Question 10 of 11: Pit Dewatering

Question 5 — Pit Dewatering (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.

Given. Total lift, sump (1650 m) to crest = 90 m (this reconciles the stated 125 m pipe length on a 45° wall: 90/sin45° ≈ 127 m — adopted in preference to the paper’s literal “1440 m crest” figure, which would imply a 210 m drop, not a 90 m lift; treated as a misprint, since the paper itself states the lift as 90 m). Two equal 45 m stages: sump (1650 m) → tandem pump platform (1695 m) → crest (1740 m, corrected). Pump curves (Fig 5.2), read off the graph: HT (433) ≈ 55 m head at 0 L/s, falling to ≈23 m at 100 L/s; MT (431) ≈ 35 m head at 0 L/s, falling to ≈10 m at 250 L/s.

Find. Whether MT suffices for both pumps (5.2); the maximum flow deliverable to the crest (5.3); pump inlet/outlet pressures (5.4); required pipe schedule (5.5); check-valve implications (5.6).

5.1 — high-volume vs. high-head pumps. A high-volume (MT) pump uses a lower-head, larger-flow-area impeller design to move large flows against modest lift — typical for bulk in-pit dewatering where the vertical lift per stage is small. A high-head (HT) pump uses a higher-speed or multi-stage impeller design trading flow capacity for head, needed where a single stage must overcome a large elevation difference, as here. Both are usually the same base pump casing/motor family (hence “431/433” siblings) re-impellered for the two duties, simplifying spares and maintenance.

Approach (5.2/5.3). The pipeline runs in two equal 45 m elevation stages, sump→1695 m platform and 1695 m→crest; because it is a single continuous pipe with (by assumption) negligible friction loss, EACH pump individually must supply at least 45 m of head at the shared operating flow Q (both pumps see the same Q, in series).

1. Test MT alone. MT’s own SHUT-OFF (zero-flow, maximum) head is ≈35 m — less than the 45 m a single stage needs even before any flow is drawn. $$\boxed{\text{MT cannot meet either stage's head at any flow} \Rightarrow \text{No, MT is not used for both pumps}}$$
2. Find the HT operating point. Fit a smooth curve through the read points (0, 55), (50, 40), (100, 23) m and solve H_HT(Q) = 45 m.
3. Solve. $$H_{HT}(Q)=45 \Rightarrow Q \approx 34\ \text{L/s}$$ — at this flow the HT curve delivers exactly the 45 m each stage requires, so BOTH pumps must be the high-head (HT) configuration, and the resulting flow is the maximum steady discharge the system can sustain.

$$\boxed{Q_{max} \approx 34\ \text{L/s, both pumps HT (433)}}$$

5.4 — inlet/outlet pressures. The lower (sump) pump draws from the open sump at essentially 0 m gauge inlet pressure (submersible, atmospheric/static sump level) and discharges at its own head, 45 m of water, into the pipeline. That discharge becomes the tandem (upper) pump’s INLET pressure — 45 m, a pressurised suction, exactly why the question specifies the upper pump must handle a pressurised inlet fitting. The upper pump then adds its own 45 m of head on top of that, so its outlet delivers 45 + 45 = 90 m of water — exactly the total static lift required to reach the crest with negligible friction loss, confirming the two-stage design closes.

5.5 — pipe schedule. Converting 90 m of water to a working pressure: 90 m × (1.41 psi per 1 m water, per the given conversion) ≈ 127 psi (≈ 876 kPa) as the maximum static pressure the upper pump’s discharge line must contain, plus a standard safety margin for surge/water-hammer on pump start/stop. For HDPE pipe this level of sustained pressure calls for at least SDR 17 (PN 10, rated ≈ 1000 kPa at 20°C) class pipe on the upper (higher-pressure) discharge run, with the lower pump’s shorter, lower-pressure (45 m ≈ 64 psi ≈ 440 kPa) run able to use a lighter SDR 26 (PN 6) class — in both cases a generous safety factor above the static figure is prudent given the confirmed water-hammer risk noted in 5.6.

5.6 — check valve modifications. Fitting a check (gate) valve at the top pump’s outlet stops the pipeline from draining back into the sump when the pumps stop (protecting the lower pump from a reverse-flow restart surge and avoiding refilling the sump with the pipe’s own contents every shutdown) — but it also means the FULL 90 m static column is now permanently trapped and held by the valve and pipe between shutdowns rather than draining back, so the pipe, fittings and valve itself must all be rated for continuous static holding pressure (not just transient pumping pressure), and a small air-release/vacuum-relief valve should be added just below the check valve to prevent column separation and vacuum-induced pipe collapse when the pumps restart against the still-full column.