PE Water Resources cheat sheet

Manning equation: Q = (1.486/n) A R^(2/3) S^(1/2) in US customary units (constant = 1.0 in SI); R = A/P, and n ≈ 0.013 for new concrete pipe, 0.024–0.035 for natural channels.

Energy equation between sections: p1/γ + z1 + V1²/2g = p2/γ + z2 + V2²/2g + hL, with hL = f (L/D)(V²/2g) + ΣK(V²/2g) for friction plus minor losses.

Hazen-Williams (water, US units): V = 1.318 C R^0.63 S^0.54; C ≈ 130–140 for new cement-lined or PVC pipe, dropping to near 100 for old unlined steel.

Rational method: Q = CiA, with rainfall intensity i taken from the IDF curve at a duration equal to the time of concentration; limited to small watersheds (roughly under 200 acres).

NRCS runoff depth: Q = (P − 0.2S)²/(P + 0.8S) with S = 1000/CN − 10 inches; composite CN is area-weighted and increases with urbanization and poorer hydrologic soil group.

Froude number Fr = V/√(gD): Fr = 1 is critical flow at minimum specific energy, Fr < 1 subcritical (tranquil), Fr > 1 supercritical; a hydraulic jump passes from supercritical to subcritical.

Structure flow: sharp-crested rectangular weir Q = 3.33 L H^1.5 (cfs); submerged orifice Q = C A √(2gΔh) with C ≈ 0.6–0.65.

Frequency: annual exceedance probability p = 1/T; probability of at least one event in n years = 1 − (1 − 1/T)^n, so a 100-yr event has a 1% chance every year.

Unit hydrograph assumptions: linearity (scale by runoff depth), time invariance, and uniform rainfall distribution; the SCS synthetic UH peaks near D/2 + 0.6Tc.

BOD progression: BOD5 = UBOD(1 − e^(−k·5)); with k ≈ 0.23/day at 20 °C, BOD5 ≈ 0.68 UBOD, and k is temperature-corrected by θ^(T−20) with θ ≈ 1.047.

Activated sludge SRT θc = (V·MLSS)/(Qw·Xr + Qe·Xe); conventional design 5–15 days, extended aeration 20+ days, and nitrification requires SRT above the nitrifier minimum at the coldest month.

F/M = Q·S0/(V·X); low ratios (0.05–0.15) give long SRT, low sludge production, and nitrification, while high ratios risk poor settling and high effluent BOD.

Clarifier sizing checks both surface overflow rate (primary 600–1200 gpd/ft², secondary 400–800 gpd/ft²) and solids loading rate (Q + Qr)·MLSS/A.

Sludge volume index SVI = (30-min settled volume, mL/L × 1000)/MLSS mg/L; roughly 80–150 mL/g settles well, and above about 200 mL/g indicates filamentous bulking.

Disinfection CT = residual concentration (mg/L) × contact time (min); required CT rises with target log inactivation and pH (for free chlorine) and falls as temperature rises.

Conventional surface water train: coagulation (alum or ferric, optimum pH about 5–7), flocculation (G ≈ 20–70 s⁻¹), sedimentation (0.5–1.0 gpm/ft²), filtration (4–8 gpm/ft²), disinfection.

Langelier saturation index LSI = pH − pHs, with pHs derived from calcium hardness, total alkalinity, temperature, and TDS; positive is scale-forming, negative is corrosive.

Typical secondary effluent limits are 30 mg/L BOD5 and 30 mg/L TSS (10/10 for advanced treatment); compliance also requires disinfection CT and a maintained residual in distribution.

Rippl mass curve: plot cumulative inflow versus time; storage required for a constant demand equals the maximum vertical gap between the demand line and the mass curve over the critical drawdown period.

Storage–yield behavior is nonlinear: each additional unit of firm yield needs progressively more storage until the reservoir becomes inflow-limited.

Log-Pearson Type III flood frequency: fit mean, standard deviation, and skew of log10 annual peak flows (Bulletin 17C practice), with regional skew and low-outlier screening.

Darcy's law Q = KIA; transmissivity T = Kb; confined storativity is roughly 0.00005–0.005 while unconfined specific yield is typically 0.10–0.30.

Theis solution: s = Q·W(u)/(4πT) with u = r²S/(4Tt); the Cooper-Jacob straight-line approximation applies when u < 0.01.

Dam freeboard = wave runup + wind setup + settlement allowance + safety margin, measured from the spillway design pool for normal freeboard and from the PMF pool for minimum freeboard on high-hazard dams.

Economic comparison discounts all benefits and costs to present worth at the project rate; B/C ≥ 1.0 is required, and the analysis period is normally the project economic life.

Reservoir sedimentation: trap efficiency increases with the capacity-to-annual-inflow ratio (Brune curve), and reservoir life ≈ capacity / (annual sediment inflow × trap efficiency).

Level-pool flood routing uses the storage-indication relation (2S/Δt + O) plotted against outflow O; high-hazard dams are typically sized for the probable maximum flood.

The critical path is the longest path through the network; it fixes project duration and every activity on it has zero total float.

Total float = LS − ES = LF − EF; free float = ES of the successor − EF of the activity; float belongs to the path, not to an individual activity.

PERT expected duration = (O + 4M + P)/6 with variance ((P − O)/6)²; CPM uses single deterministic durations, PERT uses three-point estimates.

Earned value: CV = EV − AC, SV = EV − PV, CPI = EV/AC, SPI = EV/PV; CPI < 1 is over budget, SPI < 1 is behind schedule, and EAC ≈ BAC/CPI when variance is typical.

Contract risk allocation: lump sum puts quantity risk on the contractor, unit price puts it on the owner, and cost-plus puts most cost risk on the owner.

Schedule compression: crashing adds resources and cost to critical activities; fast-tracking overlaps design and construction and raises coordination risk.

Delay classification: excusable-compensable (owner-caused, differing site conditions), excusable-noncompensable (severe weather, force majeure), and non-excusable (contractor-caused); only compensable delay earns time and money.

Substantial completion makes the work usable for its purpose, starts the warranty, and stops liquidated damages; final completion releases retainage per contract terms.

OSHA 29 CFR 1926 requires a competent person for excavations, cave-in protection at 5 ft depth, and hazard communication for site chemicals.