CELE Hydraulics & Fluid Mechanics — Hydrology and Water SupplyRevision Notes

Formulas

Exam Tips

• Board problems on the hydrologic cycle are mostly conceptual or qualitative; know the sequence and the engineering terms.
• tc is not directly computed on most board problems — it is usually given. Focus on using it correctly to find i from IDF data.
• If the problem gives return period and duration, select i from the given IDF table or equation; do not invent a value.

Key Points

• The hydrologic cycle describes the continuous movement of water through the environment: precipitation → interception/infiltration → surface runoff → streamflow → evaporation/transpiration → back to precipitation.
• Engineering hydrology focuses on the runoff fraction — the portion of precipitation that flows over the surface and must be managed by drainage or storage structures.
• Losses in the cycle include infiltration (absorbed by soil), interception (held by vegetation), evaporation (liquid to vapor from surfaces), and transpiration (vapor release from plants). The sum is called evapotranspiration (ET).
• The water balance equation is: Runoff = Precipitation − Infiltration − Evapotranspiration − Surface storage.
• Rainfall duration, intensity, and return period determine the design storm for any drainage or flood-control structure.
• The time of concentration (tc) is the travel time from the most remote point of the catchment to the outlet; it governs the design rainfall duration in the rational method.

Definitions

Section Title

The Hydrologic Cycle

Common Mistakes

• Confusing the time of concentration with the storm duration — they are set equal only for the rational method design condition.
• Forgetting that intensity DECREASES as storm duration increases; using a short-duration intensity for a large catchment with long tc overestimates Q dangerously.
• Treating the hydrologic cycle as only precipitation and runoff; ignoring infiltration and ET leads to over-design.

Formulas

Exam Tips

• Memorize Q = CiA/360 exactly — this is the most-tested formula in board hydrology problems.
• When given C as separate sub-areas, always compute composite C before applying the rational method.
• Double-check units: i in mm/hr? A in ha? Then divide by 360. Any other combination requires unit conversion first.
• The 360 factor derivation: 1 mm/hr × 1 ha = (1/1000 m/hr) × (10 000 m²) = 10 m³/hr = 10/3600 m³/s ≈ 1/360 m³/s. Hence Q[m³/s] = CiA/360.
• Board exam C values are always given or standard tabulated values — you will not derive C from first principles.

Key Points

• The rational method gives the PEAK discharge Q from a catchment for a storm whose duration equals tc.
• The fundamental formula in pure consistent units is Q = C·i·A, where i must be in m/s and A in m² to get Q in m³/s.
• The board-exam practical SI form uses intensity in mm/hr and area in hectares, requiring the 360 conversion factor: Q = C·i·A / 360.
• The runoff coefficient C is dimensionless (0 < C ≤ 1); it accounts for imperviousness, slope, and land cover.
• For mixed catchments, the weighted (composite) C is: C_composite = Σ(Ci·Ai) / ΣAi.
• The rational method is valid for small catchments (typically < 80 ha or < 200 ha in some references); for larger areas, use hydrograph methods.
• The method assumes: uniform rainfall over the catchment, storm duration ≥ tc, and steady-state runoff at the outlet.
• Typical C values: pavement/roofs 0.85–0.95; lawns/parks 0.10–0.35; agricultural land 0.20–0.40; urban mixed 0.40–0.70.

Definitions

Section Title

The Rational Method — Peak Runoff

Common Mistakes

• CRITICAL: Forgetting the 360 factor when i is in mm/hr and A is in ha — omitting it gives a result 360× too large.
• Using the wrong area units: if A is given in km², convert to ha first (1 km² = 100 ha) before applying the formula.
• Applying the rational method to large catchments (>500 ha) where the steady-state assumption breaks down; board problems will stay within the valid range.
• Selecting rainfall intensity at a duration shorter than tc; the correct design condition is duration = tc.
• Forgetting to compute composite C for mixed land-use catchments — using only one C value introduces significant error.

Formulas

Exam Tips

• For volume problems, the key steps are: convert P to metres, convert A to m², then multiply C × P × A.
• Board problems on volume often ask for the answer in ML — always check the requested unit.
• If P is given as intensity × duration (e.g., 25 mm/hr for 3 hr), compute P = 75 mm before using V = CPA.
• Runoff volume and peak discharge use the same C but different storm parameters (P for volume, i for peak Q).

Key Points

• While the rational method gives PEAK FLOW (m³/s), runoff volume is the total volume of water (m³) generated by a storm.
• Runoff volume formula: V_runoff = C · P · A, where P is rainfall depth (m) and A is catchment area (m²).
• This formula treats C as a volume ratio: fraction of total rainfall depth that becomes runoff volume.
• Runoff depth = C × P (in mm or m), which equals the equivalent depth of runoff uniformly spread over the catchment.
• Volume can be expressed in m³, ML (megalitres, 1 ML = 1000 m³), or Mm³.
• Volume calculations are used for reservoir sizing, detention pond design, and flood routing.
• The SCS Curve Number (CN) method is an alternative volume method, but the PRC board primarily tests the C·P·A approach.

Definitions

Section Title

Runoff Volume

Common Mistakes

• Using P in mm and A in m² directly — always convert P to metres before multiplying: P(m) = P(mm)/1000.
• Confusing runoff depth (C·P, units of mm) with runoff volume (C·P·A, units of m³).
• Using area in km² without converting to m² (1 km² = 1 × 10⁶ m²) — a factor of 10⁶ error.
• Reporting volume in m³ when the problem asks for ML or vice versa without conversion (1 ML = 1000 m³).

Formulas

Exam Tips

• Board problems will provide either a table, a graph, or an equation for IDF — you will not need to recall specific intensity values.
• Practice substituting tc into IDF equations quickly; this is a straightforward algebra step.
• If tc and return period are given, select i directly from a provided table — no interpolation needed for most board problems.

Key Points

• IDF curves relate rainfall intensity (mm/hr) to storm duration (hr or min) for various return periods (years).
• Key relationship: intensity DECREASES as duration INCREASES for the same return period.
• Key relationship: intensity INCREASES as return period INCREASES for the same duration.
• Design return periods by structure type: residential drainage 2–10 yr; arterial roads 10–25 yr; major infrastructure 50–100 yr.
• For the rational method, always select the intensity at duration = tc from the appropriate return-period curve.
• IDF equations are often given in board problems in the form: i = a / (t + b)^n or i = kT^m / t^n, where t is duration in minutes and T is return period in years.
• PAGASA provides IDF data for Philippine stations — local IDF data may differ significantly from generic values.

Definitions

Section Title

Rainfall Intensity-Duration-Frequency (IDF)

Common Mistakes

• Using the peak intensity from the IDF curve regardless of tc — always pick i at duration = tc.
• Reading IDF intensity at a different return period than specified in the design criteria.
• Confusing intensity (mm/hr) with depth (mm) — intensity is a rate, depth is the total accumulated volume per unit area.

Formulas

Exam Tips

• Memorize: ADD = N × q; MDD = 1.5 × ADD; PHD = 2.5 × ADD (unless the problem specifies a different factor).
• For unit conversions: 1 m³/day = 1/86 400 m³/s ≈ 1.157 × 10⁻⁵ m³/s; 1 L/s = 86.4 m³/day.
• Board problems on water demand are straightforward multiplication — set up unit conversions carefully and you will not lose marks.
• If the problem asks for the design flow of a pipe serving a community, use MDD or PHD, not ADD.
• Fire demand problems add a fixed fire flow (L/s) to MDD — check if the problem specifies fire demand consideration.

Key Points

• Water demand is classified as: average daily demand (ADD), maximum daily demand (MDD), and peak hourly demand (PHD).
• ADD = population × per-capita consumption (L/person/day). Typical Philippine per-capita: 150–250 L/person/day for urban areas.
• MDD ≈ 1.5 × ADD (maximum day factor = 1.5).
• PHD ≈ 2.0 to 3.0 × ADD (peak hour factor = 2–3, commonly 2.5 for board problems unless stated).
• Design pipelines and pumps for MDD; design storage reservoirs for PHD or fire demand.
• Water sources: surface water (rivers, lakes, reservoirs) and groundwater (wells, springs).
• Well yield: the sustainable pumping rate without excessive drawdown, governed by Darcy's Law and Dupuit-Thiem well equations.
• Reservoir sizing: mass-balance (Rippl diagram) — accumulate (inflow − demand) over time to find required storage volume.
• Per-capita demand increases with economic development; Philippine water utilities (governed by LWUA and local ordinances) target 150–250 LCD for service levels.
• Fire demand is an additional design consideration (not per capita) — typically added to MDD for distribution system design.

Definitions

Section Title

Water Supply Fundamentals — Demand and Sources

Common Mistakes

• Using per-capita consumption in L/person/day without converting to m³/person/day when computing demand in m³: 1 L = 0.001 m³.
• Forgetting to multiply ADD by the peak factor — designing for ADD alone will cause shortfalls during peak demand.
• Confusing MDD (1.5× ADD for daily variation) with PHD (2–3× ADD for hourly variation); PHD is always larger.
• Not converting daily demand to m³/s when comparing with pipeline capacity: divide m³/day by 86 400.
• Assuming per-capita = domestic only; in Philippine water supply, per capita includes domestic + commercial + unaccounted-for water (UFW).

Formulas

Exam Tips

• For Problem 4 shortcut: C_composite = (0.90)(0.40) + (0.20)(0.60) = 0.36 + 0.12 = 0.48 — using area fractions directly gives the same answer and is faster.
• Always re-read the problem to check if the answer is needed in m³/s, m³/day, L/s, or another unit — unit mismatch is the top source of errors.
• Write the formula first, then substitute — this habit prevents formula errors under exam pressure.

Key Points

• Practice all three formula types: Q (peak runoff), V (runoff volume), and water demand.
• Always write out given data, identify the formula, substitute with units, and check the answer for reasonableness.
• Typical board problem structure: one unknown, all other values given, single formula needed.

Section Title

Worked Board-Style Problems

Common Mistakes

• In composite C problems, using total area = 100% (fraction) instead of actual hectares — both give the same result only if computed correctly, but using fractions directly: C = Σ(Ci × fi) where fi is fraction, is an equivalent shortcut.
• In Problem 3, forgetting to divide by 86 400 to get m³/s when the question asks for flow rate rather than daily volume.