2.2 Engineering Sciences
Key Takeaways
- Engineering Sciences is 4-6 of 110 FE Civil questions covering work/energy, basic thermodynamics, heat transfer, basic DC electricity, and fluid/material property fundamentals.
- Work-energy: the work-energy theorem W = ΔKE = ½m(v₂² − v₁²); power P = W/t; potential energy PE = mgh — all in the Handbook 'Dynamics' and 'Statics' chapters.
- Ohm's law V = IR, power P = VI = I²R = V²/R, and series/parallel resistor combination are the only electricity tools tested.
- Steady 1-D conduction uses Fourier's law q = kA·ΔT/L; convection uses Newton's law of cooling q = hA·ΔT; thermal expansion is δ = αLΔT.
- Density ρ, specific weight γ = ρg, and specific gravity SG = ρ/ρ_water (ρ_water ≈ 1,000 kg/m³ = 62.4 lb/ft³) connect mass, weight, and buoyancy problems.
Why this section matters
Engineering Sciences is only 4-6 questions, but they are fast points because each one reduces to a single NCEES FE Reference Handbook formula. The civil-relevant slice is narrow: work and energy, basic thermodynamics and heat transfer, basic direct-current electricity, and fluid/material property fundamentals. Treat these as definitions plus substitution.
Work, energy, and power
Work by a constant force is W = F·d (force component along the displacement). The work-energy theorem states net work equals the change in kinetic energy:
W = ΔKE = ½m·v₂² − ½m·v₁²
Potential energy is PE = mgh, and mechanical energy is conserved when only conservative forces act: KE₁ + PE₁ = KE₂ + PE₂. Power is the rate of doing work, P = W/t = F·v. Use these Handbook 'Dynamics' relations for falling masses, braking distances, and pump/lifting power.
Basic electricity
Only DC fundamentals appear. Ohm's law is V = IR. Electrical power has three equivalent forms — P = VI = I²R = V²/R — so pick the one matching the given quantities. Resistor combination:
| Configuration | Equivalent resistance |
|---|---|
| Series | R_eq = R₁ + R₂ + R₃ + … |
| Parallel (two) | R_eq = R₁R₂ / (R₁ + R₂) |
| Parallel (general) | 1/R_eq = 1/R₁ + 1/R₂ + … |
Basic thermodynamics and heat transfer
First-law energy balance: Q − W = ΔU for a closed system. Sensible heat is Q = m·c·ΔT, where c is specific heat. Linear thermal expansion is δ = αL·ΔT (α is the coefficient of thermal expansion) — directly relevant to bridge expansion joints and rail.
Heat transfer has two tested modes:
- Conduction (Fourier's law): q = kA·ΔT / L, where k is thermal conductivity, A area, L thickness.
- Convection (Newton's law of cooling): q = hA·ΔT, where h is the convection coefficient.
For a plane wall, the steady heat rate is the temperature difference divided by thermal resistance R = L/(kA) for conduction or 1/(hA) for convection; series walls add resistances like resistors.
Fluid and material properties
Density ρ = mass/volume. Specific weight γ = ρg (weight per unit volume). Specific gravity SG = ρ_substance / ρ_water, dimensionless. Standard water values to memorize: ρ_water ≈ 1,000 kg/m³ = 62.4 lb/ft³, γ_water ≈ 9.81 kN/m³. Viscosity appears as dynamic μ and kinematic ν = μ/ρ; these feed Reynolds number in the fluid mechanics section. Pressure from a fluid column is p = γh = ρgh.
Exam tip: answer choices that differ by a factor of g (≈9.81) usually mean density and specific weight were swapped. Choices off by a factor of 1,000 are a kg/m³ vs g/cm³ or kPa vs Pa unit slip — always carry units through the substitution.
A 1,500 kg vehicle traveling at 20 m/s brakes to a complete stop. Using the work-energy theorem, how much work do the brakes do?
A plane concrete wall is 0.20 m thick with thermal conductivity k = 1.7 W/m·K and area 10 m². The inside surface is 25°C and the outside is 5°C. What is the steady conduction heat-transfer rate?