Pump Selection for a Variable-Demand Irrigation Line
A farm's irrigation main must deliver 18 L/s through 240 m of pipe to a centre-pivot. Two pumps are quoted. Pump A is a fixed-speed centrifugal unit with a measured duty point of 18 L/s at 42 m head and 78% efficiency; throttling it to 12 L/s (the night-time demand) drops efficiency to 61%. Pump B is a variable-speed drive unit that holds 74% efficiency across 12-18 L/s but costs $4,800 more and adds a VSD that consumes 0.9 kW of its own losses. Electricity is $0.31/kWh. The line runs 5 h/day at 18 L/s and 7 h/day at 12 L/s, 350 days/year. Friction head at 18 L/s is 11 m; at 12 L/s it falls to about 5 m. Static lift is 22 m. The client wants the lowest 5-year cost and asks which pump to buy.
1. Estimate the annual energy use of each pump and state which has the lower 5-year cost.
Read the worked answer
Water power = ρgQH. At 18 L/s and 42 m: P_h = 1000×9.81×0.018×42 = 7.42 kW. At 78% efficiency, Pump A draws 7.42/0.78 = 9.51 kW for 5 h = 47.6 kWh/day.
At 12 L/s the required head is static 22 m plus friction 5 m = 27 m. P_h = 1000×9.81×0.012×27 = 3.18 kW. Throttled efficiency 61% gives 5.21 kW for 7 h = 36.5 kWh/day. Pump A total ≈ 84.1 kWh/day = 29,400 kWh/year ≈ $9,120/year.
Pump B at 18 L/s: 7.42/0.74 = 10.03 kW plus 0.9 kW VSD = 10.93 kW × 5 h = 54.7 kWh. At 12 L/s: 3.18/0.74 = 4.30 kW plus 0.9 = 5.20 kW × 7 h = 36.4 kWh. Total ≈ 91.1 kWh/day = 31,900 kWh/year ≈ $9,890/year.
Pump A is cheaper to run by about $770/year and $4,800 cheaper to buy, so Pump A wins on 5-year cost. The key judgement is that the VSD's fixed parasitic loss outweighs its efficiency advantage at these low flows, and that throttling losses are modest because the flow turndown is only 1.5:1.
2. The farmer reveals the pivot may later expand, raising peak flow to 26 L/s. Reassess the decision.
Read the worked answer
At 26 L/s friction rises roughly with Q², so from 11 m at 18 L/s: 11×(26/18)² ≈ 23 m, plus 22 m static = 45 m head. Pump A's fixed-speed curve was set at 18 L/s/42 m; pushing to 26 L/s moves it far out on its curve where head falls and efficiency drops sharply - it likely cannot hold 45 m at all, so throttling cannot fix this. Pump B can raise speed to meet the new duty while staying near its best efficiency band.
The earlier conclusion was correct for the stated duty but is conditional on flow staying at or below 18 L/s. A good answer flags that the 5-year cost comparison ignores expandability, and that a pump unable to meet a plausible future duty has an implicit replacement cost far exceeding the $4,800 premium. Recommend Pump B, or a larger Pump A impeller trimmed for the higher duty, and note the decision hinges on the probability of expansion.