PE Agricultural cheat sheet

Crop evapotranspiration: ETc = Kc × ETo; net irrigation requirement = ETc − effective rainfall − allowable soil-water depletion, with units in depth per period.

Seed rate = target plant population ÷ (germination fraction × purity fraction) × seed weight per seed; adjust for expected field emergence.

Feed conversion ratio = feed consumed ÷ live-weight gain; lower FCR indicates more animal product per unit feed.

Steady processing mass balance: product mass = feed mass × product yield; byproduct mass = feed mass − product mass when no accumulation occurs.

Conveyor capacity Q = A × v × ρ × fill factor; keep A in m², v in m/s, and ρ in kg/m³ to obtain kg/s.

HTST milk pasteurization commonly uses 72°C for 15 s; LTLT uses 63°C for 30 min; flow-diversion valves prevent underprocessed milk from leaving the holder.

Grain storage: corn is typically held near 13–15% moisture and soybeans near 11–13%; higher moisture increases mold growth and respiration losses.

Milk cooling: bulk raw milk is commonly cooled to 7°C or below and held cold until pickup; warmer storage shortens shelf life and raises bacterial growth.

D-value = time at a given temperature for a 90% (1-log) reduction in microbial population; z-value = temperature change causing a 10-fold change in D-value.

F0 = D121 × log10(N0/N); for low-acid canned foods a 12D Clostridium botulinum cook is a common minimum target.

Thermal lethality: F = ∫10^((T−Tref)/z) dt; a larger z means lethality changes more slowly with temperature.

Microbial growth: N = N0 e^(μt); generation time g = ln(2)/μ.

Michaelis-Menten: v = Vmax S / (Km + S); Km equals substrate concentration at half of Vmax.

Power-law fluid: τ = K γdot^n; n < 1 is shear-thinning, n = 1 is Newtonian, n > 1 is shear-thickening.

Biot number Bi = hL/k; Bi much less than 1 suggests internal conduction resistance is small relative to surface convection.

Freezing point depression: ΔTf = Kf × molality × i; i is the van't Hoff factor for solute dissociation.

USLE: A = R × K × LS × C × P; A is average annual soil loss, R erosivity, K erodibility, LS slope, C cover, and P support practice.

NRCS curve number runoff: Q = (P − 0.2S)^2 / (P + 0.8S); S = 25400/CN − 254 for Q and P in mm.

Water balance: ΔS = P + I − ET − Q − D; negative ΔS means soil or storage water is being depleted.

Darcy law: Q = K A i; i is hydraulic gradient, K is hydraulic conductivity, and flow is from high to low hydraulic head.

First-order BOD: BODt = BODu (1 − e^(−kt)); k is a base-e reaction rate constant with units of 1/time.

Active composting targets: C:N near 25–30:1 and moisture near 50–60% by weight; too wet causes anaerobic zones.

Manure available N = total N × availability factor; the factor accounts for volatilization, leaching, and mineralization timing.

No manure application when soil is frozen, snow-covered, or saturated, or within required setbacks from surface water and wells.

Drawbar power P = F × v; use N and m/s to get W, then divide by 745.7 for horsepower.

Hydraulic cylinder force F = p × A; extension uses bore area, retraction uses bore area minus rod area.

Pump power P = ρ g Q H / η; add motor efficiency for electrical input power.

Fan laws at constant air density: Q ∝ N, pressure ∝ N², power ∝ N³.

Balanced three-phase power P = √3 × VL × IL × power factor.

Beam bending stress σ = M c / I; maximum stress is at the greatest distance c from the neutral axis.

Effective field capacity = width × speed × field efficiency / unit constant; field efficiency accounts for turns, overlaps, and stops.

Gear ratio = driven teeth / driving teeth; torque multiplies by the ratio while speed divides by it, ignoring losses.

Psychrometric drying: air water-holding capacity rises with temperature; drying rate depends on vapor-pressure deficit and airflow.

Critical path = longest-duration path through the network; its total float is zero and it sets project duration.

Total float = late start − early start = late finish − early finish; positive float means schedule flexibility.

PERT expected time = (optimistic + 4 × most likely + pessimistic) / 6; variance = ((pessimistic − optimistic)/6)^2.

NPV = Σ cash flow_t / (1 + r)^t; accept independent projects with NPV > 0 at the required return.

Benefit-cost ratio = present value of benefits ÷ present value of costs; BCR > 1 means benefits exceed costs.

Lump-sum contract: fixed price for a defined scope; contractor carries cost-overrun risk unless scope changes are authorized.

Hierarchy of controls: elimination, substitution, engineering controls, administrative controls, then PPE; effectiveness generally decreases in that order.

Professional seal rule: seal only work prepared under your responsible charge and within your competence; retain supporting calculations and records.