Hydrology & Rainfall-Runoff Analysis

Quick Answer: Small sites → Rational Q = CiA. Larger or storage-sensitive → SCS CN for runoff depth. Always estimate time of concentration and use consistent units (cfs, acres, inches/hr). Water resources (~10% of FE Environmental) includes stormwater, flood routing concepts, and reservoir yield. Hydrology items reward handbook fluency and unit discipline.

Hydrologic Cycle Review Precipitation partitions into infiltration, surface runoff, evapotranspiration, and groundwater recharge. Engineering designs focus on peak and volume of runoff to size pipes, culverts, and detention. | Land cover | Typical CN range (AMC II) | |------------|---------------------------| | Pavement | 98 | | Residential lawn | 61–75 | | Forest | 55–70 | | Agricultural row crops | 70–80 | Antecedent Moisture Condition (AMC) adjusts CN for dry (I), normal (II), or wet (III) preceding conditions.

Rational Method $Q = C \cdot i \cdot A$ | Variable | US customary | SI caution | |----------|--------------|------------| | Q | cfs | m³/s (different C factor forms) | | C | dimensionless runoff coefficient 0–1 | use handbook conversion | | i | inches/hr intensity for duration = tc | mm/hr | | A | acres | hectares/km² | Assumptions: Uniform rainfall intensity for duration ≥ time of concentration; small, homogeneous watershed. Worked example: C = 0.85 (pavement); i = 3.0 in/hr; A = 2.5 acres. $Q = 0.85 \times 3.0 \times 2.5 = 6.4 \text{ cfs}$ Convert to gpm or MGD if the stem requires.

Time of Concentration $t_c = t_{overland} + t_{shallow} + t_{channel}$ Handbook provides Kirpich, Manning overland, or tabulated velocities. tc selects rainfall intensity from IDF curves — longer tc → lower i but not always lower Q (depends on curve). Exam trap: Using peak regional rainfall without matching duration to tc.

IDF Curves Intensity-duration-frequency curves give rainfall rate i for chosen duration and return period (10-yr, 100-yr). Climate-resilient designs may use updated IDF; exam supplies numbers.

SCS (NRCS) Curve Number Method Runoff depth for a single storm: $S = \frac{1000}{CN} - 10 \quad \text{(inches, US form)}$ $Q = \frac{(P - I_a)^2}{P - I_a + S} \quad \text{when } P > I_a$ Initial abstraction $I_a \approx 0.2S$ (classic SCS). P = total rainfall depth. Worked example: CN = 70 → S = 1000/70 − 10 = 4.29 in. P = 5.0 in → Ia = 0.86 in → Pe = 4.14 in. $Q = \frac{(4.14)^2}{4.14 + 4.29} = \frac{17.1}{8.43} = 2.03 \text{ in runoff depth}$ Multiply by area for runoff volume.

Composite CN For mixed land use within a drainage area: $CN_{composite} = \frac{\sum (CN_i \cdot A_i)}{\sum A_i}$ Convert to weighted CN before computing S — do not average runoff depths from separate sub-areas incorrectly.

Unit Hydrograph (Conceptual) 1-inch (or 1-mm) effective rainfall over duration Δt produces watershed outflow hydrograph. Convolution of effective rainfall with UH yields design hydrograph for detention routing. FE may ask peak discharge factor or base time qualitatively.

Detention and Retention Detention delays peak; retention holds volume for infiltration or reuse. Routing (storage-indication, reservoir routing) appears conceptually — outflow depends on stage-storage-discharge relationships.

Evaporation and Water Balance Reservoir yield problems: $\Delta S = P + I - E - O - Q$ Precipitation P, inflow I, evaporation E, outflow O, withdrawals Q, storage change ΔS — sign conventions matter.

FE Strategy 1. Identify method: Rational vs. CN vs. given hydrograph. 2. Compute tc before picking i. 3. Convert acres ↔ ft² ↔ cfs using handbook factors. 4. Sanity-check: Q increases with imperviousness and storm intensity. > Exam trap: Rational C is not CN/100 directly — they are different methods; do not interchange without handbook relationships. Hydrology underpins stormwater BMP sizing, culvert design, and flood studies — pair this section with open-channel flow for complete water resources preparation.

Design Storm Selection Return period (10-year, 25-year, 100-year) links to allowable conveyance capacity and floodplain regulations. Intensity increases with shorter duration on IDF curves — do not use 24-hour depth with 5-minute intensity without conversion.

Hydrograph Concepts Time to peak and peak discharge from unit hydrograph convolution depend on watershed time of concentration and storage. Reservoir routing attenuates peaks — flood control dams reduce downstream Q_peak at cost of higher stage upstream.

Urban Hydrology Modifications Depression storage on pavement captures initial rainfall before runoff begins. Infiltration models (Green-Ampt, Horton) appear conceptually — FE more often uses CN or Rational. Worked example — CN change: CN rises from 60 to 80 for suburbanization on 100 acres; 5-inch storm runoff depth increases from ~1.5 in to ~3.2 in using SCS equation — detention volume must roughly double if peak timing unchanged.

FE Time Savers Pre-convert acres to ft², in/hr to cfs using handbook factors before iterative steps. Label AMC I/II/III when problem states antecedent moisture.

Design Storm Selection Return period (10-year, 25-year, 100-year) links to allowable conveyance capacity and floodplain regulations. Intensity increases with shorter duration on IDF curves — do not use 24-hour depth with 5-minute intensity without conversion.

Hydrograph Concepts Time to peak and peak discharge from unit hydrograph convolution depend on watershed time of concentration and storage. Reservoir routing attenuates peaks — flood control dams reduce downstream Q_peak at cost of higher stage upstream.

Urban Hydrology Modifications Depression storage on pavement captures initial rainfall before runoff begins. Infiltration models (Green-Ampt, Horton) appear conceptually — FE more often uses CN or Rational. Worked example — CN change: CN rises from 60 to 80 for suburbanization on 100 acres; 5-inch storm runoff depth increases from ~1.5 in to ~3.2 in using SCS equation — detention volume must roughly double if peak timing unchanged.

FE Time Savers Pre-convert

Study Structure

• Skim the Quick Answer, then the table above
• Close with one practice quiz item before moving on