Question 3 of 7

Problem 3 (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) The natural hydrologic cycle of a watershed draining to a lake (7 marks)

The cycle is a closed mass balance of water moving between atmosphere, land and water body. Precipitation falling on the watershed splits at the ground surface: part is intercepted by vegetation and evaporates directly back to the atmosphere; part infiltrates into the soil, replenishing soil moisture and, where it exceeds field capacity, recharging groundwater; and the remainder, once depression storage is satisfied, becomes surface runoff that concentrates in rills and channels and flows overland and through the stream network to the lake. Infiltrated water that does not stay in the root zone moves laterally as interflow or percolates to the water table and discharges slowly to the lake as groundwater baseflow, sustaining lake and stream levels between storms. From the lake and the watershed surface (and via transpiration from vegetation), evaporation and evapotranspiration return moisture to the atmosphere, where it condenses into clouds and eventually falls again as precipitation, closing the cycle. The watershed boundary (the topographic divide) defines the entire contributing area for this mass balance — every drop of precipitation within it is accounted for by evapotranspiration, change in storage (soil, groundwater, snowpack), and net outflow at the lake.

(ii) In-line storage in a stormwater collection system (7 marks)

In-line storage provides temporary detention volume within the storm sewer conveyance system itself — for example an oversized trunk pipe, box culvert or storage tunnel segment placed in the flow path — rather than as a separate off-line pond that flow is diverted into. Two important design considerations are: (1) the storage volume and outlet control (an orifice, weir or vortex regulator) must be sized together by hydraulic routing of the design inflow hydrograph, since the outlet restricts outflow and creates the very backwater that fills the in-line storage — undersizing the outlet risks unacceptable surcharging or upstream flooding, while oversizing it defeats the attenuation purpose; and (2) because in-line storage segments run at reduced velocity for much of the storm, they are prone to sediment and debris deposition, so access for inspection, flushing and cleanout (manholes, adequate pipe slope where possible, or a low-flow channel) must be built into the design.

Its primary function is peak-flow attenuation: by temporarily storing a portion of the storm runoff volume within the pipe network and releasing it at a controlled rate after the peak of the inflow hydrograph has passed, in-line storage reduces the peak discharge delivered to the downstream trunk sewer or receiving water, mitigating downstream surcharging, flooding and erosion without requiring a separate surface facility.

(iii) Assumptions underlying Manning's Equation for storm sewer sizing (6 marks)

$$Q = \frac{1}{n}\,A\,R^{2/3}\,S^{1/2}$$

1. Steady, uniform (normal) flow. The equation assumes the energy grade line, water surface and bed all run parallel ($S_0 = S_f = S_w$) at a constant depth along the reach — valid for a prismatic pipe run at normal depth, but not through junctions, bends, transitions or backwater zones where depth and velocity change along the pipe.
2. A single, representative roughness coefficient $n$ that is independent of Reynolds number/velocity. Manning's $n$ is treated as a constant material/condition property (new PVC vs. aged concrete, for example) even though real resistance can vary somewhat with flow depth and velocity; using an inappropriate $n$ for the pipe material, age or partial-flow condition is a common source of error.
3. A prismatic channel/pipe of essentially constant cross-section and slope along the design reach. The geometry (and hence $A$ and $R$) is assumed not to change over the length being sized; composite sections, sudden slope breaks, or a pipe run with mixed materials require the reach to be broken into sub-segments each satisfying the assumption, or a more detailed gradually-varied-flow analysis.