΔT/L for one-dimensional steady conduction, with k in W/(m·K). Thermal resistance is R = L/(kA), and series resistances add like electrical resistances.

Newton's law of cooling

q = hA(T_s − T_∞), where h is the convection coefficient in W/(m²·K). Convection resistance is 1/(hA) and dominates when h is small, as in air.

Stefan–Boltzmann radiation

q = εσAT⁴ with σ = 5.67×10⁻⁸ W/(m²·K⁴). Net exchange between a small body and large surroundings is q = εσA(T_s⁴ − T_sur⁴); temperature must be absolute.

Carnot efficiency

η_max = 1 − T_C/T_H for a heat engine, and COP_max = T_C/(T_H − T_C) for a refrigerator. These bound all real cycles operating between the same two reservoirs.

Thermal efficiency of a cycle

η = W_net/Q_in = 1 − Q_out/Q_in. For an ideal Rankine cycle, heat added and rejected are evaluated from steam-table enthalpies at the boiler and condenser pressures.

Statics equilibrium conditions

ΣF_x = 0, ΣF_y = 0, and ΣM = 0 about any point. A two-force member carries only axial force along the line joining its two pins, simplifying truss analysis.

Axial stress and deformation

σ = F/A and δ = FL/(AE), where E is Young's modulus. Positive values denote tension; the same relations give compression if the load reverses sign.

Bending stress formula

σ = Mc/I, with c the distance from the neutral axis and I the area moment of inertia. Maximum stress occurs at the outermost fiber of the cross-section.

Maximum bending moment cases

Simply supported beam with central point load P gives M_max = PL/4; with uniform load w it gives wL²/8. A cantilever with end load P gives M_max = PL at the fixed end.

Area moment of inertia

For a rectangle, I = bh³/12 about the centroidal axis parallel to b. For a circle, I = πd⁴/64. Parallel-axis theorem: I = I_c + Ad² when the axis is offset.

Ohm's law and power

V = IR, P = VI = I²R = V²/R. In series, resistances add and current is common; in parallel, conductances add and voltage is common across each branch.

Kirchhoff's circuit laws

Current into a node equals current out (KCL), and the sum of voltage changes around any closed loop is zero (KVL). Together they give the node and mesh equations used for circuit analysis.

Three-phase power

P = √3 V_L I_L cos θ for a balanced three-phase load, with line voltage and line current. For a wye-connected load, phase voltage is line voltage divided by √3.

Material properties: stress and strain

Young's modulus E is the slope of the elastic stress–strain curve. Yield strength marks the onset of permanent deformation; Poisson's ratio ν = −ε_lateral/ε_axial, typically 0.25–0.35 for metals.

Thermal expansion stress

Fully constrained bar: σ = EαΔT, with α the coefficient of thermal expansion. Free expansion causes no stress; only restraint generates it.

pH and acid–base relations

pH = −log[H⁺] and pOH = −log[OH⁻], with pH + pOH = 14 at 25 °C. A solution with pH below 7 is acidic; each unit change is a tenfold change in hydrogen ion concentration.

Half-life and first-order decay

For first-order kinetics, C = C₀e^(−kt) and t½ = 0.693/k. After n half-lives the remaining fraction is (1/2)^n, independent of the starting concentration.

Material balance on a process

Accumulation = Input − Output + Generation − Consumption. At steady state accumulation is zero, so unknown stream flows or compositions are found by solving the balance on each species.

R-value and U-factor

Thermal resistance R = L/k in SI or ft²·°F·h/Btu in US units; the overall heat transfer coefficient U = 1/R_total. Series layers add resistances, and q = UAΔT.

Unit conversion: horsepower

1 hp = 550 ft·lbf/s = 33,000 ft·lbf/min = 0.7457 kW. Pump or motor problems stated in horsepower must be converted before combining with SI-based formulas.

Hydrostatic pressure

P = γh = ρgh, where h is depth below the free surface. Pressure depends only on depth, not on the shape or volume of the containing vessel.

Buoyancy (Archimedes' principle)

The buoyant force equals the weight of displaced fluid: F_b = ρ_fluid g V_displaced. A floating body displaces its own weight, so submerged fraction equals body density divided by fluid density.

Logarithm and exponential rules

ln(ab) = ln a + ln b, ln(a^b) = b ln a, and e^(ln x) = x. These identities linearize exponential decay and growth relations and simplify pH and half-life calculations.

Significant figures in answers

Report a computed result to the precision of the least precise given data, and select the answer option that matches. Distractors frequently differ only by a misplaced decimal or rounding error.

FE exam question pacing

About 110 questions in roughly 320 minutes of testing time, averaging under three minutes each. Flag long calculations, answer every question since there is no guessing penalty, and return to flagged items.