Booster Pump Cavitating Under Low Sump Level
A pump takes suction from an open sump whose water surface sits 3.0 m below the pump centerline. The suction line is DN150 (internal diameter 150 mm) with an equivalent length of 12 m and a total minor-loss coefficient of 4.5; take f = 0.020. Design flow is 40 L/s of water at 30 °C (density 996 kg/m³, vapor pressure 4.25 kPa); atmospheric pressure is 101.3 kPa. The selected pump requires 4.5 m of NPSH. Operators report rattling and pitting on the impeller after the sump was drawn down during a high-demand week, and the pump loses head shortly after start-up whenever the sump level is low.
1. Compute the net positive suction head available at design flow and compare it with the pump requirement.
Read the worked answer
Velocity and velocity head in the suction line:
$$A = \frac{\pi(0.150)^2}{4} = 0.01767 \text{ m}^2, \quad v = \frac{0.040}{0.01767} = 2.26 \text{ m/s}$$
$$\frac{v^2}{2g} = \frac{2.26^2}{19.62} = 0.261 \text{ m}$$
Suction losses:
$$h_f = f\frac{L}{D}\frac{v^2}{2g} = 0.020\cdot\frac{12}{0.150}\cdot 0.261 = 0.418 \text{ m}$$
$$h_m = K\frac{v^2}{2g} = 4.5(0.261) = 1.175 \text{ m}$$
Total = 1.59 m.
Available NPSH:
$$NPSH_A = \frac{p_{atm} - p_v}{\rho g} + z - h_L = \frac{(101.3 - 4.25)\times10^3}{996 \times 9.81} - 3.0 - 1.59$$
$$= \frac{97{,}050}{9{,}771} - 3.0 - 1.59 = 9.93 - 3.0 - 1.59 = 5.32 \text{ m}$$
Against a required 4.5 m, the margin is only 0.82 m - about 18% over the requirement, which is thin for a system whose sump level moves.
2. Explain the observed symptoms quantitatively, including what happens when the sump draws down.
Read the worked answer
NPSH_A is linear in sump level: every metre the surface drops removes a full metre of margin.
| Sump level below pump CL | NPSH_A | Margin vs 4.5 m |
|---|---|---|
| 3.0 m (design) | 5.32 m | +0.82 m |
| 4.5 m | 3.82 m | −0.68 m |
| 5.0 m | 3.32 m | −1.18 m |
When NPSH_A falls below the required 4.5 m, the lowest-pressure point in the impeller eye drops below vapor pressure, the liquid flashes, and the bubbles collapse as they move to higher pressure. That is exactly the reported signature: rattling (bubble collapse), pitting of the impeller (localized erosion at the collapse zone), and loss of head shortly after start-up (the head-flow curve breaks down once the vapor cavity occupies enough of the passage).
This is a hydraulic problem, not a worn-pump problem - replacing the impeller without changing the suction condition will simply erode the new one. A 1.5 m drawdown is well within normal operating range for a demand-driven sump, so the design margin, not the operator, is at fault.
3. Evaluate two fixes - upsizing the suction line to DN200 versus lowering the pump or raising sump level - and recommend.
Read the worked answer
Option 1: DN200 suction line.
$$A = 0.03142 \text{ m}^2,\quad v = 1.27 \text{ m/s},\quad \frac{v^2}{2g} = 0.0826 \text{ m}$$
$$h_f = 0.020\cdot\frac{12}{0.200}\cdot 0.0826 = 0.099 \text{ m};\quad h_m = 4.5(0.0826) = 0.372 \text{ m}$$
Total loss 0.47 m (vs 1.59 m), so $NPSH_A = 9.93 - 3.0 - 0.47 = 6.46$ m - a gain of 1.14 m. At a 4.5 m sump level, NPSH_A ≈ 4.96 m, which now clears the requirement.
Option 2: Lower the pump / raise minimum sump level by 1.5 m. Gains 1.5 m directly, giving NPSH_A = 6.8 m at design level - the largest single gain, and it costs almost nothing if the foundation or a low-level control setpoint can be changed.
Recommendation: the cheapest reliable fix is a minimum-level setpoint (and, if the drawdown is truly needed, lowering the pump by ~1 m); the pipe upsizing is the capital fix if the sump must be drawn down further. Either way, verify with a margin target of at least 1.0–1.5 m, and check the harsher case of warmer water: at 40 °C the vapor pressure rises to ~7.4 kPa, which removes another ~0.3 m of available NPSH.