Question 4 of 7: Stormwater Dry Ponds, Cold-Water Fishery Protection and a Centrifugal Pump Impeller Change

Problem 4: Stormwater Dry Ponds, Cold-Water Fishery Protection and a Centrifugal Pump Impeller Change (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) Stormwater Dry Pond — Purpose and Design Basis

A dry pond is normally empty between storms and is sized to temporarily detain the design storm's runoff volume, releasing it slowly through a metered low-flow outlet (orifice or riser) to attenuate the peak discharge down to a target (often the pre-development) rate, thereby preventing the increased imperviousness of urban development from increasing downstream flood peaks and channel erosion. Its key design basis is a storage-indication (routing) analysis: the inflow hydrograph for the design storm is routed through the pond's stage-storage and stage-discharge relationships to size the storage volume and outlet structure so the peak outflow does not exceed the target rate, with an emergency spillway sized for a larger (e.g., 100-year or PMF-derived) storm to safely pass overtopping flow without failing the embankment. Because it lacks a permanent pool, a dry pond provides comparatively limited water-quality (sediment/pollutant) treatment relative to a wet pond — its design basis is fundamentally a quantity-control (peak-attenuation), not a quality-control, problem.

(ii) Cold-Water Fishery Temperature Mitigation Measures

Three measures to reduce the thermal impact of pond effluent on a downstream cold-water fishery: (1) subsurface (bottom) withdrawal outlet — drawing the discharge from near the pond bottom rather than skimming warm surface water, since a stratified pond's bottom layer stays several degrees cooler through the summer; (2) shade the pond and outlet channel with retained or planted riparian vegetation, reducing solar heat gain to the permanent pool and to the discharge channel before it reaches the receiving stream; and (3) infiltration/exfiltration or a subsurface gravel discharge (thermal mitigation trench) in place of a direct open-channel outfall — routing effluent through soil or gravel before it reaches the watercourse cools it toward ambient groundwater temperature and adds a further quantity-control benefit, consistent with CCME/provincial guidance for stormwater discharges to sensitive cold-water habitat.

(iii) Impeller Diameter Change: New Operating Point via the Pump Affinity Laws

Given.

Find. The new BEP capacity $Q_2$, head $H_2$, brake power $P_2$, expected efficiency $\eta_2$, and the % capacity improvement.

Approach. At constant speed, geometrically similar impeller trims within the same casing obey the pump affinity laws: $Q\propto D$, $H\propto D^2$, $P\propto D^3$, with efficiency approximately unchanged for a modest trim ratio. This is exactly equivalent to reading the new BEP off the intersection of the $D_2$ curve with the parabola $H=(H_1/Q_1^2)Q^2$ passing through the origin and the original BEP — the standard graphical technique for a multi-diameter pump chart.

1. Diameter ratio. $$r=\frac{D_2}{D_1}=\frac{140}{110}=\boxed{1.273}.$$
2. New capacity (affinity law, $Q\propto D$). $$Q_2=Q_1\,r=0.0140\times1.273=\boxed{0.0178\ \text{m}^3/\text{s}}\ (17.8\ \text{L/s}).$$
3. New head (affinity law, $H\propto D^2$). $$H_2=H_1\,r^2=20.0\times(1.273)^2=\boxed{32.4\ \text{m}}.$$
4. Efficiency and brake power. Efficiency is assumed essentially unchanged for a geometrically similar trim, $\eta_2\approx\eta_1=\boxed{70\%}$. Brake power follows either $P\propto D^3$ or directly from $P=\rho g Q H/\eta$: $$P_2=\frac{\rho g Q_2 H_2}{\eta_2}=\frac{1000\times9.81\times0.0178\times32.4}{0.70}=\boxed{8.09\ \text{kW}}.$$
5. Percent capacity improvement. This follows directly from the diameter ratio alone, independent of the assumed BEP reading: $$\%\ \text{improvement}=(r-1)\times100\%=\boxed{27.3\%}.$$