PE Exam Exam > PE Exam Notes > Civil Engineering (PE Civil) > Cheatsheet: Hydrology
Cheatsheet: Hydrology
1. Hydrologic Cycle and Water Balance
1.1 Hydrologic Cycle Components
| Component | Description |
|---|---|
| Precipitation | Water falling from atmosphere as rain, snow, sleet, or hail |
| Evaporation | Conversion of liquid water to vapor from open water bodies and soil |
| Transpiration | Water vapor release from plants through stomata |
| Evapotranspiration (ET) | Combined evaporation and transpiration losses |
| Infiltration | Movement of water from surface into soil |
| Percolation | Downward movement of water through soil to groundwater |
| Runoff | Water flowing over land surface to streams and water bodies |
| Interception | Precipitation captured by vegetation before reaching ground |
1.2 Water Balance Equation
| Formula | Variables |
|---|---|
| P = Q + ET + ΔS | P = Precipitation, Q = Runoff, ET = Evapotranspiration, ΔS = Change in storage |
| I = O ± ΔS | I = Total inflow, O = Total outflow, ΔS = Change in storage |
2. Precipitation
2.1 Precipitation Measurement
| Method | Details |
|---|---|
| Standard Rain Gauge | 8-inch diameter collector, 20-inch overflow can, measures depth in inches |
| Recording Rain Gauge | Weighing, tipping bucket, or float type for continuous recording |
| Radar | Weather radar estimates rainfall intensity over large areas |
2.2 Areal Precipitation Methods
| Method | Description |
|---|---|
| Arithmetic Mean | P̄ = (P₁ + P₂ + ... + Pₙ)/n; simple average of all gauges |
| Thiessen Polygons | P̄ = Σ(AᵢPᵢ)/A; weighted by area of influence for each gauge |
| Isohyetal Method | Contours of equal rainfall; most accurate but labor intensive |
2.3 Rainfall Intensity-Duration-Frequency (IDF)
| Parameter | Description |
|---|---|
| Intensity (i) | Rate of rainfall, in/hr or mm/hr |
| Duration (t) | Length of time over which intensity is measured |
| Return Period (T) | Average recurrence interval in years (2, 5, 10, 25, 50, 100 yr) |
| IDF Equation | i = a/(t + b)ⁿ where a, b, n are regional constants |
2.4 Design Storm Distributions
- SCS Type I: Pacific maritime climate with wet winters
- SCS Type IA: Coastal side of Sierra Nevada and Cascade Mountains
- SCS Type II: Remainder of U.S., moderate rainfall, most common
- SCS Type III: Gulf of Mexico and Atlantic coastal areas, high intensity
- 24-hour storm has peak intensity at specific time (e.g., Type II peaks at 12 hours)
2.5 Probable Maximum Precipitation (PMP)
- Greatest depth of precipitation for given duration that is physically possible over a drainage area
- Used for critical structures (dams, nuclear plants) with no acceptable risk of failure
- Determined from storm maximization and transposition studies
3. Evaporation and Evapotranspiration
3.1 Evaporation Estimation Methods
| Method | Formula/Description |
|---|---|
| Pan Evaporation | E = Kₚ × Eₚₐₙ; Kₚ = 0.70-0.85 for Class A pan |
| Meyer Equation | E = C(eₛ - eₐ)(1 + W/10); C = constant, e = vapor pressure, W = wind speed |
| Water Budget | E = P - Q - ΔS for lake or reservoir |
3.2 Evapotranspiration Methods
| Method | Formula |
|---|---|
| Penman Equation | Combines energy balance and aerodynamic methods |
| Blaney-Criddle | ET = kF; F = Σp(0.46T + 8.13); k = crop factor, p = % daylight hours, T = temp °F |
| Thornthwaite | Based on mean monthly temperature and daylight hours |
| FAO Penman-Monteith | Standard method using net radiation, temperature, humidity, wind speed |
3.3 Reference ET and Crop Coefficients
- Reference ET (ET₀): evapotranspiration from standardized grass surface
- Actual ET = Kc × ET₀ where Kc = crop coefficient
- Kc varies by crop type and growth stage (0.3-1.3)
4. Infiltration
4.1 Infiltration Concepts
| Term | Definition |
|---|---|
| Infiltration Capacity | Maximum rate at which soil can absorb water |
| Infiltration Rate (f) | Actual rate of water entry into soil, decreases with time |
| Cumulative Infiltration (F) | Total depth of water infiltrated over time |
4.2 Horton Infiltration Equation
| Component | Details |
|---|---|
| Formula | f = fc + (f₀ - fc)e⁻ᵏᵗ |
| Variables | f = infiltration rate, fc = final constant rate, f₀ = initial rate, k = decay constant, t = time |
| Cumulative | F = fct + [(f₀ - fc)/k](1 - e⁻ᵏᵗ) |
4.3 Green-Ampt Infiltration Model
| Component | Details |
|---|---|
| Formula | f = K[1 + (ψΔθ)/F] |
| Variables | K = hydraulic conductivity, ψ = wetting front suction head, Δθ = moisture deficit, F = cumulative infiltration |
| Application | Physically based, uses soil properties, suitable for modeling |
4.4 Philip Infiltration Equation
| Formula | Description |
|---|---|
| f = (S/2)t⁻⁰·⁵ + A | S = sorptivity, A = constant related to hydraulic conductivity |
| F = St⁰·⁵ + At | Cumulative infiltration form |
4.5 SCS Curve Number Method
| Component | Formula/Value |
|---|---|
| Runoff Equation | Q = (P - Ia)²/(P - Ia + S) for P > Ia; Q = 0 for P ≤ Ia |
| Initial Abstraction | Ia = 0.2S |
| Potential Retention | S = (1000/CN) - 10; S in inches, CN = curve number |
| Curve Number Range | CN: 0-100; higher CN = more runoff, less infiltration |
4.5.1 CN Values by Hydrologic Soil Group
- Group A: Low runoff potential, high infiltration (sand, gravel) CN = 30-49
- Group B: Moderate infiltration (sandy loam) CN = 50-69
- Group C: Slow infiltration (silty loam) CN = 70-79
- Group D: High runoff potential, very slow infiltration (clay) CN = 80-98
- CN varies with land use and antecedent moisture condition (AMC I, II, III)
5. Runoff and Hydrograph Analysis
5.1 Hydrograph Components
| Component | Description |
|---|---|
| Rising Limb | Increasing discharge from rainfall excess |
| Peak Flow (Qp) | Maximum discharge rate |
| Time to Peak (Tp) | Time from start of runoff to peak discharge |
| Recession Limb | Decreasing discharge after rainfall ends |
| Base Flow | Groundwater contribution to stream flow |
| Direct Runoff | Precipitation excess that reaches outlet, excludes base flow |
| Time of Concentration (Tc) | Time for water to travel from most remote point to outlet |
| Lag Time (tL) | Time from centroid of rainfall to peak discharge; tL ≈ 0.6Tc |
5.2 Time of Concentration Methods
5.2.1 Kirpich Equation
| Formula | Variables |
|---|---|
| Tc = 0.0078L⁰·⁷⁷S⁻⁰·³⁸⁵ | Tc in minutes, L = length in feet, S = slope in ft/ft |
5.2.2 NRCS Velocity Method
- Tc = Σ(Li/Vi) where Li = segment length, Vi = velocity
- Separate flow into sheet flow, shallow concentrated flow, channel flow
- Sheet flow: Tc = 0.007(nL)⁰·⁸/(P₂⁰·⁵S⁰·⁴); limited to 300 ft max
- n = Manning's roughness, L = length (ft), P₂ = 2-yr 24-hr rainfall (in), S = slope
5.2.3 Other Methods
- Kerby Equation: short overland flow on grass/turf
- Izzard Equation: paved surfaces
- Manning's Equation: open channel flow
5.3 Rational Method
| Component | Details |
|---|---|
| Formula | Q = CiA (US units) or Q = 0.278CiA (SI units) |
| Variables | Q = peak discharge (cfs or m³/s), C = runoff coefficient, i = rainfall intensity (in/hr or mm/hr), A = area (acres or ha) |
| Limitations | Small areas < 200="" acres,="" uniform="" rainfall,="" tc="">< storm=""> |
| Runoff Coefficient C | 0.05-0.30 (pervious), 0.70-0.95 (impervious); weighted average for mixed areas |
5.4 SCS/NRCS Unit Hydrograph Method
5.4.1 Dimensionless Unit Hydrograph
- Unit hydrograph: hydrograph from 1 inch of rainfall excess over duration D
- SCS provides dimensionless shape, scales to any watershed
- Time to Peak: Tp = D/2 + tL where D = rainfall duration, tL = lag time
- Peak Discharge: Qp = 484 A/Tp (US); A in mi², Tp in hours, Qp in cfs
- Qp = 2.08 A/Tp (SI); A in km², Tp in hours, Qp in m³/s
5.4.2 SCS Lag Time
| Formula | Variables |
|---|---|
| tL = (L⁰·⁸(S + 1)⁰·⁷)/(1900Y⁰·⁵) | tL = lag (hr), L = hydraulic length (ft), S = potential retention (in), Y = average slope (%) |
| Alternative | tL = 0.6Tc where Tc = time of concentration |
5.4.3 Synthetic Unit Hydrograph Application
- Select rainfall distribution (Type I, IA, II, or III)
- Calculate Tc and tL
- Determine D (duration): D = 0.133Tc to 0.2Tc
- Calculate excess precipitation using CN method
- Generate unit hydrograph ordinates
- Convolve with excess precipitation to get direct runoff hydrograph
- Add base flow for total hydrograph
5.5 Hydrograph Convolution
- Qn = Σ(Pi × Un-i+1) for i = 1 to n
- Qn = discharge at time n, Pi = excess rainfall at time i, U = unit hydrograph ordinate
- Used to generate hydrograph from excess rainfall and unit hydrograph
6. Stream Flow and Flow Frequency Analysis
6.1 Stream Flow Measurement
| Method | Description |
|---|---|
| Stage-Discharge Rating | Relationship between water level and flow rate; Q = C(h - h₀)ⁿ |
| Velocity-Area Method | Q = Σ(ViAi); cross section divided into segments |
| Current Meter | Measures velocity at 0.6 depth or average of 0.2 and 0.8 depth |
| Weirs and Flumes | Calibrated structures with known head-discharge relationships |
6.2 Flow Duration Curve
- Plot of discharge versus percent of time flow exceeded
- Shows variability of flow: steep curve = variable flow, flat curve = sustained flow
- Q50 = median flow, Q90 = low flow (exceeded 90% of time)
- Used for water supply, hydropower, aquatic habitat assessment
6.3 Flood Frequency Analysis
6.3.1 Weibull Plotting Position
| Formula | Variables |
|---|---|
| P = m/(n + 1) | P = exceedance probability, m = rank (1 = largest), n = number of years |
| T = 1/P = (n + 1)/m | T = return period in years |
6.3.2 Log-Pearson Type III Distribution
- Standard method recommended by federal agencies (Bulletin 17C)
- log Q = mean(log Q) + K × SD(log Q)
- K = frequency factor (function of skew coefficient and return period)
- Uses logarithms (base 10) of annual peak flows
- Calculate mean, standard deviation, and skew coefficient of log-transformed data
- Regional skew maps available; weighted skew = (MSE(regional) × station skew + MSE(station) × regional skew)/(MSE(regional) + MSE(station))
6.3.3 Gumbel Extreme Value Distribution
| Formula | Variables |
|---|---|
| XT = X̄ + K × σ | XT = flow for return period T, X̄ = mean, σ = standard deviation |
| K = (yT - ȳn)/Sn | yT = -ln[-ln(1-1/T)], ȳn and Sn from tables for sample size n |
6.4 Return Period and Exceedance Probability
| Concept | Formula |
|---|---|
| Exceedance Probability | P = 1/T where T = return period |
| Risk of Exceedance | R = 1 - (1 - 1/T)ⁿ where n = project life in years |
- 100-year flood: 1% annual chance of exceedance, 26% chance over 30 years
- Return period does not mean event occurs every T years
6.5 Base Flow Separation
- Separates direct runoff from groundwater contribution
- Straight-line method: connect start of rise to point on recession N days after peak
- N = A⁰·² where A = drainage area in square miles; N in days
- Constant slope method: project pre-storm recession under hydrograph
7. Groundwater Hydrology
7.1 Aquifer Properties
| Property | Definition |
|---|---|
| Porosity (n) | n = Vv/VT; ratio of void volume to total volume |
| Specific Yield (Sy) | Volume of water released per unit volume of aquifer per unit decline in head |
| Specific Retention (Sr) | Volume of water retained in aquifer; n = Sy + Sr |
| Storativity (S) | Volume released per unit area per unit head decline; S = Sy (unconfined), S = Ss×b (confined) |
| Specific Storage (Ss) | Volume released per unit volume per unit head decline |
| Hydraulic Conductivity (K) | Rate of flow through unit area under unit gradient; units of velocity |
| Transmissivity (T) | T = Kb; rate of flow through vertical strip of unit width; b = aquifer thickness |
7.2 Darcy's Law
| Formula | Variables |
|---|---|
| Q = -KiA = -KA(dh/dl) | Q = discharge, K = hydraulic conductivity, i = hydraulic gradient, A = cross-sectional area |
| v = Ki = K(dh/dl) | v = Darcy velocity (specific discharge) |
| vs = v/n = Ki/n | vs = seepage velocity (actual pore velocity), n = porosity |
7.3 Well Hydraulics - Steady State
7.3.1 Confined Aquifer (Thiem Equation)
| Formula | Description |
|---|---|
| Q = 2πT(h₂ - h₁)/ln(r₂/r₁) | Q = discharge, T = transmissivity, h = head, r = radius |
| T = Q×ln(r₂/r₁)/(2π(h₂ - h₁)) | Solve for transmissivity from two observation wells |
7.3.2 Unconfined Aquifer (Dupuit Equation)
| Formula | Description |
|---|---|
| Q = πK(h₂² - h₁²)/ln(r₂/r₁) | Q = discharge, K = hydraulic conductivity, h = saturated thickness |
| K = Q×ln(r₂/r₁)/(π(h₂² - h₁²)) | Solve for K from two observation wells |
7.4 Well Hydraulics - Transient Flow
7.4.1 Theis Equation (Confined Aquifer)
| Formula | Description |
|---|---|
| s = (Q/4πT)W(u) | s = drawdown, Q = discharge, T = transmissivity, W(u) = well function |
| u = r²S/(4Tt) | u = dimensionless parameter, r = distance, S = storativity, t = time |
| W(u) = -0.5772 - ln(u) + u - u²/2×2! + u³/3×3! - ... | Well function (infinite series); tabulated values available |
7.4.2 Cooper-Jacob Approximation
| Formula | Application |
|---|---|
| s = (2.3Q/4πT)log(2.25Tt/r²S) | Valid for u < 0.01="" (late="" time);="" straight="" line="" on="" semi-log=""> |
| T = 2.3Q/(4πΔs) | Δs = drawdown change per log cycle of time |
| S = 2.25Tt₀/r² | t₀ = time intercept where straight line extrapolates to s = 0 |
7.5 Groundwater Flow Equation
- Confined: ∂²h/∂x² + ∂²h/∂y² = (S/T)(∂h/∂t) (2D horizontal flow)
- Unconfined: K(∂²h²/∂x² + ∂²h²/∂y²) = 2Sy(∂h/∂t) (Boussinesq equation)
- Steady state: ∂h/∂t = 0, reduces to Laplace equation
7.6 Safe Yield and Groundwater Mining
- Safe Yield: maximum rate of withdrawal without adverse effects
- Adverse effects: depletion of storage, saltwater intrusion, land subsidence, stream depletion
- Sustainable yield considers long-term balance and environmental impacts
8. Reservoir and Storage Routing
8.1 Reservoir Storage Concepts
| Term | Definition |
|---|---|
| Active Storage | Volume between normal low level and top of conservation pool |
| Dead Storage | Volume below lowest operational level |
| Flood Storage | Volume reserved for temporary flood detention |
| Surcharge Storage | Volume above spillway crest, temporary during floods |
8.2 Reservoir Routing - Level Pool Method
8.2.1 Storage Indication Method
| Equation | Description |
|---|---|
| I₁ + I₂ - O₁ - O₂ = 2(S₂ - S₁)/Δt | Continuity equation for time interval Δt |
| (2S₂/Δt + O₂) = (I₁ + I₂) + (2S₁/Δt - O₁) | Storage indication form; solve iteratively |
| Procedure | Plot (2S/Δt + O) vs O; route inflow hydrograph to find outflow |
8.3 Channel Routing - Muskingum Method
| Component | Details |
|---|---|
| Storage Equation | S = K[xI + (1-x)O]; K = travel time, x = weighting factor (0-0.5) |
| Routing Coefficients | C₀ = (-Kx + 0.5Δt)/(K - Kx + 0.5Δt) |
| C₁ = (Kx + 0.5Δt)/(K - Kx + 0.5Δt) | |
| C₂ = (K - Kx - 0.5Δt)/(K - Kx + 0.5Δt); C₀ + C₁ + C₂ = 1 | |
| Routing Equation | O₂ = C₀I₂ + C₁I₁ + C₂O₁ |
| Parameter x | x = 0: maximum attenuation (reservoir); x = 0.5: no attenuation (translation only); x = 0.2-0.3: typical rivers |
8.4 Spillway Hydraulics
8.4.1 Ogee Spillway
| Formula | Description |
|---|---|
| Q = CLH³/² | Q = discharge, C = coefficient (3.0-4.0), L = effective length, H = head |
| Effective Length | L = L' - 2(NKp + Ka)H; L' = crest length, N = number of piers, Kp = pier contraction, Ka = abutment contraction |
8.4.2 Gated Spillway
- Q = CdAv where Cd = discharge coefficient (0.6-0.8), A = gate opening area, v = approach velocity
- Free flow or submerged flow conditions depending on tailwater
9. Urban Hydrology
9.1 Effects of Urbanization
- Increased impervious area reduces infiltration
- Higher peak flows and volumes
- Reduced time to peak and time of concentration
- Decreased base flow and groundwater recharge
- Increased frequency of bankfull flows
- Water quality degradation from pollutants
9.2 Composite Curve Number
- CNc = Σ(Ai × CNi)/Σ Ai for weighted composite
- Account for different land uses, soil types, and cover conditions
- Connected impervious areas have higher CN than unconnected
9.3 Detention Basin Design
9.3.1 Detention Basin Concepts
| Type | Description |
|---|---|
| Detention | Temporary storage with complete drawdown, normally dry |
| Retention | Permanent pool, captures and infiltrates or evaporates volume |
| On-line | All flow passes through facility |
| Off-line | Only excess flow diverted to facility |
9.3.2 Design Objectives
- Peak flow reduction: post-development ≤ pre-development for design storm
- Volume control: capture water quality volume or runoff reduction
- Water quality treatment: settling, filtration, biological uptake
- Determine required storage volume and outlet structure sizing
9.3.3 Outlet Structures
- Orifice: Q = CdA√(2gh); Cd ≈ 0.6, A = opening area, g = 32.2 ft/s², h = head
- Weir: Q = CLH³/²; C = 3.0-3.3 for sharp-crested, L = length, H = head
- Multiple stages: low-flow orifice, mid-level weir, high-flow spillway
- Riser pipe with trash rack: prevent clogging, emergency overflow
9.4 Best Management Practices (BMPs)
| BMP Type | Function |
|---|---|
| Bioretention | Infiltration, filtering, uptake; landscaped depression with engineered soil |
| Permeable Pavement | Infiltration through voids in pavement structure |
| Green Roof | Retention, evapotranspiration; vegetation on rooftop |
| Swale | Conveyance, infiltration, filtering; vegetated channel |
| Infiltration Trench | Subsurface infiltration; gravel-filled trench |
| Constructed Wetland | Treatment through settling, uptake, filtration |
9.5 Water Quality Volume
- WQV = capture and treat runoff from small frequent storms
- Common standard: 1.0 to 1.5 inches of runoff over watershed area
- WQV (acre-ft) = (P)(Rv)(A)/12; P = depth (in), Rv = 0.05 + 0.009(I) where I = % impervious
- First flush contains majority of pollutant load
10. Hydraulic Structures and Culverts
10.1 Culvert Types and Flow Conditions
| Flow Type | Characteristics |
|---|---|
| Inlet Control | Headwater, inlet geometry, barrel slope control flow; downstream conditions do not affect capacity |
| Outlet Control | Full culvert length, roughness, entrance loss, exit loss, tailwater affect capacity |
| Type I (Inlet, Unsubmerged) | Free surface through barrel, critical depth at inlet |
| Type II (Inlet, Submerged) | Inlet submerged, orifice flow at entrance |
| Type III (Outlet, Free) | Flows part full or full, exit not submerged |
| Type IV (Outlet, Submerged) | Full flow, both inlet and outlet submerged |
10.2 Culvert Capacity - Inlet Control
| Condition | Formula |
|---|---|
| Unsubmerged (Weir) | Q/A = K(HW/D)ᵐ; Q = flow, A = area, HW = headwater depth, D = diameter/height |
| Submerged (Orifice) | Q/A = K(HW/D - 0.5S)⁰·⁵; S = culvert slope |
| Nomographs | FHWA HDS-5 nomographs for various inlet configurations |
10.3 Culvert Capacity - Outlet Control
| Component | Formula |
|---|---|
| Energy Equation | HW = H + hL - LSo; H = depth at outlet, hL = losses, L = length, So = slope |
| Friction Loss | hf = (n²V²L)/(2.22R⁴/³) where n = Manning's n, R = hydraulic radius |
| Entrance Loss | he = keV²/(2g); ke = 0.2 to 0.9 depending on inlet type |
| Exit Loss | Usually neglected or V²/(2g) for sudden expansion |
| Total Head Loss | hL = he + hf = (ke + 29n²L/R⁴/³)V²/(2g) |
10.4 Inlet Types and Entrance Loss Coefficients
| Inlet Type | ke Value |
|---|---|
| Projecting (no headwall) | 0.9 |
| Headwall, square edge | 0.5 |
| Headwall, groove end | 0.2 |
| Headwall, beveled edge | 0.2 |
| Wingwall flares (30-75°) | 0.4-0.5 |
| Side-tapered inlet | 0.2 |
10.5 Manning's Roughness Coefficients
| Material | Manning's n |
|---|---|
| Concrete pipe | 0.012-0.015 |
| Corrugated metal pipe (CMP) | 0.024-0.027 |
| Polyethylene (smooth wall HDPE) | 0.012 |
| Corrugated HDPE | 0.020-0.025 |
| Cast iron | 0.013-0.015 |
11. Open Channel Flow
11.1 Manning's Equation
| Formula | Units |
|---|---|
| Q = (1.486/n)AR²/³S¹/² | US Customary: Q in cfs, A in ft², R in ft |
| Q = (1/n)AR²/³S¹/² | SI: Q in m³/s, A in m², R in m |
| V = (1.486/n)R²/³S¹/² | Velocity form: V = Q/A |
- A = cross-sectional area, R = hydraulic radius = A/P, P = wetted perimeter, S = slope
11.2 Normal Depth and Critical Depth
| Depth Type | Definition |
|---|---|
| Normal Depth (yn) | Uniform flow depth where gravity force equals friction; determined from Manning's equation |
| Critical Depth (yc) | Depth at minimum specific energy; Fr = 1 |
| Froude Number | Fr = V/√(gy); y = hydraulic depth = A/T; T = top width |
| Subcritical Flow | Fr < 1;="" y=""> yc; tranquil, controlled from downstream |
| Supercritical Flow | Fr > 1; y < yc;="" rapid,="" controlled="" from=""> |
| Critical Flow | Fr = 1; y = yc; minimum specific energy |
11.3 Specific Energy and Critical Flow
| Concept | Formula |
|---|---|
| Specific Energy | E = y + V²/(2g) = y + Q²/(2gA²) |
| Critical Condition | dE/dy = 0; Q²T/(gA³) = 1 |
| Rectangular Channel | yc = (Q²/gb²)¹/³ where b = width; Vc = √(gyc) |
11.4 Channel Geometry Formulas
11.4.1 Rectangular Channel
- A = by where b = width, y = depth
- P = b + 2y
- R = by/(b + 2y)
- T = b
11.4.2 Trapezoidal Channel
- A = (b + zy)y where z = side slope (H:V)
- P = b + 2y√(1 + z²)
- R = (b + zy)y/(b + 2y√(1 + z²))
- T = b + 2zy
11.4.3 Triangular Channel
- A = zy²
- P = 2y√(1 + z²)
- R = zy/(2√(1 + z²))
- T = 2zy
11.4.4 Circular Pipe Flowing Partially Full
- A = (D²/4)(θ - sinθ) where θ in radians, θ = 2cos⁻¹(1 - 2y/D)
- P = Dθ/2
- R = D(θ - sinθ)/(4θ)
- T = D sin(θ/2)
- Maximum capacity at y/D ≈ 0.94
11.5 Gradually Varied Flow
- dy/dx = (S - Sf)/(1 - Fr²) where S = channel slope, Sf = friction slope
- M1 profile: mild slope, y > yn > yc, backwater curve
- M2 profile: mild slope, yn > y > yc, drawdown curve
- S2 profile: steep slope, yc > y > yn, drawdown curve
- Hydraulic jump: transition from supercritical to subcritical
12. Water Quality and Pollutant Loading
12.1 Common Stormwater Pollutants
| Pollutant | Sources and Effects |
|---|---|
| Total Suspended Solids (TSS) | Sediment from erosion; turbidity, habitat degradation, carries other pollutants |
| Nutrients (N, P) | Fertilizers, organic matter; eutrophication, algal blooms |
| Metals (Pb, Zn, Cu, Cd) | Vehicles, roofs, industry; bioaccumulation, toxicity |
| Hydrocarbons | Petroleum products, vehicles; toxicity to aquatics |
| Bacteria/Pathogens | Animal waste, sewage; human health risk |
| Chlorides | Deicing salts; aquatic toxicity, groundwater contamination |
12.2 Event Mean Concentration (EMC)
- EMC = total pollutant mass/total runoff volume for storm event
- Used to characterize pollutant concentration in runoff
- Varies by land use: residential, commercial, industrial, highway
- Mass loading = EMC × runoff volume
12.3 BMP Pollutant Removal Mechanisms
| Mechanism | Pollutants Removed |
|---|---|
| Settling/Sedimentation | TSS, particulate-bound metals and nutrients |
| Filtration | TSS, metals, bacteria, some dissolved pollutants |
| Biological Uptake | Nutrients (N, P), some metals |
| Adsorption | Metals, hydrocarbons, phosphorus |
| Infiltration | Volume reduction, many pollutants through soil processes |
12.4 Treatment Train Approach
- Multiple BMPs in series provide greater pollutant removal
- Sequence: pretreatment (settling) → primary treatment (bioretention) → polishing (wetland)
- Each BMP addresses different pollutants and mechanisms
- Redundancy improves reliability and performance
13. Low Impact Development (LID)
13.1 LID Principles
- Minimize impervious surfaces
- Maintain natural drainage patterns and sheet flow
- Disconnect impervious areas from direct drainage to streams
- Promote infiltration and evapotranspiration
- Distributed small-scale controls versus end-of-pipe solutions
- Mimic pre-development hydrology
13.2 LID Techniques
| Technique | Application |
|---|---|
| Rain Barrels/Cisterns | Capture roof runoff for reuse or slow release |
| Downspout Disconnection | Direct roof runoff to pervious areas instead of storm drain |
| Rain Gardens | Shallow planted depressions for infiltration and treatment |
| Bioretention Cells | Engineered soil mix with underdrain, high infiltration rate |
| Vegetated Filter Strips | Grassed areas for sheet flow treatment |
| Permeable Pavement | Parking lots, paths, low-traffic areas |
| Green Roofs | Vegetated roof systems for retention and evapotranspiration |
| Tree Box Filters | Streetscape stormwater planters |
13.3 Infiltration Testing
- Double-ring infiltrometer: measure in-situ infiltration rate
- Minimum rate of 0.5 in/hr for infiltration practices
- Test at depth of proposed facility bottom
- Seasonal high water table must be 2-4 ft below facility bottom
- Soil permeability: sand/loamy sand preferred, avoid clay
14. Floodplain Management
14.1 Floodplain Definitions
| Term | Definition |
|---|---|
| Base Flood | Flood with 1% annual chance of exceedance (100-year flood) |
| Base Flood Elevation (BFE) | Water surface elevation of base flood |
| Special Flood Hazard Area (SFHA) | Area inundated by base flood (Zone A, AE, AH, AO, V, VE) |
| Floodway | Channel plus adjacent areas required to convey base flood with no more than 1 ft rise |
| Freeboard | Safety factor above BFE (1-3 ft typical) |
14.2 FEMA Flood Zones
| Zone | Description |
|---|---|
| A | 100-year floodplain, no BFE determined |
| AE | 100-year floodplain, BFE determined |
| AH | Shallow flooding (1-3 ft), ponding areas |
| AO | Shallow flooding (1-3 ft), sheet flow areas |
| V, VE | Coastal high hazard area with wave action |
| X (shaded) | 0.2% annual chance (500-year floodplain) |
| X (unshaded) | Minimal flood hazard, outside 500-year floodplain |
14.3 National Flood Insurance Program (NFIP)
- Communities adopt floodplain management ordinances to participate
- Flood insurance available for structures in participating communities
- Substantial improvement/damage threshold: 50% of market value
- Lowest floor elevation requirements: BFE + freeboard minimum
- No-rise certification required for floodway development
14.4 Floodplain Hydraulic Analysis
- HEC-RAS: standard software for 1D river hydraulics and floodplain delineation
- Steady flow analysis: Manning's equation, energy balance between sections
- Water surface profile computed upstream from known boundary condition
- Effective models: adopted by FEMA for regulatory floodplain
- Required cross sections at representative locations, bridges, culverts
15. Erosion and Sediment Control
15.1 Soil Erosion Processes
| Type | Description |
|---|---|
| Sheet Erosion | Uniform removal of soil layer by overland flow |
| Rill Erosion | Small channels formed by concentrated flow |
| Gully Erosion | Large channels that cannot be removed by tillage |
| Stream Bank Erosion | Channel widening and incision from stream flow |
15.2 Universal Soil Loss Equation (USLE)
| Component | Description |
|---|---|
| Formula | A = RKLSCP |
| A | Soil loss (tons/acre/year) |
| R | Rainfall erosivity factor (from isoerodent maps) |
| K | Soil erodibility factor (0.02-0.69, higher = more erodible) |
| L | Slope length factor: (λ/72.6)ᵐ where λ = slope length (ft) |
| S | Slope steepness factor: function of slope % |
| C | Cover management factor (0-1, bare soil = 1) |
| P | Support practice factor (0-1, no practice = 1) |
15.3 Erosion Control Practices
| Practice | Application |
|---|---|
| Mulching | Temporary protection of exposed soil; straw, wood chips |
| Seeding/Sodding | Permanent vegetative stabilization |
| Erosion Control Blankets | Biodegradable or synthetic mats for slope protection |
| Silt Fence | Filter fabric barrier for sheet flow, max 0.5 cfs/ft |
| Sediment Basin | Temporary pond for concentrated flow, design for 1800 ft³ per disturbed acre |
| Check Dams | Stone or fiber logs in swales to reduce velocity |
| Inlet Protection | Filter around storm drain inlets |
15.4 Construction Site Requirements
- NPDES Construction General Permit for sites ≥ 1 acre
- Stormwater Pollution Prevention Plan (SWPPP) required
- Minimize disturbed area and duration of exposure
- Perimeter controls before land disturbance
- Stabilize within 7-14 days of final grade
- Inspect and maintain controls weekly and after 0.5 inch rain
The document Cheatsheet: Hydrology is a part of the PE Exam Course Civil Engineering (PE Civil).
All you need of PE Exam at this link: PE Exam
About this Document
Apr 20, 2026
Last updated
Related Exams
Document Description: Cheatsheet: Hydrology for PE Exam 2026 is part of Civil Engineering (PE Civil) preparation.
The notes and questions for Cheatsheet: Hydrology have been prepared according to the PE Exam exam syllabus. Information about Cheatsheet: Hydrology covers topics
like and Cheatsheet: Hydrology Example, for PE Exam 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Cheatsheet: Hydrology.
Introduction of Cheatsheet: Hydrology in English is available as part of our Civil Engineering (PE Civil)
for PE Exam & Cheatsheet: Hydrology in Hindi for Civil Engineering (PE Civil) course.
Download more important topics related with notes, lectures and mock test series for PE Exam
Exam by signing up for free. PE Exam: Cheatsheet: Hydrology
Description
Cheatsheet: Hydrology of Civil Engineering to help you remember important concepts with short tricks. Start learning for PE Exam exam & improve retention with EduRev.
Information about Cheatsheet: Hydrology
In this doc you can find the meaning of Cheatsheet: Hydrology defined & explained in the simplest way possible. Besides explaining types of
Cheatsheet: Hydrology theory, EduRev gives you an ample number of questions to practice Cheatsheet: Hydrology tests, examples and also practice PE Exam
tests
Related Searches
Viva Questions, mock tests for examination, past year papers, Cheatsheet: Hydrology, Sample Paper, Free, video lectures, Important questions, Cheatsheet: Hydrology, ppt, Exam, pdf , Objective type Questions, Summary, Cheatsheet: Hydrology, shortcuts and tricks, study material, Previous Year Questions with Solutions, Semester Notes, Extra Questions, practice quizzes, MCQs;