IESL Part I cheat sheet

Field capacity is the water retained after free drainage; permanent wilting point is where plants can no longer extract water. Available water = (field capacity − wilting point) × root-zone depth.

Reference evapotranspiration ET0 is computed by the FAO-56 Penman-Monteith equation; crop ET = ET0 × Kc, where Kc varies by crop and growth stage.

Irrigation interval (days) = (available water × management allowed depletion) ÷ crop water use per day.

Soil erosion by water is estimated with USLE: A = R × K × LS × C × P; R is rainfall erosivity, K soil erodibility, C cover and P support practice.

Sandy soils have high infiltration but low water-holding capacity; clay soils hold more water but drain slowly and are prone to waterlogging.

Cation exchange capacity (CEC) measures the soil's ability to hold exchangeable cations (cmol/kg); higher CEC means greater nutrient retention.

Soil pH controls nutrient availability: most crops favour pH 5.5–7.0; lime raises pH, elemental sulfur or gypsum lowers it.

N-P-K labels give the percentage by mass of N, P2O5 and K2O; to convert P2O5 to elemental P multiply by 0.44, and K2O to K multiply by 0.83.

Seed germination percentage = (number of seeds germinated ÷ total seeds sown) × 100; pure live seed = purity × germination.

Sensible heat gain through a building fabric: Q = U × A × ΔT, where U is the overall heat-transfer coefficient (W/m²·K).

Cooling coil total load = sensible heat + latent heat; latent load is driven by moisture, so it rises with occupancy and ventilation rate.

Air-side sensible heat: Q = 1.2 × volumetric flow (m³/s) × ΔT (K) in kW, using air density ≈ 1.2 kg/m³ and cp ≈ 1.005 kJ/kg·K.

Illuminance (lux) = luminous flux (lumens) falling on a surface ÷ area (m²); utilization factor and maintenance factor reduce the installed flux.

A lift's handling capacity depends on round-trip time, car capacity and number of stops; the 5-minute handling capacity is expressed as a percentage of building population.

Fire protection: sprinkler systems are designed to a design density (mm/min) over an assumed operating area; wet risers serve buildings too tall for fire-service pumping.

Water supply pressure in a downfeed system at a tap = static head from tank level minus friction and fitting losses along the route.

Sound pressure level in decibels: Lp = 20 log10(p/p0), with p0 = 20 µPa; combining two equal sources adds about 3 dB.

Bending stress in a beam: σ = M·y/I, where M is bending moment, y distance from neutral axis and I second moment of area.

Simply supported beam under uniformly distributed load w over span L: maximum bending moment = wL²/8 and maximum shear = wL/2.

Deflection of a simply supported beam under UDL: δmax = 5wL⁴/(384EI) at midspan.

Reinforced concrete design uses the stress-block approach; the balanced condition occurs when the neutral axis depth ratio is at the value where concrete crushing and steel yielding coincide.

Slope stability factor of safety = resisting shear strength ÷ mobilised shear stress along the failure surface; a value above 1.0 is required, with margins set by the design code.

Terzaghi bearing capacity for a strip footing: qult = cNc + qNq + 0.5γBNγ, where q is surcharge and B footing width.

Darcy's law for seepage: v = k·i, where k is hydraulic conductivity and i is the hydraulic gradient; flow rate Q = k·i·A.

Concrete mix strength is specified by characteristic cube strength at 28 days; the target mean strength is the characteristic value plus a margin for standard deviation.

Material balance: accumulation = input − output + generation − consumption; at steady state accumulation is zero.

Energy balance for a steady-flow system: Q − W = ΔH + ΔKE + ΔPE, with kinetic and potential terms often negligible.

Ideal gas law PV = nRT; at standard conditions 1 mol of ideal gas occupies about 22.4 L at 0 °C and 1 atm.

Log-mean temperature difference for a heat exchanger: ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2); apply an F correction factor for multipass units.

Heat exchanger duty Q = U·A·ΔTlm, where U is the overall coefficient and A the heat-transfer area.

Fick's first law of diffusion: J = −D·(dC/dx); flux is proportional to the concentration gradient and diffusivity.

Distillation: relative volatility α = (y/x) of the more volatile component divided by (y/x) of the less volatile; the number of stages is found by stepping between equilibrium and operating lines.

Reaction rate for a first-order reaction: −rA = k·CA; half-life t½ = ln2/k, independent of initial concentration.

Pump power = ρ·g·Q·H ÷ efficiency, where Q is volumetric flow and H the total head.

Ohm's law V = IR; power P = VI = I²R = V²/R for resistive circuits.

Three-phase power: P = √3·VL·IL·cosφ for a balanced load, where φ is the phase angle between phase voltage and current.

Transformer EMF equation: E = 4.44·f·N·Φm, with f frequency, N turns and Φm peak flux.

Synchronous speed of an induction motor: Ns = 120f/P (rpm), where P is the number of poles; slip s = (Ns − Nr)/Ns.

Thevenin's theorem replaces a linear network by an equivalent voltage source and series resistance; Norton's uses a current source with parallel resistance.

In a series RLC circuit, resonance occurs at f = 1/(2π√(LC)); at resonance impedance is purely resistive and current is maximum.

Op-amp ideal characteristics: infinite open-loop gain, infinite input impedance, zero output impedance; the inverting amplifier gain is −Rf/Rin.

Shannon capacity C = B·log2(1 + S/N), where B is bandwidth and S/N the linear signal-to-noise ratio.

Digital modulation: BPSK carries 1 bit per symbol, QPSK 2 bits, 16-QAM 4 bits and 64-QAM 6 bits.

Nyquist sampling theorem: a signal must be sampled at more than twice its highest frequency component to be reconstructed without aliasing.

Subnetting: usable hosts per subnet = 2^h − 2, where h is the number of host bits; the two addresses removed are the network and broadcast addresses.

TCP is connection-oriented and reliable via acknowledgements and retransmission; UDP is connectionless with no delivery guarantee.

The OSI model has seven layers: physical, data link, network, transport, session, presentation, application.

IPv4 addresses are 32 bits; IPv6 addresses are 128 bits.

Amdahl's law: speedup = 1 ÷ ((1 − p) + p/s), where p is the parallel fraction and s the parallel speedup.

Cache hit ratio = hits ÷ (hits + misses); average access time = hit time + miss rate × miss penalty.

Boolean algebra: De Morgan's laws state that NOT(A AND B) = (NOT A) OR (NOT B), and NOT(A OR B) = (NOT A) AND (NOT B).

First law for a closed system: Q − W = ΔU; for a steady-flow control volume: q − w = Δh + ΔKE + ΔPE per unit mass.

Ideal gas relations: PV = mRT; cp − cv = R and γ = cp/cv.

Carnot efficiency = 1 − Tc/Th, with temperatures in kelvin; no real engine between the same reservoirs can exceed it.

Otto cycle efficiency = 1 − 1/r^(γ−1), where r is the compression ratio; Diesel cycle efficiency also depends on cut-off ratio.

Heat conduction through a plane wall: Q = k·A·ΔT/L; for layers in series, resistances R = L/(kA) add.

Reynolds number Re = ρVD/μ = VD/ν; flow is laminar below about 2000 in a pipe and turbulent above about 4000.

Bernoulli's equation for steady incompressible flow: p/ρg + V²/2g + z = constant along a streamline, neglecting losses.

Bending stress in shafts and beams: σ = M·c/I; torsional shear stress in a solid circular shaft: τ = 16T/(πd³).

Gear ratio = number of teeth on driven gear ÷ number of teeth on driving gear; it equals the inverse of the speed ratio.

Newton-Raphson iteration for root finding: x(n+1) = x(n) − f(xn)/f′(xn); it converges quadratically near a simple root.

Trapezoidal rule: ∫f(x)dx ≈ h/2·[f0 + 2(f1 + … + fn−1) + fn], with h the interval width.

Euler's method for dy/dx = f(x,y): y(n+1) = yn + h·f(xn,yn); smaller h improves accuracy at the cost of more steps.

Laplace transform of a derivative: L{f′(t)} = sF(s) − f(0); for a second derivative add − s·f(0) − f′(0).

Cramer's rule solves a linear system using determinants: xi = det(Ai)/det(A), provided det(A) ≠ 0.

Critical path method: the project duration equals the longest path through the network; total float = latest start − earliest start.

Earned value: cost variance CV = EV − AC and schedule variance SV = EV − PV; negative values indicate overrun or delay.

Present worth of a single future sum: P = F/(1 + i)^n; for an annuity, P = A·[(1 + i)^n − 1]/[i(1 + i)^n].