SCE PE Water Resources & Environmental cheat sheet

Rational method: Q = C i A / 360 for Q in ft³/s, i in in/hr, A in acres; metric Q = C i A / 3.6 for Q in m³/s, i in mm/hr, A in km².

Time of concentration Kirpich: Tc = 0.0078 L^0.77 S^-0.385 (minutes, L in ft, S ft/ft); metric Tc = 0.0195 L^0.77 S^-0.385 (L in m, S m/m).

Return period T = 1/p, where p is annual exceedance probability; probability of at least one exceedance in n years is 1 - (1 - p)^n.

IDF curves: for a fixed return period, rainfall intensity decreases as duration increases; for a fixed duration, intensity increases as return period increases.

NRCS curve number runoff: Q = (P - 0.2S)^2 / (P + 0.8S) for P > 0.2S; S = 25400/CN - 254 mm or S = 1000/CN - 10 in.

Unit hydrograph assumptions: linear response, time invariance, and uniform rainfall over the watershed; ordinates scale with excess rainfall depth.

Horton infiltration: f(t) = fc + (f0 - fc)e^(-kt), where f0 is initial rate, fc final rate, and k decay constant.

Water balance for a watershed: P = ET + Q + ΔS + G, with P precipitation, ET evapotranspiration, Q streamflow, ΔS storage change, G groundwater exchange.

Continuity: Q = V A; energy equation between sections: p1/γ + z1 + V1²/2g = p2/γ + z2 + V2²/2g + hL.

Darcy-Weisbach: hf = f (L/D)(V²/2g); f depends on Reynolds number and relative roughness ε/D.

Reynolds number: Re = V D / ν; laminar Re < 2000, transitional 2000-4000, turbulent Re > 4000 for pipe flow.

Hazen-Williams SI: hf = 10.67 L Q^1.852 / (C^1.852 D^4.87); C is roughness coefficient, Q in m³/s, D in m.

Minor losses: hL = Σ K V²/(2g); K values apply for fittings, valves, bends, expansions, and contractions.

Pump power: P = ρ g Q H / η; brake power input equals hydraulic power divided by overall efficiency.

Water hammer surge: Δp = ρ a ΔV, where a is pressure-wave celerity; rapid valve closure produces larger surge than slow closure.

Pipe network decision rule: at each junction continuity ΣQin = ΣQout; around each closed loop algebraic sum of head losses equals zero.

Manning SI: V = (1/n) R^(2/3) S^(1/2); English: V = (1.486/n) R^(2/3) S^(1/2), with R = A/P.

Chezy: V = C (R S)^(1/2); Manning C = (1/n) R^(1/6) in SI.

Specific energy E = y + V²/(2g) = y + Q²/(2gA²); critical depth occurs at minimum E for a given Q.

Froude number Fr = V / sqrt(gD), D = A/T; Fr < 1 subcritical, Fr = 1 critical, Fr > 1 supercritical.

Hydraulic jump: supercritical flow transitions to subcritical flow; momentum equation gives sequent depths and energy loss.

Gradually varied flow classification uses normal depth yn and critical depth yc: mild slope yn > yc, steep slope yn < yc, critical slope yn = yc.

Best hydraulic trapezoidal section: side slope 1:√3 (60° from horizontal), hydraulic radius y/2; best rectangular section has b = 2y.

Broad-crested weir: Q = C L H^(3/2); for ideal broad-crested weir in SI, Q ≈ 1.705 L H^(3/2) with H measured upstream.

BOD progression: BODt = BODu (1 - e^(-kt)); at 20°C with k = 0.23/d, BOD5 ≈ 0.68 BODu.

Streeter-Phelps DO sag: deficit D = (k1 L0)/(k2 - k1)(e^(-k1 t) - e^(-k2 t)) + D0 e^(-k2 t); critical point where dD/dt = 0.

Activated sludge F/M = Q S0 / (V X); SRT = V X / (Qw Xr + Qe Xe); lower SRT risks nitrifier washout.

Clarifier overflow rate = Q/A; particles with settling velocity greater than overflow rate are removed; Stokes vs = g(ρp - ρw)d²/(18μ).

Disinfection CT = C T; required CT depends on organism, disinfectant, pH, and temperature.

Nitrification consumes about 4.57 mg O2 per mg NH4-N oxidized and about 7.14 mg alkalinity as CaCO3 per mg NH4-N.

Water treatment train order: coagulation, flocculation, sedimentation, filtration, disinfection; each unit has distinct design loading criteria.

Sludge solids loading = Q X / A; thickening and dewatering performance depend on solids flux, detention, and conditioning.

Benefit-cost ratio = PW benefits / PW costs; B/C > 1 indicates acceptable project under the chosen discount rate.

Single-payment present worth factor: (P/F, i, n) = 1/(1+i)^n; future worth factor is reciprocal.

Risk over design life: R = 1 - (1 - 1/T)^n; for a 100-year event and 50-year life, R ≈ 39.5%.

Detention storage estimate: required volume ≈ inflow volume minus allowable outflow volume over the design storm; check peak outflow and local criteria.

Life-cycle cost includes capital, operation, maintenance, replacement, energy, and salvage; compare alternatives on present worth or annual cost.

Sensitivity analysis varies one parameter at a time; identifies which input uncertainty most affects output and design margin.

Dimensional homogeneity: all terms in an equation must have same units; convert rainfall, area, flow, and head to consistent units before calculation.