Question 1 of 7: Conceptual Runoff Models, PVC Pipe Flow and Cross-Connections

Problem 1: Conceptual Runoff Models, PVC Pipe Flow and Cross-Connections (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) Process-Based vs. Stochastic Conceptual Runoff Models

Difference 1 — physical basis. A process-based (physically-based/deterministic) model represents the actual mechanics of rainfall-runoff transformation — interception, infiltration, overland and channel routing — through governing physical equations (e.g., Green–Ampt infiltration, the kinematic-wave or St. Venant equations), so its parameters are physically measurable quantities (soil type, land cover, slope, channel geometry). A stochastic conceptual model instead treats runoff generation as a statistical/black-box transfer function fitted directly to an observed rainfall-runoff time series (e.g., an autoregressive or unit-hydrograph-by-regression model), without explicitly representing the physical mechanism.

Difference 2 — data and transferability. A process-based model needs detailed spatial data (DEM, soils, land-use) but, because its parameters are physical, it can in principle be applied at an ungauged site by transferring parameters from a similar watershed. A stochastic model needs a long, good-quality gauged historical record to calibrate its statistical coefficients and is essentially an interpolation/extrapolation tool — its fitted coefficients are not physically transferable to a different catchment.

When each is preferred. Process-based models are preferred for design at ungauged or changing watersheds — e.g. sizing new storm infrastructure for a watershed undergoing urbanization, where historical statistics no longer apply and the engineer must test physical "what-if" land-use or LID scenarios. Stochastic conceptual models are preferred for statistical flood/drought forecasting or real-time flow forecasting at a site with a long gauged record, where a fast, well-calibrated empirical model outperforms the effort of building and calibrating a full physical model.

(ii) PVC Pipe Flow: Velocity, Reynolds Number and Friction Loss

Given.

Find. (a) $V$; (b) $Re$ and flow type; (c) $H_f$.

Approach. Continuity gives $V=Q/A$; classify the flow with $Re=Vd/\nu$; compute the Darcy–Weisbach friction loss $H_f=f(L/d)(V^2/2g)$ with $f$ from the explicit Swamee–Jain approximation to Colebrook.

1. Flow area and velocity. $$A=\frac{\pi d^2}{4}=\frac{\pi(0.300)^2}{4}=0.0707\ \text{m}^2,\qquad V=\frac{Q}{A}=\frac{0.500}{0.0707}=\boxed{7.07\ \text{m/s}}.$$
2. Reynolds number and flow type. $$Re=\frac{Vd}{\nu}=\frac{7.07\times0.300}{1.0\times10^{-6}}=\boxed{2.12\times10^{6}}\ \Rightarrow\ \textbf{turbulent}\ (Re\gg4000).$$
3. Friction factor (Swamee–Jain). $$f=\frac{0.25}{\left[\log_{10}\!\left(\dfrac{\varepsilon}{3.7d}+\dfrac{5.74}{Re^{0.9}}\right)\right]^2}=\boxed{0.0105}.$$
4. Darcy–Weisbach friction loss. Substituting connectors: with $f$, $L/d$ and $V$ known, $$H_f=f\,\frac{L}{d}\,\frac{V^2}{2g}=0.0105\times\frac{800}{0.300}\times\frac{7.07^2}{19.62}=\boxed{71.2\ \text{m}}.$$

(iii) Cross-Connection Scenarios and Prevention

Scenario 1 — back-siphonage at an unprotected fill connection. A garden hose or fill line is left submerged in a chemical tank, cooling tower or pool while the potable main upstream experiences a transient negative pressure (hydrant flushing, a water-main break, or an upstream pump shutdown); the drop in main pressure can literally siphon the tank's contaminated water backward into the distribution system through the open connection. Prevention: an atmospheric vacuum breaker (AVB) or reduced-pressure-zone (RPZ) backflow-prevention assembly — or simply a physical air gap — at every such fixture, with submerged inlets prohibited by the plumbing code.

Scenario 2 — an unprotected auxiliary-supply interconnection. An industrial or irrigation facility ties its potable main directly to a non-potable well, reclaimed-water or fire-protection loop for supply redundancy without an approved backflow preventer at the tie-in; if the potable side loses pressure while the non-potable side stays pressurized (backpressure), contaminated water is pushed into the drinking-water system. Prevention: a mandatory RPZ assembly (and ideally full physical separation, with no direct interconnection) at every auxiliary-supply tie-in, verified through the purveyor's annual cross-connection-control inspection and testing program.