IESL Part III cheat sheet

Reference evapotranspiration (ET₀) by FAO Penman-Monteith: ET₀ = [0.408Δ(Rn−G) + γ(900/(T+273))u₂(es−ea)] / [Δ + γ(1+0.34u₂)], with ET₀ in mm/day and u₂ in m/s.

Crop water requirement ETc = Kc × ET₀; Kc varies by growth stage (initial, mid-season, late-season) and must be adjusted for local climate.

Soil moisture tension: irrigation is scheduled when allowable depletion (p) of total available water (TAW) is reached; TAW = (FC − PWP) × root depth.

Drip irrigation emission uniformity EU = 100 × (1 − 1.27 CV/√n), where CV is manufacturer coefficient of variation and n is number of emitters per plant.

Universal soil loss equation A = R·K·LS·C·P: R rainfall erosivity, K soil erodibility, LS slope length/steepness, C cover management, P support practice.

Plantation spacing: plants per hectare = 10,000 / (row spacing × plant spacing in metres); triangular planting gives about 15% more plants than square.

Post-harvest: grain safe storage moisture typically ≤12–14% for cereals; drying follows the thin-layer equation MR = exp(−k·t^n) for moisture ratio.

Greenhouse ventilation rate: required air exchange = sensible heat load / (ρ·cp·ΔT), with ρ ≈ 1.2 kg/m³ and cp ≈ 1.005 kJ/kg·K at 20 °C.

Cooling load sensible heat Qs = 1.23 × L/s × ΔT (W) for air, or Qs = m·cp·ΔT; latent heat Ql = 3010 × L/s × ΔW (W) with humidity ratio in kg/kg.

Psychrometric relation: enthalpy h = 1.006T + W(2501 + 1.86T) kJ/kg dry air, T in °C, W in kg/kg.

Duct sizing by equal friction: friction loss per metre is held constant; velocity pressure pv = 0.5ρv², and round duct equivalent diameter from rectangular a×b is De = 1.30(ab)^0.625/(a+b)^0.25.

Pump and fan affinity laws: flow ∝ speed, head/pressure ∝ speed², power ∝ speed³.

Water supply: minimum residual pressure at fixture typically 1–2 bar; pipe sizing uses Hazen-Williams hf = 10.67·L·Q^1.852/(C^1.852·d^4.87).

Fire protection: sprinkler design density in mm/min over the design area; hose reel and hydrant flows per local code; pump head = static + friction + residual.

Illumination: maintained illuminance E = (N·Φ·UF·MF)/A, where N luminaires, Φ luminous flux per luminaire (lm), UF utilisation factor, MF maintenance factor.

Lift traffic: handling capacity = (300 × P × 100)/T percent of population in 5 min, where P passengers per car and T round-trip time in seconds.

Bending: σ = My/I and τ = VQ/(Ib); for rectangular section τmax = 1.5V/(bd) at the neutral axis.

Reinforced concrete (limit state): design moment Mu = 0.87 fy As (d − 0.42x) with x = 0.87 fy As/(0.36 fck b) for rectangular stress block.

Slope stability: factor of safety F = resisting moment / disturbing moment; for infinite slope F = c'/(γH cos²β tanβ) + tanφ'/tanβ.

Soil bearing: Terzaghi qu = cNc + qNq + 0.5γBNγ; allowable bearing = qu/FoS with FoS typically 2.5–3.

Concrete mix: water/cement ratio controls strength; nominal mixes 1:2:4 (M15), 1:1.5:3 (M20); target mean strength = characteristic + 1.65 × standard deviation.

Traffic: design hourly volume = AADT × K × D, where K peak-hour factor and D directional distribution; LOS from volume/capacity ratio.

Surveying: levelling height of instrument HI = backsight + reduced level; rise = previous staff − current staff.

Structural steel: tension capacity = min(Ag fy/γm0, 0.9 An fu/γm1); deflection limits typically span/250 for floors.

Material balance: accumulation = input − output + generation − consumption; for steady state accumulation = 0.

Arrhenius rate constant k = A·exp(−Ea/RT); doubling rule: rate roughly doubles per 10 °C rise near room temperature.

Heat exchanger: Q = U·A·ΔTlm, with ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2) for counter-current flow.

Distillation: minimum reflux from pinch point; Fenske equation Nmin = ln[(xD/(1−xD))((1−xB)/xB)]/ln α for constant relative volatility α.

Pump work: W = (ΔP)/(ρ·η) for incompressible flow; compressor ideal work for isentropic gas = (γ/(γ−1))·RT1[(P2/P1)^((γ−1)/γ) − 1].

Reactor sizing: CSTR volume V = FA0·X/(−rA); PFR volume V = FA0 ∫ dX/(−rA).

Fluidisation: minimum fluidisation velocity from Ergun equation balance of pressure drop and weight of bed.

Process safety: relief valve sizing uses API 520/521; two-phase flow requires homogeneous or DIERS methods; LFL/UFL bound flammable range.

Three-phase power: P = √3·VL·IL·cosφ; per-phase equivalent P = 3·Vph·Iph·cosφ.

Transformer: EMF equation E = 4.44·f·N·Φm; efficiency η = output/(output + iron loss + copper loss), maximum when copper loss = iron loss.

Induction motor: synchronous speed Ns = 120f/P; slip s = (Ns − Nr)/Ns; rotor frequency = s·f.

Transmission line: surge impedance Zc = √(L/C); SIL = V²/Zc; Ferranti effect raises receiving-end voltage on light load.

Op-amp: inverting gain = −Rf/Rin; non-inverting gain = 1 + Rf/Rin; virtual short at input terminals when negative feedback is present.

Digital: Shannon capacity C = B·log₂(1 + SNR); Nyquist rate = 2 × highest signal frequency.

Modulation: AM bandwidth = 2fm; FM Carson's rule BW ≈ 2(Δf + fm); SNR improvement from FM ≈ 3/2·β² for high β.

Protection: relay pickup and time-multiplier settings; IDMT curve t = TMS·k/((I/Is)^α − 1).

OSI seven layers: Physical, Data Link, Network, Transport, Session, Presentation, Application; TCP operates at Transport, IP at Network.

Subnetting: usable hosts = 2^h − 2, where h is number of host bits; CIDR /24 gives 254 usable addresses.

TCP three-way handshake: SYN, SYN-ACK, ACK; congestion control uses slow start, congestion avoidance, fast retransmit.

Link budget: received power Pr = Pt + Gt + Gr − Lpath − Lmisc; free-space loss Lfs = 32.45 + 20log10(fMHz) + 20log10(dkm) dB.

IPv4 header minimum 20 bytes; TTL decremented each hop; fragmentation controlled by MTU.

Relational databases: normalisation to 3NF removes transitive dependencies; ACID = Atomicity, Consistency, Isolation, Durability.

Cybersecurity: symmetric AES key sizes 128/192/256; RSA security based on integer factorisation; TLS uses asymmetric for key exchange then symmetric for data.

Cellular: frequency reuse factor N from N = i² + ij + j²; co-channel reuse ratio Q = D/R = √(3N).

Otto cycle efficiency η = 1 − 1/r^(γ−1); Diesel cycle η = 1 − (1/r^(γ−1))·[(ρ^γ − 1)/(γ(ρ − 1))], where ρ = cut-off ratio.

Rankine cycle: pump work ≈ vf·(P2 − P1); thermal efficiency = (h1 − h2 − h4 + h3)/(h1 − h4) for turbine and pump enthalpies.

Heat conduction: plane wall Q = kAΔT/L; cylindrical pipe Q = 2πkLΔT/ln(r2/r1).

Stress concentration: Kt = σmax/σnom; fatigue endurance limit for steel ≈ 0.5 Sut for Sut < 1400 MPa.

Bearings: Sommerfeld number S = (r/c)²·(μN/P); hydrodynamic lubrication requires S within design range.

Gears: module m = d/N; circular pitch p = πm; velocity ratio = N2/N1 = d2/d1 for meshing gears.

Thermodynamics: first law for closed system Q − W = ΔU; for steady flow Q − W = Δh + ΔKE + ΔPE.

Manufacturing: Taylor tool life VT^n = C; for HSS n ≈ 0.1, carbide n ≈ 0.25.