Pump Cavitation Margin at Low Sump Level
A centrifugal pump draws 40 L/s of water at 35°C from an open sump and delivers it to a cooling tower. The pump manufacturer's NPSHr at this duty is 4.5 m. The sump water surface is normally 2.5 m below the pump centreline; at the low-level alarm it is 3.7 m below. The suction line is 6 m of 150 mm inside-diameter pipe with a Darcy friction factor of 0.02 and minor losses equal to 2.5 velocity heads. Atmospheric pressure is 101.3 kPa absolute and the vapour pressure of water at 35°C is 5.6 kPa absolute. The discharge valve is currently throttled; if it is fully opened, the flow is expected to rise by about 10%. The operators report occasional rattling noise from the pump casing at low sump level. You must decide whether the pump can be operated down to the low-level alarm with the valve fully open, and what operating limit to issue.
1. Compute NPSHa at normal and low sump level at 40 L/s.
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At 40 L/s, pipe area A=π/4(0.15)^2=0.01767 m², V=0.04/0.01767=2.263 m/s, velocity head V²/2g=0.261 m. Suction losses: friction hf=f(L/D)(V²/2g)=0.02(6/0.15)(0.261)=0.209 m; minor=2.5(0.261)=0.653 m; total=0.862 m. Pressure head available=(101.3−5.6)×10³/(1000×9.81)=9.755 m. Normal level: NPSHa=9.755−2.5−0.862=6.39 m. Low level: NPSHa=9.755−3.7−0.862=5.19 m. Both exceed NPSHr=4.5 m, but the low-level margin is only 0.69 m.
2. Evaluate the 10% flow increase at low level and the effect of water warming to 40°C.
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At 44 L/s (10% up), V=2.489 m/s, velocity head=0.316 m. Losses=0.02(6/0.15)(0.316)+2.5(0.316)=0.253+0.789=1.042 m. At low level and 35°C, NPSHa=9.755−3.7−1.042=5.01 m, margin 0.51 m. If water warms to 40°C, p_v=7.38 kPa, pressure head=(101.3−7.38)×10³/9810=9.57 m, NPSHa=9.57−3.7−1.042=4.83 m, margin only 0.33 m. That is too thin for transients; the rattling is consistent with incipient cavitation. The pump should not be cleared for full-open operation at low level.
3. Recommend an operating limit and a hardware fix.
Read the worked answer
Operating limit: keep sump above the low-level alarm; if the level falls to the alarm, throttle back to 40 L/s and do not open the discharge valve fully. Add a low-level interlock/trip. For a permanent fix, replace the 6 m suction line with 200 mm ID: V=0.04/0.03142=1.273 m/s, velocity head=0.083 m, losses=0.02(6/0.2)(0.083)+2.5(0.083)=0.050+0.207=0.257 m, giving NPSHa at low level=9.755−3.7−0.257=5.80 m. That restores a margin above 1 m. Also verify NPSHr at 44 L/s, since it rises with flow.