CELE Hydraulics & Fluid Mechanics — Hydrology and Water SupplyStudy Notes

The hydrologic cycle describes the continuous movement of water across Earth's surface and atmosphere. Precipitation (rainfall or snow) falls on a catchment. Some is intercepted by vegetation and never reaches the ground; some infiltrates into soil (recharge); some flows over the surface as runoff; and some evaporates or is transpired by plants. Engineering hydrology quantifies the runoff portion—the water that must be conveyed by drainage systems, stored in reservoirs, or managed through flood control. The water-balance equation over a time period is: Precipitation = Runoff + Infiltration + Evapotranspiration ± Change in Storage For design purposes, the runoff coefficient C (ranging from 0.1 for permeable lawns to 0.95 for impervious pavement) captures the fraction of rainfall that becomes runoff, lumping infiltration and evaporation into the (1 − C) portion. This simplification is why the rational method works well for small, uniform catchments.

The rational method estimates the peak discharge (maximum flow rate) from a catchment during a design storm. It is the most widely used method for small catchments (< 100 km²) and is mandated in many Philippine drainage standards (NSCP 2015 Section 9). The fundamental equation is: Q = C × i × A Where: - Q = peak discharge (flow rate) - C = runoff coefficient (dimensionless, 0 < C < 1) - i = rainfall intensity (depth per unit time) - A = catchment area In SI practical units (commonly used in the Philippines): - i is in mm/hr - A is in hectares (ha) - Q is in m³/s With these units, the equation becomes: Q (m³/s) = [C × i (mm/hr) × A (ha)] / 360 The 360 factor is a unit-conversion constant (1 ha = 10,000 m², 1 hr = 3,600 s; thus 10,000/3,600 ≈ 2.78, and the reciprocal factored into intensity gives 360). **Key Assumption**: The entire catchment contributes to the peak discharge. This occurs when the rainfall duration equals or exceeds the time of concentration (t_c), which is the time required for water to flow from the most distant point in the catchment to the outlet. Therefore, the design intensity i is the rainfall intensity for a return period and duration equal to t_c. **Time of Concentration (t_c)**: This is estimated from empirical formulas or field observation. Common methods include: 1. **Kirpich formula** (for overland flow on natural slopes): t_c (min) = 0.0195 × [L / S^0.5]^0.77 where L is the longest path length (m) and S is the average slope (m/m). 2. **California Culverts Practice**: Sums t_c for overland flow (typically 5–10 min on grassed slopes) and channel flow (calculated from velocity in the stream). 3. **Philippine standards**: NSCP 2015 recommends t_c = 10 min as a minimum for urban drainage design; longer t_c (15–30 min) may be used for large catchments or natural streams. **Runoff Coefficient C**: This varies widely and depends on: - **Surface type**: roofs and pavement (0.85–0.95); commercial/industrial zones (0.70–0.90); residential with gardens (0.40–0.70); parks and lawns (0.10–0.35); forest and natural vegetation (0.05–0.20). - **Soil infiltration**: sandy soils have lower C; clay has higher C. - **Antecedent moisture**: wet soils reduce C; dry soils increase infiltration and reduce C. - **Slope**: steeper terrain increases runoff, raising C. For mixed catchments, the weighted average C is used: C_weighted = (C₁ × A₁ + C₂ × A₂ + ... ) / (A₁ + A₂ + ...) **Rainfall Intensity i**: Obtained from Intensity–Duration–Frequency (IDF) curves specific to the location and return period. In the Philippines, PAGASA (Philippine Atmospheric, Geophysical and Astronomical Services Administration) provides IDF data for major cities (e.g., Metro Manila, Cebu, Davao). As duration increases, intensity decreases; the design duration matches t_c. **Return Period Selection**: This is a design decision reflecting the acceptable risk of exceedance: - Minor drainage (urban streets, parking lots): 2–5 years - Primary drainage (major roads, residential areas): 5–10 years - Major drainage (bridge waterways, urban rivers, NSCP 2015): 10–50 years - Extreme projects (dams, critical infrastructure): 50–100 years or greater

While the rational method gives the peak discharge, engineers often need the total volume of runoff from a storm. This is essential for designing detention basins, stormwater ponds, and water-harvesting systems. The runoff volume over a storm event is: V_runoff = C × P × A Where: - V_runoff = total runoff volume - C = runoff coefficient - P = total rainfall depth over the event - A = catchment area All units must be consistent. Common combinations: - P in mm, A in m²: V in 10³ m³ (or ML, megalitres) - P in m, A in m²: V in m³ - P in mm, A in hectares: V in m³ (since 1 ha = 10⁴ m² and 1 mm = 10⁻³ m, the product is 10 m³/ha per mm) **Relationship to Peak Discharge**: The runoff volume is independent of how the rainfall is distributed in time; the peak discharge depends on the intensity during the critical duration (t_c). A 100 mm storm produces the same runoff volume on a given catchment regardless of whether it falls in 1 hour (intensity 100 mm/hr) or 10 hours (intensity 10 mm/hr), but the peak discharge is far higher in the 1-hour case. **Design Storm Depth**: For volume calculations, the engineer selects a design rainfall depth (e.g., 24-hour rainfall for a 10-year return period). These are typically published by PAGASA or inferred from IDF curves.

Rainfall data in the Philippines is compiled by PAGASA and presented as IDF curves—graphs showing the relationship between rainfall duration (minutes to hours), intensity (mm/hr), and return period (years). These curves are region-specific and essential for rational-method calculations. **IDF Curve Interpretation**: - **X-axis**: Duration (e.g., 5, 10, 15, 30, 60, 120 min) - **Y-axis**: Intensity (mm/hr) - **Multiple curves**: One curve per return period (e.g., 2-yr, 5-yr, 10-yr, 25-yr, 50-yr, 100-yr) - **Shape**: Intensity decreases as duration increases; a 5-minute storm is far more intense than a 2-hour storm. **Procedure**: 1. Estimate time of concentration t_c for the catchment. 2. From the IDF curve for the chosen return period and duration = t_c, read off the intensity i (mm/hr). 3. Apply the rational formula Q = (C × i × A) / 360. **Philippine Context**: PAGASA provides IDF tables and curves for major cities (Manila, Cebu, Davao, Cagayan de Oro, etc.). For locations not covered, data from the nearest station is interpolated, or historical rainfall records are analyzed to construct a local IDF. The NSCP 2015 (Section 9) recommends using a 10-year return period for primary urban drainage and 25 years for major waterways. **Important Note**: IDF curves assume point rainfall. For large catchments (> 50 km²), an areal reduction factor (typically 0.85–0.95) is applied to account for non-uniform rainfall distribution.

Water supply design requires estimation of the quantity of water needed by a community or facility. Demand varies with time (daily, hourly, seasonal), population growth, and usage patterns. The engineer must size sources, storage, and distribution to meet peak demands reliably. **Average Daily Demand (ADD)**: ADD = Population × Per Capita Consumption (L/person/day) Per-capita consumption varies by region, income level, and climate: - Rural/low-income areas: 80–100 L/person/day - Urban residential: 100–150 L/person/day - Metro areas (Manila, Cebu): 150–200 L/person/day - Industrial/commercial areas: Additional demand (varies by facility) The RA 544 (Public Works and Highways) and National Water Code (Presidential Decree 1067) define minimum service standards; municipal water utilities often use 150 L/person/day for planning. **Peak Demands**: Demand is not uniform. Peak demands occur during specific hours (morning, evening) and seasons. Designers must size conveyance and storage for these peaks: 1. **Maximum Day Demand (MDD)**: The highest single-day demand in a year, typically 1.3 to 1.5 times ADD. Common practice: MDD ≈ 1.5 × ADD. 2. **Peak Hour Demand (PHD)**: The highest hourly demand during the peak day, typically 2.0 to 3.0 times ADD. Common practice: PHD ≈ 2.5 × ADD (or 1.6 to 2.0 × MDD). 3. **Design Factors**: These are project-specific. Small systems in rapid-growth areas use higher factors (e.g., MDD = 1.8 × ADD, PHD = 3.5 × ADD) to accommodate growth; mature systems use lower factors. **Example Demand Profile**: - Population: 50,000 - Per-capita: 150 L/person/day - ADD = 50,000 × 150 = 7,500,000 L/day = 7,500 m³/day - MDD ≈ 1.5 × 7,500 = 11,250 m³/day - PHD ≈ 2.5 × 7,500 = 18,750 m³/day (or ≈ 1.67 × MDD) **System Components Sized for Each Demand**: - **Intake/well**: Sized for PHD or a sustained maximum rate; must have storage to buffer intermittent demand. - **Transmission main**: Sized for MDD or PHD depending on whether storage exists downstream. - **Reservoir**: Sized from mass balance (inflow vs. daily demand variation). - **Distribution network**: Sized for PHD at the furthest consumer (often critical for fire-flow requirements as well). **Water Loss and Unaccounted Water**: Philippine water utilities often experience 30–50% water loss due to leakage, unauthorized connections, and metering errors. System demand must account for this: Actual production = ADD / (1 − loss fraction). For design, assume loss upfront.

Civil engineers select water sources based on availability, reliability, quality, and cost. The Philippines has abundant water resources but faces seasonal and regional variability, particularly during dry seasons (November–April) and in Mindanao and Visayas where water stress is more acute. **Surface Water Sources**: 1. **Rivers and streams**: Direct intake or ponded water. Advantages: high yield, accessible. Disadvantages: seasonal flow variation, flood risk, quality issues (silt, pollution). 2. **Lakes and natural reservoirs**: Relatively stable; fewer quality issues if in forested catchments. Limited availability in the Philippines; most designed reservoirs (like Laguna de Bay, San Roque Reservoir) are engineered. 3. **Engineered reservoirs (dams)**: Planned storage to meet seasonal demand. Requires hydrologic analysis (inflow, outflow, spillway capacity per NSCP 2015 Section 8) and mass-balance design. **Groundwater Sources**: 1. **Wells and boreholes**: Access to deep aquifers; generally stable yield and quality. Disadvantages: high drilling cost, depletion risk in overexploited areas, requires pumping energy. 2. **Spring discharge**: Natural groundwater outlet; low-cost collection if quantity is adequate. 3. **Infiltration galleries**: Shallow, riverbed wells; moderate yield, moderate cost. **Well Hydraulics (Basic Concepts)**: For a single well pumped at steady rate Q, the water table around the well drops (drawdown). The drawdown s at distance r from the well is given by: s = (Q / 2πT) × ln(R / r) (Theis equation, confined aquifer) Where: - Q = pumping rate (m³/day or m³/s) - T = transmissivity of the aquifer (m²/day or m²/s) - R = radius of influence (distance where drawdown becomes negligible, typically 100–300 m) - r = distance from well center - s = drawdown at radius r Transmissivity T = K × b, where K is hydraulic conductivity (m/day) and b is aquifer thickness (m). **Well Yield**: The yield is limited by: 1. The available drawdown (difference between static water table and pump inlet, minus safety margin). 2. The transmissivity of the aquifer. 3. Interference from multiple wells (in a well field, drawdown is cumulative). **Practical Design**: For a municipal well field: 1. Conduct a pumping test to estimate T and the aquifer's storativity (S). 2. Calculate the allowable drawdown (typically 0.6–0.8 of the initial head, leaving 0.2–0.4 as safety margin). 3. Use the Theis or Jacob-Cooper formula to estimate steady-state yield. 4. Design the pump and treatment plant for the estimated yield; include redundancy (multiple wells or backup sources for reliability). **Surface-Water Reservoir Design**: A reservoir is sized to store water during the wet season and release it during the dry season. The mass-balance method (or continuity equation) is applied: Storage required = ∫ (Inflow − Outflow) dt over the critical dry period Inflow is estimated from the hydrologic analysis of the catchment (runoff, as discussed earlier). Outflow is the demand (ADD × number of days). For the Philippines, the critical dry season is typically March–May; storage is designed to cover 90–120 days without significant inflow.

A complete water supply system comprises intake, treatment, transmission, storage, distribution, and wastewater disposal. Each component is sized based on demand profiles, source characteristics, and regulatory standards. **System Levels**: 1. **Level 1 (Basic)**: Hand pumps or small gravity systems; minimal treatment; serves 100–1,000 people (rural barangays). 2. **Level 2 (Intermediate)**: Small piped systems, low-pressure distribution; primary treatment (sedimentation, chlorination); serves 1,000–50,000 people. 3. **Level 3 (Urban)**: High-pressure distribution, multi-stage treatment (coagulation, clarification, filtration, disinfection); serves > 50,000 people (municipalities, cities). **Component Sizing**: **1. Intake Structure**: - **Surface intake**: Sized for MDD or PHD, plus allowance for silt (intake loss); minimizes disturbance to river ecology (per RA 6969, RA 7586). - **Well intake**: Sized for sustained maximum yield of the well field plus redundancy. - **Design flow**: Typically MDD or PHD, depending on downstream storage. **2. Treatment Plant**: - **Capacity**: MDD or PHD (whichever governs the design); includes sedimentation tanks, filters, disinfection units. - **Residence time**: Coagulation basins (2–5 min), sedimentation (1–3 hr), filtration (2–4 m/hr). - **Chemical dosing**: Based on water quality (turbidity, color, hardness); jar tests determine optimal coagulant dose. **3. Transmission Main (Primary Line)**: - **Sizing**: For MDD or PHD (depends on whether a clear well exists downstream). - **Hydraulic diameter**: Chosen to minimize energy loss and cost; economic diameter balances friction loss (energy cost) and capital (pipe size). - **Velocity**: Typically 0.6–1.5 m/s; higher velocity increases friction loss and noise; lower velocity allows settling (undesirable). **4. Elevated Storage (Reservoir / Clear Well)**: - **Volume**: Sized to handle peak-hour demand variation and provide emergency supply. Typical design: V = (PHD − ADD) × time to recover (e.g., 2 hr) plus 25% safety margin. - **Example**: If ADD = 10,000 m³/day, PHD = 25,000 m³/day, and recovery time = 2 hr: Peak excess = (25,000 − 10,000) × (2/24) ≈ 1,250 m³ Plus safety margin: Storage ≈ 1,500 m³ - **Elevation**: Must provide minimum residual pressure at the highest consumer (typically 20–30 m head, or 200–300 kPa). **5. Distribution Network**: - **Sizing**: For PHD (or 1.5 × MDD); accounts for fire-flow requirements. - **Pipe classes**: Pressure classes PVC (Class 10, 14, 16) or HDPE; ductile iron for large main sections. - **Velocity**: 0.3–1.5 m/s in distribution; lower in dead-end branches to reduce stagnation. - **Minimum pressure**: 20–30 m (200–300 kPa) at end consumers, 10–15 m for extreme high-elevation areas. **Fire-Flow Requirements**: - **Commercial/industrial areas**: 100–250 L/s for 2–4 hours (Australian, European standards; Philippines uses similar but lower in practice). - **Residential areas**: 30–60 L/s. - **Simultaneous demand + fire flow**: Distribution is sized for ADD or MDD plus fire flow (often the governing case for line sizing in high-demand areas). **Regulatory Framework (RA 544, LWUA Standards)**: - **RA 544 (Public Works and Highways)** defines geometric design and load standards for water infrastructure. - **LWUA (Local Water Utilities Administration)** rates water quality (color, turbidity, bacteria, hardness) and operational standards. - **NSCP 2015** (National Structural Code) provides structural design for water facilities. - **Philippine National Standards (PNS 3227:1995, ICS 13.060.20)** define drinking water quality (WHO/EPA standards adapted).

The PRC Civil Engineer Licensure Examination frequently tests hydrology and water supply. Here are critical errors to avoid and strategies to succeed. **Rational Method Pitfalls**: 1. **Forgetting the 360 factor**: Q = C × i × A gives Q in m³/s only if i is in mm/hr and A is in ha. Failing to apply 360 is the single most common error. Memorize: 1 ha·mm/hr = 1/360 m³/s. 2. **Wrong intensity duration**: Intensity must be read from IDF curves at duration = t_c, not at an arbitrary duration. If t_c = 20 min, use i(20 min); if you use i(60 min) (which is lower), your discharge will be underestimated and the design will be unsafe. 3. **Neglecting weighted C**: If a catchment is 50% pavement (C = 0.9) and 50% lawn (C = 0.2), use C_avg = 0.55, not C = 0.9 (a common mistake for students focused on the worst case). 4. **Unit mismatch in area**: Confusing km² with ha. 1 km² = 100 ha; converting 12 km² to 1,200 ha is easy to botch. 5. **Estimating t_c incorrectly**: Kirpich formula can give very small t_c (< 5 min) for steep, short catchments. NSCP 2015 sets a practical minimum of 10 min for urban areas; use this when Kirpich gives lower values. **Runoff Volume Pitfalls**: 1. **Confusing volume and peak**: A storm produces one volume (V = C × P × A, independent of duration), but many peak discharges depending on intensity and duration. Board exams mix these; read carefully. 2. **Unit inconsistency**: P in mm, A in m² → V in 10³ m³. P in m, A in m² → V in m³. P in mm, A in ha → V in m³. Know these relationships. 3. **Forgetting loss factors**: The runoff volume is C × P × A; students sometimes use P directly without C, inflating the answer. **Water-Supply Pitfalls**: 1. **ADD vs. peak demand**: Design the intake and treatment for MDD or PHD as appropriate. Many students confuse which. Rule: design for the highest flow rate in the system at each point. Intake may be sized for MDD (if a clear well exists); distribution is sized for PHD or 1.5 × MDD. 2. **Forgetting water loss**: If a system has 40% loss, the production must be 1.67 times the consumer demand. Many exam questions sneak this in; read for "water loss" or "unaccounted water." 3. **Demand factors**: MDD ≈ 1.5 × ADD and PHD ≈ 2.5 × ADD are typical, but the exam may specify different factors (e.g., "in this region, MDD = 1.8 × ADD"). Use the given factor. 4. **Return period**: Choosing the correct return period (2–5 yr for minor, 10 yr for primary urban, 25+ yr for major) depends on project type. The exam specifies; if not, assume 10 yr for municipal work. 5. **Storage volume calculation**: A clear well sized for V = (PHD − ADD) × time is only valid if the treatment plant operates at a constant rate (ADD). If the plant is only operated during certain hours, the calculation differs. Exam questions often specify; read carefully. **Well and Reservoir Design Pitfalls**: 1. **Drawdown direction**: Drawdown increases (s increases) as you approach the well (r decreases). At r = R_influence, s ≈ 0. Students sometimes reverse this. 2. **Pumping test interpretation**: A pumping test measures drawdown over time. The Theis equation applies to steady-state (long-term); early data are transient. Exams usually give steady-state values; if transient, use the Cooper-Jacob approximation. 3. **Reservoir mass balance**: Inflow + stored water − demand = remaining storage. Over a dry season with no inflow, storage must equal cumulative demand. Students sometimes confuse daily and seasonal time scales. **Key Exam Strategies**: 1. **Draw a sketch**: Rational method exams benefit from a labeled catchment sketch showing C regions, t_c path, and outlet. 2. **Unit tracking**: Write units at every step (m³/s, mm/hr, ha, etc.). This catches errors and shows your reasoning. 3. **Round sensibly**: Final answers to 2–3 significant figures (e.g., Q = 5.2 m³/s, not 5.234). Exams expect engineering precision, not mathematical exactness. 4. **State assumptions**: If IDF data is absent, state "Assuming i = X mm/hr from regional IDF curves." Exams reward clarity. 5. **Check reasonableness**: A 5 ha catchment yielding 100 m³/s is unreasonable (equiv. to ~20 mm/hr, which is extreme). Conversely, 0.001 m³/s for a 100 ha catchment is too low. Quick sanity checks prevent major errors. 6. **Practice with Philippine data**: Use PAGASA IDF curves for Metro Manila, Cebu, and other regions. Familiarize yourself with regional variation (Manila has higher intensity than Baguio or Cagayan due to rainfall patterns).