AMIE Section B Mechanical flashcards

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

Euler buckling load

Critical axial load at which a slender column buckles: π²EI divided by the square of the effective length. Effective length equals the actual length times an end-condition factor K.

Laplace transform of derivative

For a function f(t) with transform F(s), the transform of its first derivative is sF(s) minus f(0). This converts linear differential equations into algebraic equations in s.

First-angle projection

Projection method in which the object lies between observer and plane. The top view is placed below the front view and the left-side view is placed on the right.

Tolerance versus allowance

Tolerance is the total permitted size variation of one part. Allowance is the intentional difference between the sizes of two mating parts, positive for clearance and negative for interference.

Carnot efficiency

Maximum possible efficiency of a heat engine operating between hot and cold reservoirs: one minus the ratio of cold to hot absolute temperatures. No real engine exceeds it.

Biot number

Dimensionless group equal to the convective coefficient times a characteristic length divided by thermal conductivity. Small values mean internal resistance is negligible and lumped analysis is valid.

Reynolds number

Dimensionless ratio of inertial to viscous forces, equal to density times velocity times diameter divided by viscosity. Pipe flow is laminar below about 2000 and turbulent above 4000.

Specific speed of turbine

Speed of a geometrically similar turbine that would develop unit power under unit head. Low values indicate Pelton wheels, medium Francis runners, and high Kaplan turbines.

Section modulus

Ratio of a section's second moment of area to its distance from the neutral axis. Bending stress equals bending moment divided by section modulus; for a rectangle it is bd²/6.

Grashof condition

A four-bar linkage has at least one fully rotating link when the sum of shortest and longest links is less than or equal to the sum of the other two.

Goodman fatigue criterion

Design rule for fluctuating stress: alternating stress divided by endurance limit plus mean stress divided by ultimate strength equals one at the failure boundary.

Belt tension ratio

For a belt on a pulley, the tight-side tension divided by the slack-side tension cannot exceed e raised to the product of friction coefficient and wrap angle in radians.

Taylor tool life equation

Empirical relation stating that cutting speed multiplied by tool life raised to an exponent n is constant. The exponent is small for high-speed steel and larger for carbide.

Chvorinov's rule

Solidification time of a casting is proportional to the square of volume divided by surface area, so a compact riser stays molten longer than a thin section.

Economic order quantity

Order size that minimises the sum of ordering and holding costs, equal to the square root of twice annual demand times ordering cost divided by holding cost per unit.

PERT expected time

Weighted average activity duration using optimistic, most likely, and pessimistic estimates: (a + 4m + b) divided by six. Variance is the square of (b − a)/6.

Series resonance

Condition in an RLC series circuit where inductive and capacitive reactances cancel. Impedance becomes purely resistive and minimum, current is maximum, and frequency equals one over two pi root LC.

Transformer turns ratio

Secondary voltage divided by primary voltage equals secondary turns divided by primary turns, and also equals primary current divided by secondary current for an ideal transformer.

Binary search complexity

Search on a sorted array that halves the interval each step, giving logarithmic time. It is much faster than linear search but requires prior sorting.

Stack versus queue

A stack removes the most recently added item (last in, first out). A queue removes the earliest added item (first in, first out).

Accuracy versus precision

Accuracy describes how close a reading is to the true value. Precision describes how closely repeated readings agree with each other, regardless of their correctness.

Systematic versus random error

Systematic error shifts all readings consistently in one direction and is removed by calibration. Random error scatters readings about a mean and is reduced by averaging.

Poisson's ratio

Negative ratio of lateral strain to longitudinal strain in a loaded member. For most metals it lies between 0.25 and 0.35, and it approaches 0.5 for rubber.

Continuity equation

For steady incompressible flow, the product of cross-sectional area and velocity is constant along a stream tube, so velocity rises where the area narrows.

LMTD

Log mean temperature difference used in heat exchanger design: the difference of terminal temperature differences divided by the natural logarithm of their ratio.

Key design

A flat key transmits torque between shaft and hub and is checked for shear and crushing. Its width is typically one quarter of the shaft diameter.

Vernier least count

Smallest measurement a vernier instrument can read, equal to one main scale division minus one vernier scale division. A common caliper reads to 0.02 mm.

Critical path method

Network scheduling technique in which the longest path sets the project duration. Activities on this path have zero total float and must not be delayed.

Ohm's law

Current through a conductor is directly proportional to applied voltage and inversely proportional to resistance, expressed as voltage equals current times resistance.

Induction motor slip

Fractional difference between synchronous speed and actual rotor speed, divided by synchronous speed. Rotor frequency equals slip times supply frequency.

Pointer dereferencing

Operation that accesses the value stored at the address held by a pointer. It lets a function modify the caller's variable when the address is passed as an argument.

Calibration correction

Adjustment added to an instrument reading, obtained as the standard value minus the indicated value, so that systematic instrument error is compensated.

Uncertainty propagation

Rule for combining measurement errors: absolute uncertainties add for sums and differences, while relative uncertainties add for products and quotients.