CELE Hydraulics & Fluid Mechanics — Hydrology and Water SupplySummary

Water continuously moves through atmosphere, land, and subsurface in a closed loop: precipitation → interception (canopy/surface retention) → infiltration (entry into soil) or surface runoff → streamflow → evapotranspiration (evaporation from soil/water bodies plus plant transpiration) → atmosphere. In engineering terms, on any catchment, precipitation is partitioned into runoff (the portion reaching a stream or drainage system), infiltration, and storage. The runoff coefficient C quantifies this partition: runoff volume = C × precipitation × area. In the Philippines, monsoon rainfall is intense and seasonal; infiltration varies widely depending on soil type (clay-rich valley soils infiltrate less than volcanic uplands).

A dimensionless factor (0 to 1) representing the fraction of rainfall that becomes runoff. Values depend on surface imperviousness and soil infiltration: lawns/natural areas 0.1–0.3; mixed urban 0.4–0.6; dense urban/pavement 0.75–0.95; roofs 0.75–0.95. For composite catchments (e.g., 40% pavement + 60% lawn), the weighted average applies: C_avg = 0.4(0.9) + 0.6(0.2) = 0.36 + 0.12 = 0.48. The remaining fraction (1 – C) is lost to infiltration, surface storage, and evaporation during the storm.

The time required for rainfall to travel from the farthest point in a catchment to the outlet. In practice, rainfall intensity from IDF curves is taken at duration t_c, because once a storm lasts at least t_c, the entire catchment contributes to runoff. Estimation methods include the kinematic-wave formula or the Philippines-specific velocity method (overland flow velocity ≈ 0.5 m/s, channel velocity ≈ 1–2 m/s). For small urban catchments typical of board problems, t_c often ranges 10–30 minutes. If a design storm is shorter than t_c, not all the catchment contributes.

Peak runoff (design discharge) is calculated from Q = C × i × A / 360, where C is the runoff coefficient (dimensionless), i is rainfall intensity (mm/hr) at the design duration (= t_c), A is catchment area (hectares), and Q is discharge (m³/s). The factor 360 converts mm/hr and hectares to m³/s: 1 mm = 0.001 m; 1 ha = 10,000 m²; 1 hr = 3600 s; thus (0.001 m) × (10,000 m²) / (3600 s) = 10 m³ / 3600 s = 1/360 m³/s per mm/hr per ha. In base SI units (m, m², m³/s), no factor is needed: Q = C × i × A. The method is deterministic (not probabilistic) but is applied with design rainfall from a specified return period (e.g., 10-year, 25-year).

Empirical relationships showing how rainfall intensity varies with storm duration and return period (frequency). For a given return period (e.g., 5-year, 25-year), intensity decreases as duration increases: a 5-minute storm is more intense than a 60-minute storm. IDF data are specific to each location; the Philippines publishes IDF curves for major cities (Manila, Cebu, Davao, etc.) based on historical rainfall records. To use the rational method, you select the design return period (based on structure importance and acceptable risk), estimate t_c for your catchment, read i from the appropriate IDF curve at that t_c, and apply Q = CiA/360. Mismatching duration to t_c is a common error.

Total water volume reaching a stream or drain from a storm is V = C × P × A, where P is rainfall depth (m or mm), A is area (m² or ha consistent with P), and C is the runoff coefficient. Example: a 120 mm storm on 12 km² with C = 0.45 gives V = 0.45 × 0.12 m × 12 × 10⁶ m² = 648 × 10³ m³ = 648 ML (megaliters) or 648,000 m³. This differs from peak discharge Q (m³/s); volume is total water, while Q is the maximum instantaneous rate. Volume is used for reservoir sizing and stormwater detention; peak discharge is used for channel/pipe sizing.

Design of water-supply infrastructure requires estimating total demand: average daily demand (ADD) = population × per-capita consumption (L/person/day). Typical Filipino standard: 150–200 L/person/day for urban areas (per NWRB or MWSS guidelines). Peak demands are multipliers of average: maximum day ≈ 1.3–1.5× ADD; peak hour ≈ 2–3× ADD (varies by code and consumer behavior). Conveyance pipes and treatment capacity are sized for the peak hour; storage (elevated tanks, reservoirs) must buffer the difference between steady inflow and fluctuating demand. For a town of 10,000 at 150 L/c/day: ADD = 1.5 million L/day = 1,500 m³/day ≈ 17.4 L/s average; max day ≈ 2,250 m³/day ≈ 26 L/s; peak hour (factor 2.5) ≈ 43.75 L/s.

Surface-water sources (rivers, reservoirs, lakes) capture runoff; capacity is determined by inflow (streamflow duration curve) versus demand. A reservoir is sized to store the shortfall when inflow is less than demand, using mass-balance analysis: required storage = cumulative (demand – inflow) when inflow < demand. Groundwater sources are wells; yield depends on aquifer properties and is estimated from well-hydraulics formulas (Theis, Jacob, or Dupuit equations). Drawdown (water level drop in well) is proportional to pumping rate and aquifer transmissivity. Safe yield is the sustainable rate without long-term depletion. In the Philippines, groundwater is critical in non-irrigable uplands; surface water (dams, rivers) in lowlands. The NWRB (National Water Resources Board) regulates allocation.

A catchment (or watershed) is the land area from which all rainfall drains toward a common outlet (stream gauge, dam, or stormwater inlet). Boundaries are determined from topographic divides (ridgelines). Area is measured in hectares (ha) or km² and is essential input to the rational method. Small catchments (<10 km²) are treated as having uniform C and i (rational method); larger basins often require subdivision or more sophisticated methods (e.g., unit hydrograph, HEC-HMS). Slope, shape, and orientation influence t_c and runoff characteristics. In the Philippines, DEM (digital elevation model) and GIS tools are increasingly used to delineate catchments; board exams may provide a sketch or ask you to estimate area from coordinates.

Infiltration is the entry of water into soil; it is opposed by the runoff coefficient (C represents the fraction *not* lost to infiltration). Abstractions include infiltration, surface storage (depressions, puddles), and evaporation during the storm. Initial abstractions occur before significant runoff; for design purposes, they are lumped into C. In the Philippines, volcanic soils of the central Luzon plain and Visayas have high infiltration capacity (C ≈ 0.2–0.4); clay-rich deltaic soils lower (C ≈ 0.5–0.7); urban impervious areas near zero (C ≈ 0.9). The rational method implicitly assumes all abstractions are captured in C; more detailed analyses use the Green–Ampt or Horton infiltration models.

The rational method in practical units: Q (m³/s) = [C × i (mm/hr) × A (ha)] / 360. In pure SI: Q (m³/s) = C × i (m/s) × A (m²), no factor. Conversions: 1 km² = 100 ha; 1 ha = 10,000 m²; 1 mm/hr = 1/(3.6 × 10⁶) m/s ≈ 2.78 × 10⁻⁷ m/s; 1 ML = 10⁶ L = 1,000 m³. Board exams mix units: rainfall in mm, area in km² or ha, intensity in mm/hr, discharge in m³/s. The 360 factor is the conversion constant for the specific units; forgetting it is a classic error (common on PRC exams). Example: A = 5 km² = 500 ha; if you accidentally use 500 in Q = CiA, you get 5.56× too large a Q.

A T-year return period (e.g., 10-year, 25-year, 100-year) means the rainfall/flood has a 1/T probability of occurring in any given year (not guaranteed every T years). A 10-year storm has 63% probability of occurring within a 10-year design life; a 100-year storm has 39% probability in 50 years. Design choice reflects acceptable risk: minor drainage (parking lots) may use 5-year; residential areas 10–25-year; hospitals and critical infrastructure 50–100-year. The PRC board typically specifies the return period or leaves it to the engineer's judgment based on structure type. In the Philippines, NWRB and MWSS guidelines recommend 10–25-year for urban water-supply conveyance and 50–100-year for dam spillways.

Both use the runoff coefficient C but serve different purposes. Q = CiA/360 calculates instantaneous peak rate (m³/s) used for pipe/channel sizing. V = CPA calculates total water depth/volume (m³) used for storage (detention basin, reservoir) sizing. A storm may produce small peak discharge but large volume (long, gentle rain) or large peak but small volume (intense, brief storm).

A 50 ha mixed-use catchment (30% roofs, 50% roads/pavement, 20% landscaping) requires a stormwater pipe to a creek. Engineer estimates C by weighted average: C = 0.3(0.85) + 0.5(0.80) + 0.2(0.25) ≈ 0.665. For a 25-year design storm, the local IDF curve gives i = 60 mm/hr at t_c ≈ 15 min. Peak discharge Q = (0.665)(60)(50) / 360 ≈ 5.54 m³/s. The pipe diameter is selected to convey 5.54 m³/s at safe velocity and headroom. In Manila, typical IDF curves for 25-year storms range 40–80 mm/hr depending on duration; a detailed pipe network may subdivide the catchment and route flows through retention basins before reaching the creek.

A commercial development on 8 ha must detain a 10-year storm to avoid overwhelming existing drainage. The catchment C ≈ 0.75 (mostly pavement, roofs, and minimal landscaping). A 60 mm rainfall (typical 10-year 24-hour storm in the Philippines) produces runoff volume V = 0.75 × 0.06 m × 8 × 10⁴ m² = 36,000 m³. If the site can discharge only 200 L/s (0.2 m³/s) to the creek (limited by available creek capacity), detention time is V / (0.2 m³/s × 3600 s/hr) ≈ 50 hours. A basin or pond sized for ~36,000 m³ capacity (e.g., 120 m × 100 m × 3 m deep) with controlled outfall ensures on-site detention. This is critical in Metro Manila where creeks often exceed design capacity during monsoons.

A barangay of 8,000 residents currently uses 120 L/person/day (below the 150–200 L/c/day standard for urban areas). Current ADD = 8,000 × 120 = 960 m³/day ≈ 11.1 L/s. If demand is upgraded to 150 L/c/day as living standards improve, ADD = 1,200 m³/day = 13.9 L/s; max day (factor 1.4) = 1,680 m³/day ≈ 19.4 L/s; peak hour (factor 2.5) = 3,000 m³/day ≈ 34.7 L/s. The water-supply pipeline must be sized for 34.7 L/s (or larger for growth), an elevated tank for ~1,680 m³ (1.4× ADD to cover demand fluctuation over 24 hours), and a source (well or surface intake) yielding at least 20 L/s average (allowing for peaking and losses). In remote areas like mountain barangays, groundwater (hand-dug or tube wells) may provide 2–5 L/s each; multiple wells may be required.

A farmer in Pangasinan wants to store dry-season runoff from a 2 km² hillside catchment for irrigation. Rainfall in monsoon months (Jun–Oct) averages 1,500 mm; the catchment C ≈ 0.4 (mixed forest, grassland, exposed soil). Monsoon runoff volume ≈ 0.4 × 1.5 m × 2 × 10⁶ m² = 1.2 × 10⁶ m³ = 1,200 ML. Dry-season irrigation demand is 2 ML/day for 120 days = 240 ML. Required storage ≈ 240 ML (gross storage must be larger to account for evaporation losses ~10%, seepage ~5%, and dead storage ~10%, so ~330 ML total). A pond 300 m × 200 m × 5.5 m average depth ≈ 330 ML is feasible on flat valley land. Peak inflow during monsoon is calculated via rational method if t_c ≈ 2 hours (hillside catchment): Q ≈ (0.4)(80 mm/hr)(200 ha) / 360 ≈ 17.8 m³/s at peak; spillway must pass this without overtopping.

A water utility proposes a deep well in Pampanga to supplement surface-water supply during dry season. A test pumping at 15 L/s (0.015 m³/s) causes drawdown of 2 m in 1 hour. Using simplified analysis (assumption: steady-state or brief-duration test), the transmissivity T and storativity S of the aquifer can be estimated via Theis or Jacob curves. If the safe yield (drawdown <5 m) corresponds to 20 L/s, this well can provide supplemental supply during low-flow months. Multiple wells may be required if single-well yield is insufficient. In alluvial plains (Pampanga, Nueva Ecija), aquifer yields are typically 10–50 L/s; in volcanic rock areas, 5–15 L/s is common.

A municipality in Quezon province wants to delineate flood-prone areas for land-use planning. Historical flood extents and hydraulic modeling (using rational-method peak discharge) are combined. A catchment of 120 km² draining toward the town (C ≈ 0.55 mixed urban–agricultural) has t_c ≈ 90 minutes. For a 25-year storm, i ≈ 50 mm/hr (from regional IDF curves). Peak discharge Q = (0.55)(50)(1,200 ha) / 360 ≈ 91.7 m³/s. This discharge is routed through the river valley using Manning's equation or HEC-RAS software to determine flood depth and extent. Areas with simulated depth >1 m are classified as high-hazard zones; 0.3–1 m as moderate; <0.3 m as low. Zoning restrictions (no ground-floor residences, elevated structures, etc.) reduce risk.

A provincial road crossing a creek in Ilocos region must be designed to pass the design flood. The catchment upstream of the crossing is 15 km², C ≈ 0.50 (slopes 25–50%, partial forest, exposed ridges). Estimated t_c ≈ 50 minutes. For a 50-year return period, IDF curves (specific to Ilocos) give i ≈ 55 mm/hr at 50-min duration. Peak discharge Q = (0.50)(55)(150 ha) / 360 ≈ 11.5 m³/s. The bridge or culvert must accommodate 11.5 m³/s without excessive headwater rise (typically <0.5 m for smooth passage). Culvert diameter/area is selected via Manning's equation; if too small, water backs up and floods the approach road or inundates the roadway.

A potential run-of-river (RoR) hydroelectric site is evaluated. The catchment (85 km², t_c ≈ 3 hours) has mean annual precipitation 2,500 mm, runoff coefficient C ≈ 0.45 (tropical forest with steep slopes). Mean annual runoff ≈ 0.45 × 2.5 m × 85 × 10⁶ m² ≈ 95.6 × 10⁶ m³/year. Mean discharge ≈ 3.04 m³/s. For design, the flow-duration curve (showing how often each discharge is exceeded) is required. RoR turbines typically operate at 40–60% of mean flow (to ensure continuous operation during low-flow months). Capacity ≈ 0.5 × 3.04 = 1.52 m³/s. With a 50 m head, power ≈ ρ g Q H ≈ (1000)(9.81)(1.52)(50) ≈ 745 kW ≈ 0.75 MW (before efficiency losses). Seasonal variation and dry-season low flows are critical design constraints.