ESE GS&EA flashcards

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

SI unit of pressure

The pascal (Pa) equals one newton per square metre. One bar is 10⁵ Pa and one standard atmosphere is 101.325 kPa.

Dimensional homogeneity

Every term in a physically valid equation, and both sides of it, must carry identical base dimensions. This rule validates formulas and detects errors in derived expressions.

Reynolds number

A dimensionless group Re = ρvD/μ comparing inertial to viscous forces. Low Re indicates laminar flow, high Re turbulent flow, with transition near 2000–4000 in pipes.

Significant figures rule

A computed result should retain the least number of significant figures present among the input values, since the least precise measurement limits the reliability of the outcome.

Hooke's law

Within the proportional limit, stress is directly proportional to strain, written σ = Eε. The constant E is Young's modulus, a measure of material stiffness.

Poisson's ratio

Defined as the negative ratio of lateral strain to longitudinal strain under axial loading. Typical metals fall between 0.25 and 0.35; a value of 0.5 means incompressible.

Thermal stress formula

A fully constrained bar prevented from expanding develops stress σ = EαΔT, where α is the linear expansion coefficient and ΔT the temperature change.

Bernoulli equation

For steady, incompressible, frictionless flow along a streamline, p/ρg + v²/2g + z remains constant. It expresses conservation of energy per unit weight of fluid.

Continuity equation

For steady incompressible flow through a duct, the product of cross-sectional area and velocity is constant: A₁v₁ = A₂v₂. Narrower sections therefore carry faster flow.

Fourier conduction law

Heat conduction rate equals −kA dT/dx, where k is thermal conductivity, A the area, and dT/dx the temperature gradient. The negative sign shows heat flows toward lower temperature.

Stefan–Boltzmann law

Radiant heat transfer from a grey body is q = εσA(T⁴ − Tsurr⁴), with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ and ε the surface emissivity between 0 and 1.

Ohm's law

Current through a conductor is proportional to applied voltage and inversely proportional to resistance: V = IR. Power dissipated is P = VI = I²R = V²/R.

Vernier least count

The least count of a vernier calliper equals one main-scale division minus one vernier-scale division, typically 0.1 mm or 0.02 mm for common instruments.

Toughness versus hardness

Toughness is the energy a material absorbs before fracture, given by the area under the stress–strain curve. Hardness is resistance to local indentation or scratching.

Fatigue failure

Progressive fracture under repeated or fluctuating stress at levels below the material's ultimate tensile strength, often initiating at surface defects or stress concentrations.

Environmental Impact Assessment

A structured pre-project appraisal identifying likely environmental effects and mitigation measures, used by regulators to decide whether to grant clearance for a proposed project.

Precautionary principle

Where serious or irreversible environmental harm is possible, lack of full scientific certainty should not justify postponing cost-effective measures to prevent degradation.

Net present value

The sum of future cash flows discounted to present value minus initial investment. A positive NPV indicates the project earns more than the discount rate.

Internal rate of return

The discount rate at which a project's net present value becomes zero. A project is acceptable when its IRR exceeds the required rate of return.

Coefficient of variation

The ratio of standard deviation to mean, often expressed as a percentage. It compares relative dispersion across datasets with different units or very different magnitudes.

Normal distribution rule

For a normal distribution, roughly 68% of observations lie within one standard deviation of the mean, 95% within two, and 99.7% within three.

Correlation coefficient

A value r between −1 and 1 measuring the strength and direction of linear association between two variables; its square gives the proportion of variance explained.

Least-squares slope

In simple linear regression, the slope equals Σ(x − x̄)(y − ȳ) divided by Σ(x − x̄)², minimising the sum of squared vertical deviations from the fitted line.

Addition rule of probability

For any two events, P(A ∪ B) = P(A) + P(B) − P(A ∩ B). The intersection is subtracted because it is counted twice when adding the individual probabilities.

Conditional probability

The probability of event A given that B has occurred equals P(A ∩ B)/P(B), provided P(B) is greater than zero.

Combinations formula

The number of ways to choose r items from n without regard to order is nCr = n!/[r!(n − r)!]. Permutations nPr additionally count different orderings.

Sum of first n integers

The series 1 + 2 + … + n equals n(n + 1)/2, while the sum of squares 1² + 2² + … + n² equals n(n + 1)(2n + 1)/6.

Divisibility by three

A whole number is divisible by 3 if the sum of its digits is divisible by 3. The same digit-sum test applies for divisibility by 9.

Syllogism validity

A conclusion is valid only if it necessarily follows from the premises in every possible interpretation; a single consistent counterexample is enough to disprove it.

Shear force and bending moment

The shear force at a beam section equals the rate of change of bending moment along the span, so moment is maximum where shear force is zero.

Kirchhoff's laws

The current law states that currents entering a node equal those leaving, expressing charge conservation. The voltage law states that voltages around a closed loop sum to zero.

Micrometer least count

The least count of a screw gauge equals its pitch divided by the number of divisions on the circular scale, commonly 0.5 mm divided by 50, giving 0.01 mm.