Question 1 of 7

Problem 1 (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) Sanitary sewer diameter for a peak flow of 200 L/s (7 marks)

Given.

Find. Required sewer diameter $D$; check whether the velocity condition is met.

Approach. For a circular pipe flowing full, $R=D/4$; substituting into Manning's equation collapses it to a single closed-form power law in $D$, solved directly, then the resulting full-flow velocity is checked against the stipulated window.

1. Collapse Manning's equation for full flow.$$Q=\frac{1}{n}AR^{2/3}S^{1/2}=\frac{1}{n}\left(\frac{\pi D^2}{4}\right)\left(\frac{D}{4}\right)^{2/3}S^{1/2}=\frac{0.3117}{n}D^{8/3}S^{1/2}$$
2. Solve for $D$.$$D=\left(\frac{Qn}{0.3117\sqrt{S}}\right)^{3/8}=\left(\frac{(0.200)(0.015)}{0.3117\sqrt{0.05}}\right)^{3/8}=\boxed{0.307\ \text{m}}$$
3. Check the full-flow velocity.$$A=\frac{\pi D^2}{4}=0.0742\ \text{m}^2\qquad V=\frac{Q}{A}=\boxed{2.69\ \text{m/s}}$$Since $0.6\ \text{m/s}<2.69\ \text{m/s}<8\ \text{m/s}$, both velocity conditions are met at the stated 5% bedding slope — no corrective slope or diameter is required.

(ii) On-site stormwater runoff control systems for a 25-year design life (6 marks)

Two common on-site (source-control, lot-level) stormwater controls are a soakaway pit / infiltration trench and a rooftop or parking-lot detention (flow-control roof/ponding) system, both located at or immediately adjacent to the property generating the runoff, rather than downstream at a regional facility.

A soakaway pit or infiltration trench is a gravel-filled excavation (often wrapped in geotextile, with a perforated distribution pipe) sized from the measured native soil infiltration rate and a target drawdown time (typically 24–48 h) to capture and infiltrate roof or driveway runoff before it reaches the piped system. Its design driver is the site's percolation rate (a safety factor of 2 is typical to allow for silting), and over a 25-year design life the dominant operation/maintenance issue is progressive clogging of the infiltration surface by fines washed in from the contributing area — requiring periodic inspection of the drawdown time and, if it lengthens materially, excavation/replacement of the gravel media or the addition of upstream pre-treatment (a leaf/sediment trap).

A rooftop or parking-lot detention system (flow-control roof drains, or a shallow surface ponding area with a restricted outlet) instead stores runoff temporarily and releases it slowly through an orifice sized to not exceed a target release rate, reducing peak flow into the downstream minor system without relying on soil infiltration at all. Its design driver is the roof/lot's own storage-outflow relationship rather than soil permeability, so it works even on tight clay sites where infiltration systems fail; its 25-year O&M burden is mechanical (the restrictor orifice and roof drains must be kept clear of debris, and the structural roof loading from the extra ponded water depth must be checked and re-verified periodically as roofing is replaced).

In short, the infiltration trench trades soil-permeability risk and clogging for genuine runoff-volume reduction, while rooftop/lot detention trades structural loading and mechanical-outlet reliability for peak-flow control that works regardless of soil type — a 25-year life makes clogging management the controlling maintenance issue for the former and outlet/structural inspection the controlling issue for the latter.

(iii) Log-normal distribution for flood/streamflow frequency analysis (7 marks)

Although the MOE flood information service recommends the log-Pearson Type III distribution as the general standard for annual-maximum flood and minimum-streamflow frequency analysis, the log-normal distribution remains particularly useful for three reasons:

(1) Simplicity and a strong physical basis. Streamflow (and many other hydrologic) extremes arise from the multiplicative combination of many independent physical factors (antecedent moisture, storm intensity, basin response); by the central limit theorem, the product of many independent positive random variables tends toward a log-normal distribution, giving log-normal a genuine physical justification rather than being purely an empirical curve fit.

(2) Only two parameters (mean and standard deviation of the log-transformed data) need to be estimated, compared with the log-Pearson III's three parameters (which also requires estimating a skew coefficient, notoriously unstable/unreliable from short records) — making log-normal more robust and easier to fit reliably from the typically short streamflow records available in Canada.

(3) It transforms cleanly to a straight line on log-probability paper, which makes graphical fitting, visual outlier/goodness-of-fit checking, and manual frequency-curve extension straightforward — a practical advantage for field engineers and for cross-checking a computer-fitted log-Pearson III curve.

Limitation. The log-normal distribution is symmetric in log-space (zero skew by construction), so it cannot represent the pronounced positive or negative skewness that many actual flood-frequency datasets exhibit; forcing a skewed dataset into a symmetric log-normal fit systematically mis-estimates the rare, high-return-period design floods that dam-safety and major infrastructure design actually depend on — which is exactly why the log-Pearson III (with its explicit skew parameter) is preferred as the general recommended standard despite its extra estimation burden.