PEP flashcards

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

Quadratic formula

For ax² + bx + c = 0, the roots are x = [−b ± √(b² − 4ac)]/(2a). A negative discriminant yields complex conjugate roots; a zero discriminant gives one repeated real root.

Ideal gas law

PV = nRT relates pressure, volume, moles, and absolute temperature. R equals 8.314 J/(mol·K); temperature must be in kelvin, and one mole occupies about 22.41 L at STP.

Arrhenius equation

k = A·e^(−Ea/RT) describes how a rate constant rises with temperature. Plotting ln k against 1/T gives a straight line whose slope equals −Ea/R.

Standard error of the mean

The standard error equals the sample standard deviation divided by the square root of sample size, s/√n. It quantifies uncertainty of the estimated mean and shrinks as n grows.

Axial deformation formula

A prismatic bar under axial load deforms by δ = FL/(AE), where F is load, L is length, A is cross-sectional area, and E is elastic modulus. Stiffness therefore rises with area and modulus.

Beam bending stress

Bending stress is σ = Mc/I, where M is the bending moment, c is distance from the neutral axis, and I is the second moment of area. For a rectangle, I equals bh³/12.

Euler buckling load

The critical buckling load is P_cr = π²EI/(KL)², where K is the effective length factor. K equals 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, and 2.0 fixed-free.

Bernoulli equation

For steady, incompressible, frictionless flow along a streamline, P/γ + z + v²/(2g) stays constant. It converts pressure, elevation, and velocity head into one another.

Reynolds number

Re = ρvD/μ compares inertial to viscous forces. Pipe flow is generally laminar below about 2100, transitional to 4000, and turbulent above 4000.

Gear train ratio

The ratio equals the product of driven teeth divided by the product of driving teeth. Speed ratio is the inverse, so a larger driven gear reduces output speed and increases torque.

Grashof condition

A four-bar linkage has at least one fully rotating link when the shortest plus longest link lengths do not exceed the sum of the other two. Equality gives a change-point linkage.

Stress concentration factor

K_t multiplies nominal stress at a geometric discontinuity such as a hole or fillet. The fatigue notch factor K_f is usually smaller because of local yielding at the notch root.

Endurance limit

The stress amplitude below which a ferrous alloy survives a very large number of cycles, conventionally 10⁶ to 10⁷. Nonferrous alloys such as aluminum have no true endurance limit.

Shaft critical speed

A rotating shaft resonates when its speed matches a natural frequency, which scales with √(EI/mL⁴). Operation within roughly twenty percent of a critical speed is avoided.

Factor of safety

FS equals failure strength divided by allowable or actual stress, or allowable load divided by applied load. The failure mode and reference strength must be stated for the value to be meaningful.

Von Mises stress

For plane stress, the equivalent stress is √(σx² − σxσy + σy² + 3τxy²). It is compared with yield strength for ductile materials under combined loading.

Worst-case tolerance stack

Worst-case assembly tolerance equals the sum of individual tolerances, assuming every part at its extreme. The statistical root-sum-square method, √(Σtᵢ²), gives a smaller value for independent distributions.

Modified Goodman criterion

For combined mean and alternating stress, σ_a/S_e + σ_m/S_ut = 1/FS predicts fatigue failure. It is a straight-line approximation commonly used for ductile materials with stress concentration.

Series reliability

Components in series all must function, so system reliability is the product R₁·R₂·…·R_n. Adding components in series always lowers overall system reliability.

Standard versus code

A standard is a voluntary consensus technical document; a code is a standard adopted into law by a jurisdiction. Adoption, not publication, creates legal obligation.

Load and resistance factor design

LRFD applies factored loads such as 1.2D + 1.6L and multiplies nominal resistance by a factor φ below one. Allowable stress design instead uses service loads with a safety factor.

ASME Section VIII

Section VIII of the ASME Boiler and Pressure Vessel Code governs design, fabrication, inspection, and testing of pressure vessels. Section IX separately covers welding and brazing qualification.

Sealing engineering work

Only a licensed professional engineer may seal and sign engineering documents for public use. Sealing work outside the engineer's demonstrated competence violates professional rules.

Conflict of interest duty

An engineer must disclose in writing any personal financial interest that could bias professional judgment, and must withdraw from decisions where that interest exists.

Hierarchy of safety controls

Hazards are addressed by elimination first, then substitution, engineering controls, administrative controls, and finally personal protective equipment. Higher levels are more reliable because they do not depend on behavior.

Absolute temperature rule

Gas-law, Carnot-efficiency, and radiation calculations require kelvin. Using degrees Celsius produces large errors; convert with K = °C + 273.15 before substituting.

Sign convention discipline

Before writing equilibrium or energy equations, state the assumed positive direction, such as tension positive or heat into the system. Inconsistent signs are a leading source of wrong answers.

Carbon steel designation

AISI/SAE four-digit grades encode alloy family and carbon content. In 1045, the 10 series indicates plain carbon and the last two digits indicate roughly 0.45 percent carbon.

Fillet weld throat

The throat of a fillet weld equals 0.707 times the leg size for a 45-degree weld. Weld shear strength is checked on the throat area times the effective length.

Galvanic corrosion

Galvanic corrosion requires dissimilar metals, an electrolyte, and electrical contact. The more anodic metal corrodes, so material pairing and insulation control the rate.

Capital recovery factor

It converts a present amount to an equivalent uniform annual amount: A = P·[i(1 + i)ⁿ]/[(1 + i)ⁿ − 1]. It is the reciprocal of the present worth annuity factor.

Net present value rule

A positive net present value means discounted benefits exceed costs at the minimum attractive rate of return. The internal rate of return is the discount rate making NPV zero.

Break-even quantity

Break-even quantity equals fixed cost divided by unit price minus unit variable cost. Above that volume each additional unit contributes to profit.

Process capability index

C_p equals specification width divided by six sigma. C_pk equals the smaller of the upper and lower specification distances divided by three sigma, so it penalizes an off-center process.

Poisson probability

P(x) = e^(−λ)·λˣ/x! gives the probability of x rare events in a fixed interval when events are independent and the mean count is λ.

Type I error

A Type I error rejects a true null hypothesis, occurring with probability equal to the significance level alpha. A Type II error fails to reject a false null hypothesis.

Thevenin equivalent circuit

Any linear network reduces to an open-circuit voltage source in series with the resistance seen from the terminals with sources deactivated. It simplifies load-current and power calculations.

First-order time constant

For an RC or L/R circuit, the time constant equals RC or L/R. The response reaches about 63.2 percent of its final change in one time constant and 95 percent in three.

Three-phase power

For a balanced three-phase load, real power is √3·V_L·I_L·cos θ, where V_L is line-to-line voltage and θ is the impedance phase angle.

Darcy-Weisbach head loss

Major pipe head loss is h_f = f·(L/D)·(v²/2g), where f depends on Reynolds number and relative roughness. Minor losses use h = K·v²/(2g).

Pump power requirement

Shaft power equals ρgQH/η, with density, gravity, flow in cubic meters per second, head in meters, and efficiency. Lower efficiency raises required input power for the same duty.

Log-mean temperature difference

For a heat exchanger, ΔT_lm equals (ΔT₁ − ΔT₂) divided by the natural log of ΔT₁/ΔT₂. Heat transfer equals U·A·ΔT_lm times a configuration correction factor.