Diode Pump Versus Gravity Feed in a Micro-irrigation Line
A smallholder installs a drip line fed from a 1.5 m elevated tank through 30 m of 16 mm internal-diameter pipe, then a manifold with 20 emitters each rated 2 L/h at 100 kPa. The tank surface is open to atmosphere and the outlet is at the base. The farmer measures total delivery of only about 12 L/h and finds the far emitters barely dripping. He proposes adding a cheap 12 V diaphragm pump rated at 1.2 bar and 6 L/min, powered by a 20 W panel. A neighbour says the pipe is too narrow and he should switch to 25 mm pipe instead. Assume water density 1000 kg/m^3 and g = 9.81 m/s^2.
1. Estimate the pressure available at the manifold from the elevated tank alone and explain the observed shortfall.
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Static head. A 1.5 m column gives Δp = ρgh = 1000 × 9.81 × 1.5 ≈ 14.7 kPa, or about 0.15 bar.
Compare with emitter rating. Emitters are rated 2 L/h at 100 kPa (1 bar). At 14.7 kPa the flow through a nominally turbulent (orifice-type) emitter scales roughly as sqrt(Δp), so each emitter would pass about 2 × sqrt(14.7/100) ≈ 2 × 0.38 ≈ 0.77 L/h. For 20 emitters that is ~15 L/h - close to the observed 12 L/h once friction losses in 30 m of 16 mm pipe are subtracted.
Friction. At ~15 L/h the velocity is tiny (Q ≈ 4.2×10^-6 m^3/s, A ≈ 2.0×10^-4 m^2, v ≈ 0.02 m/s), so pipe friction is small compared with the 14.7 kPa head. The dominant limitation is simply that gravity head is far below the emitter design pressure. The shortfall is a pressure problem, not mainly a diameter problem, though the narrow pipe worsens distribution along the line.
2. Evaluate the proposed 12 V pump: does its rated pressure and flow solve the problem, and what does the 20 W panel imply?
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Pressure. The pump is rated 1.2 bar ≈ 120 kPa, comfortably above the 100 kPa emitter rating. If it truly delivers that head at the manifold, emitters would run near their rated 2 L/h, giving ~40 L/h total - over three times the current output.
Flow check. The pump's free-flow rating is 6 L/min = 360 L/h, far above the 40 L/h the emitters demand. So the pump is not flow-limited; the emitter array sets the flow. The pump will operate far to the left of its free-delivery point, near shut-off head, which is fine as long as 1.2 bar exceeds the 100 kPa plus friction.
Power check. Delivered hydraulic power at 40 L/h and 100 kPa: P = QΔp = (40/3600/1000) × 100000 ≈ 1.1 W. Even at 30% pump efficiency the electrical demand is only a few watts, well within a 20 W panel in good sun. The pump is oversized in flow but adequately powered; a smaller pump would do, but this one will work.
Caveat. Panel output falls sharply in cloud and at low sun angle, so a battery or direct-connection matching check is advisable; the pump may stall at dawn and dusk.
3. Assess the neighbour's advice to upsize the pipe to 25 mm and recommend a course of action.
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Effect of upsizing. At the design flow of ~40 L/h the velocity in 16 mm pipe is about 0.055 m/s; in 25 mm pipe it falls to about 0.023 m/s. Friction head scales roughly with 1/D^5 at fixed flow (Darcy–Weisbach), so a jump from 16 to 25 mm cuts friction losses by a factor of roughly (25/16)^5 ≈ 9. But the absolute friction loss at these flows is already small - a fraction of a metre of head over 30 m - so the gain is minor compared with the 100 kPa the emitters need.
Diagnosis. The real deficit is pressure, not pipe bore. Upsizing pipe alone, with the gravity tank, would still leave only ~14.7 kPa at the manifold and emitters still underperform. The neighbour has misattributed a pressure problem to a diameter problem.
Recommendation. Install the pump (or raise the tank by roughly 10 m, which is impractical). Keep the 16 mm line unless distribution uniformity along the row proves poor; if far emitters still lag after pressurisation, then consider a larger submain or pressure-compensating emitters. Verify with a pressure gauge at the manifold before and after, and measure emitter output at the near and far ends to confirm uniformity.