Dewatering Pump Selection: System Head, NPSH and the Cost of a Small Pipe
A foundation pit for a barrage cut-off wall is being dewatered to keep the excavation dry. The sump water surface is 12.0 m below the outfall invert, and the pump is mounted on a platform 4.0 m above the sump water surface. The discharge line is 130 m of 100 mm internal diameter pipe with a friction factor of 0.020 and minor losses equal to 12% of the friction loss. The required duty is 20 litres per second, running continuously; sump inflow is steady. A pump has been offered whose published duty point is 24 m total head at 20 l/s, with NPSH required of 3.5 m. Site water temperature is 30 °C and the suction line loss is estimated at 0.6 m. A second quotation offers a 150 mm discharge line at higher capital cost, to be used with the same pump. The engineer must decide which to buy.
1. Compute the system total head at 20 l/s and decide whether the offered pump will deliver the duty.
Read the worked answer
Pipe bore and velocity: A = π(0.05)² = 7.854 × 10⁻³ m²; v = 0.020 / 7.854 × 10⁻³ = 2.55 m/s.
Velocity head: v²/2g = 6.48/19.62 = 0.33 m.
Friction loss: hf = f (L/d)(v²/2g) = 0.020 × (130/0.100) × 0.33 = 0.020 × 1300 × 0.33 = 8.59 m.
Minor losses: 0.12 × 8.59 = 1.03 m.
System head: 12.0 + 8.59 + 1.03 + 0.33 = 21.95 m, say 22 m.
The pump gives 24 m at 20 l/s, so it will deliver slightly more than 20 l/s at about 22 m - the duty is met, but with only a ~2 m (9%) margin. A 2.55 m/s velocity in a 100 mm line is high for continuous dewatering; erosion at bends and a high friction bill follow from it. The pump is acceptable, but the pipe is the weak link.
2. Check the NPSH available and state the operating conditions under which the pump would cavitate.
Read the worked answer
NPSHa = (Patm − Pv)/(ρg) − suction lift − suction losses.
At 30 °C, vapour pressure of water ≈ 4.25 kPa, atmospheric ≈ 101.3 kPa, and ρg ≈ 9.79 kN/m³:
(101.3 − 4.25)/9.79 = 97.05/9.79 = 9.91 m.
NPSHa = 9.91 − 4.0 − 0.6 = 5.31 m.
Against an NPSHr of 3.5 m this gives a margin of 1.8 m, which is adequate (a margin of at least 0.5–1.0 m is normally insisted upon, and more where the duty is continuous).
The margin disappears if: the sump level falls below the assumed level while the platform stays fixed (every 1 m of extra lift costs 1 m of NPSHa); the suction strainer or foot valve chokes (the 0.6 m allowance rapidly becomes metres); water temperature rises, which matters little up to 40 °C but is worth checking in summer; or the pump is run at a higher flow than design, which raises suction loss. Install a low-level cut-out and a strainer-cleaning routine, and record sump level against suction vacuum so that choking is detected before cavitation damage starts.
3. Evaluate the 150 mm option on head and running cost, and give a recommendation.
Read the worked answer
150 mm bore: A = 0.01767 m², v = 0.020/0.01767 = 1.13 m/s, v²/2g = 0.065 m.
hf = 0.020 × (130/0.150) × 0.065 = 0.020 × 866.7 × 0.065 = 1.13 m; minor losses = 0.14 m.
System head = 12.0 + 1.13 + 0.14 + 0.065 = 13.3 m.
Head saved: 21.95 − 13.3 = 8.6 m at the same 20 l/s.
Power saved: hydraulic power = ρgQH = 1000 × 9.81 × 0.020 × 8.6 = 1.69 kW. At a pump efficiency of about 65% and motor efficiency of about 90%, this is roughly 2.9 kW of electrical input, i.e. about 69 kWh/day at 24-hour running - around 25,000 kWh a year. Even at ₹7 per unit that is over ₹1.7 lakh a year, which will normally pay back the extra cost of bigger pipe within the project duration, before counting the better NPSH margin, lower velocity and lower erosion.
Recommendation: buy the 150 mm line. It also drops the operating point further out on the pump curve, so verify the resulting flow against sump inflow and fit a throttle or trim the impeller if the pump would otherwise run out too far.