Energy cost of a drip irrigation pump with a clogging filter
A 0.5-ha drip-irrigated orchard pumps water from a reservoir whose surface is 12 m below the drip-line inlet. At a flow of 8.0 m3/h, the pipe and filter cause 3.5 m of head loss, and the drip system requires 1.0 bar (10.2 m of water) at the filter outlet. The pump has an efficiency of 65%, the motor 90%, and electricity costs USD 0.12 per kWh. The system runs 6 h/day for 90 days. Use g = 9.81 m/s2 and water density 1000 kg/m3. The grower wants to know the seasonal energy cost. The manager also proposes postponing filter cleaning until the end of the season, arguing that a dirty filter cannot change the pump's energy use because the pump curve is fixed. The suction strainer is already partly blocked, and the pump sometimes makes a rattling noise.
1. Calculate the daily electrical energy use and the seasonal electricity cost under the stated clean-filter conditions. Show the head, hydraulic power and efficiency steps.
Read the worked answer
Total head H = elevation lift + friction loss + pressure head = 12 + 3.5 + 10.2 = 25.7 m. Flow Q = 8.0 m3/h ÷ 3600 s/h = 2.222 × 10^-3 m3/s. Hydraulic power = rho g Q H = 1000 × 9.81 × 2.222 × 10^-3 × 25.7 = 560 W. Overall efficiency = 0.65 × 0.90 = 0.585. Electrical power = 560 / 0.585 = 958 W = 0.958 kW. Daily energy = 0.958 kW × 6 h = 5.75 kWh/day. Seasonal energy = 5.75 × 90 = 517 kWh. Seasonal cost = 517 × 0.12 = USD 62.1 (approximately USD 62).
2. If clogging raises the pipe/filter loss from 3.5 m to 7.0 m, recalculate the seasonal cost. Explain why a blocked suction strainer can damage the pump even if the motor still runs.
Read the worked answer
New total head = 12 + 7.0 + 10.2 = 29.2 m. Hydraulic power = 1000 × 9.81 × 2.222 × 10^-3 × 29.2 = 637 W. Electrical power = 637 / 0.585 = 1089 W = 1.089 kW. Daily energy = 1.089 × 6 = 6.53 kWh/day; seasonal energy = 6.53 × 90 = 588 kWh; cost = 588 × 0.12 = USD 70.6. The extra head raises the seasonal cost by about USD 8.5, or roughly 14%. The manager is wrong that a dirty filter cannot change energy use: at a given flow, the pump must produce more head, so power rises. A blocked suction strainer is more serious than a dirty discharge filter. It lowers the pressure at the pump inlet and reduces the net positive suction head available. If this falls below the pump's required NPSH, cavitation occurs: vapour bubbles form and collapse, causing noise, vibration, erosion of the impeller and loss of performance. The pump can be damaged even while the motor continues to run.