Pump Suction Lift, Cavitation Margin, and Where to Throttle
A centrifugal pump draws water at 60 °C from an open sump and delivers 45 m³/h to a header. The pump centreline is 4.2 m above the sump free surface. The suction line is 6 m of 100 mm inside-diameter commercial steel with two 90° elbows (K = 0.9 each), a fully open gate valve (K = 0.2), and a square-edged inlet (K = 0.5); take the Darcy friction factor as 0.022. At 60 °C, density is 983 kg/m³ and vapour pressure is 19.9 kPa; atmospheric pressure is 101.3 kPa. The manufacturer's NPSH required at 45 m³/h is 4.0 m. A new operator proposes throttling the suction valve to reduce flow to 35 m³/h because the motor is overloaded; another proposes throttling the discharge valve instead. The pump curve is flat near the duty point, and the suction valve is already one-third closed.
1. Calculate the available NPSH at 45 m³/h and decide whether cavitation is likely. State the dominant term in your result.
Read the worked answer
At 45 m³/h, Q = 45/3600 = 0.0125 m³/s. The pipe area is A = π(0.1)^2/4 = 7.854e-3 m², so V = Q/A = 1.59 m/s. The velocity head is V²/(2g) = 1.59²/(2 × 9.81) = 0.129 m. Major loss = f(L/D)(V²/2g) = 0.022 × (6/0.1) × 0.129 = 0.170 m. Minor-loss coefficient sum = 2(0.9) + 0.2 + 0.5 = 2.5, so minor loss = 2.5 × 0.129 = 0.323 m. Total suction loss = 0.493 m. The pressure head available above vapour pressure is (101.3 - 19.9) × 1000/(983 × 9.81) = 8.44 m. Therefore NPSHa = 8.44 - 4.2 - 0.493 = 3.75 m. Since NPSHr = 4.0 m, NPSHa is below the required value by 0.25 m, so cavitation is likely at the duty point, especially with any fouling. The dominant terms are the static lift and the vapour-pressure head; friction is secondary but still matters.
2. Evaluate the two throttling proposals. Which one, if either, reduces cavitation risk, and why? Quantify the change in suction loss at 35 m³/h assuming the same loss coefficients.
Read the worked answer
Throttling the suction valve adds a resistance upstream of the pump. It lowers the pressure at the pump inlet and therefore lowers NPSHa, so it makes cavitation worse even though it reduces flow. Throttling the discharge valve reduces flow without adding suction-side loss; it also moves the pump to a lower-flow point where NPSHr is usually smaller. At 35 m³/h, Q = 0.00972 m³/s and V = 0.00972/7.854e-3 = 1.24 m/s. The velocity head is 1.24²/(19.62) = 0.0784 m. Major loss = 0.022 × 60 × 0.0784 = 0.103 m. Minor loss = 2.5 × 0.0784 = 0.196 m. Total suction loss is 0.299 m, so NPSHa = 8.44 - 4.2 - 0.299 = 3.94 m. That is still below 4.0 m at the original NPSHr, but the required NPSH at 35 m³/h should be lower; the discharge-throttle proposal is the only one of the two that moves in the safe direction. The suction-throttle proposal should be rejected.
3. What minimum reduction in static suction lift would make the original 45 m³/h duty satisfy NPSHa ≥ NPSHr with a 0.5 m margin?
Read the worked answer
The target is NPSHa ≥ 4.0 + 0.5 = 4.5 m. At 45 m³/h the existing NPSHa is 3.75 m with a static lift of 4.2 m. The deficit is 4.5 - 3.75 = 0.75 m. Since NPSHa decreases one-for-one with static lift, the lift must be reduced by at least 0.75 m, from 4.2 m to 3.45 m or lower. Equivalently, the sump level must be raised or the pump lowered by 0.75 m. This assumes the same flow, suction-line loss, and vapour pressure. If the suction valve is left one-third closed, its additional loss must be included, so the required reduction would be larger. The calculation shows that the margin is controlled by the static lift, not by the pipe friction, and that a modest layout change is more effective than trying to tune the valve.