Question 2 of 7: Rural Hydrologic Cycle, Storm-Sewer Peaking Factor and Sewer Design Bases

Problem 2: Rural Hydrologic Cycle, Storm-Sewer Peaking Factor and Sewer Design Bases (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) Rural-Watershed Hydrologic Cycle — Three Key Processes

Three key processes and how each affects rural-watershed runoff: (1) Precipitation is the driving input — its intensity and duration relative to the soil's infiltration capacity determine what fraction converts to runoff at all; a rural watershed with permeable, unfrozen soil converts very little of a light, long-duration rain to runoff, while an intense short storm on the same soil produces a much larger runoff fraction because the infiltration capacity is exceeded ("infiltration-excess" or Hortonian runoff). (2) Infiltration, governed by soil type, vegetative cover and antecedent moisture, is typically the dominant loss pathway in an undeveloped rural watershed (unlike an urbanized one), so runoff volumes and peak flows are correspondingly much lower per unit rainfall — land-use changes such as agricultural tilling or forest clearing reduce infiltration capacity and materially increase rural runoff. (3) Overland (surface) and channel routing — the time water takes to travel from where it falls to the stream (time of concentration), controlled by slope, vegetative roughness and channel/ditch density — determines how "peaky" versus attenuated the resulting hydrograph is; a rural watershed with dense vegetation and long overland flow paths produces a flatter, delayed hydrograph than a watershed with straightened ditches and cleared land.

(ii) The Babbitt Formula for the Dry-Weather Peaking Factor

Given. Babbitt's formula, $PF=5/EP^{0.2}$, where $EP$ is the equivalent (tributary) population served, expressed in thousands.

Find. How the formula is used to size a storm (or, more precisely, a sanitary) sewer's dry-weather peak flow for storm-sewer sizing purposes.

The Babbitt formula converts an average dry-weather (sanitary) flow into the peak dry-weather flow the sewer must be sized to carry, by exploiting the empirical observation that peaking intensity decreases as the tributary population grows (a small population has a large peaking factor because a few simultaneous flush/fixture events dominate the flow; a large population averages many independent events together, smoothing the peak). To use it: (1) compute the average dry-weather flow from the tributary equivalent population and a per-capita sewage generation rate; (2) compute $EP$ in thousands and evaluate $PF=5/EP^{0.2}$; (3) multiply, $Q_{\text{peak,dry}}=PF\times Q_{\text{avg,dry}}$, to obtain the design dry-weather peak used, together with the design storm's peak wet-weather (infiltration/inflow-inclusive) flow, to size the downstream sewer — a storm sewer specifically is normally sized for the wet-weather peak alone, but a combined sewer (Problem 2(iv)) must carry both the Babbitt-peaked dry-weather flow and the storm flow simultaneously.

(iii) Rational Method / IDF Design Basis for Stormwater Collection

The Rational Method, $Q=CiA/360$ ($Q$ in m³/s, $C$ dimensionless runoff coefficient, $i$ in mm/h, $A$ in ha), is the standard sizing basis for small-to-moderate urban storm sewers. Its use requires an intensity-duration-frequency (IDF) curve family for the site: the designer selects a return period (e.g., 5- or 10-year for a minor system), estimates the catchment's time of concentration $t_c$ (the longest travel time to the design point), and reads the rainfall intensity $i$ at duration $t_c$ off the IDF curve for that return period — the underlying assumption being that the storm producing the peak runoff has a duration equal to $t_c$, since a shorter storm does not have the whole catchment contributing simultaneously and a longer one has a lower average intensity. The Rational Method assumes $C$ is constant over the storm and the catchment is small enough (typically <80 ha) that travel-time and rainfall-intensity spatial variability can be ignored; larger or more complex catchments instead use a full IDF-driven unit-hydrograph or continuous-simulation model.

(iv) Combined Sewers vs. Storm Sewers — Two Design Differences

(1) Design flow composition. A storm sewer is sized only for the peak wet-weather (rainfall-runoff) flow at the chosen return period. A combined sewer must be sized for the sum of the Babbitt-peaked dry-weather (sanitary) flow AND the wet-weather peak — occurring simultaneously — which for the same service area produces a materially larger design flow and pipe size, and (in older systems without full conveyance/treatment capacity) requires combined sewer overflow (CSO) structures to relieve the pipe during large storms rather than surcharging into basements. (2) Minimum (self-cleansing) velocity criterion. A storm sewer only needs to self-clean during storm events (when it is flowing near-full anyway), so the minimum-velocity check at design flow is usually the binding case; a combined sewer must ALSO maintain self-cleansing velocity at the much smaller dry-weather flow (so that sanitary solids do not settle out between storms) — this typically forces a steeper minimum grade, or an egg-shaped/composite cross-section (narrower invert to keep velocity up at low flow while still providing capacity at peak flow) rather than the circular section usually sufficient for a storm-only sewer.