The Branch Tap That Stopped Flowing: A Hill Water Supply Scheme
A Water User Committee in a hill village of Gorkha manages a 2,000-litre ferro-cement tank whose water surface, when full, is 20 m above the main tapstand serving 18 households and 7 m above a branch tapstand serving 5 households further up the slope. The main pipe is 40 mm internal diameter; the branch is 20 mm internal diameter and 60 m long with five bends. In April the committee connected five more households to the branch, and the branch tap now gives only a thin stream, while the main tapstand still flows strongly. A joint on the branch has been leaking for weeks and nobody has repaired it. Villagers at the branch say the pipe 'has no pressure' and want the tank raised. The spring feeding the tank yields about 1.5 litres per second in April, and the committee meets on Saturday with Rs 40,000 to spend.
1. Using the heights given, estimate the pressure at each tapstand when the tank is full (take g = 10 m s⁻² and the density of water as 1000 kg m⁻³), and say whether raising the tank is a good use of the committee's money.
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Pressure is given by P = hρg.
- Main tapstand: h = 20 m → P = 20 × 1000 × 10 = 2.0 × 10⁵ Pa (about 2 atmospheres).
- Branch tapstand: h = 7 m → P = 7 × 1000 × 10 = 7.0 × 10⁴ Pa (about 0.7 atmosphere).
So the branch already has only about one-third of the driving head of the main tap.
Flow, however, is not fixed by pressure alone; it depends on head divided by the resistance of the pipe. Resistance rises steeply as diameter falls (roughly as 1/d⁴) and also rises with length and with every bend. A 60 m run of 20 mm pipe with five bends, a leaking joint and five extra households is therefore low head plus high resistance plus increased demand - together that explains the thin stream.
Raising the whole tank by 2 m would add only 2 × 1000 × 10 = 2 × 10⁴ Pa, about 10 per cent, at every tap, would consume a large share of Rs 40,000, and would put extra pressure on the older main. It treats a symptom, not the cause.
2. Rank the actions the committee should take with Rs 40,000 and justify the order.
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- Measure before spending (a few hundred rupees). Fit a pressure gauge or do a bucket-and-stopwatch flow test at both taps, and check for an airlock at the highest bend and for a partly closed valve. If the branch is blocked, replacing pipe would waste money.
- Replace the 20 mm branch with 32–40 mm pipe over its 60 m, remove two of the five bends, and repair the leaking joint. This gives the largest gain per rupee because resistance falls sharply as diameter increases; 60 m of 32 mm HDPE is a small fraction of the budget.
- Use the remainder for air and demand management. Fit an air-release valve at the highest bend, stop wastage at the main tapstand, and only if pressure is still marginal add a 1,000-litre relay tank at the branch cluster filled at night when demand is low.
Reject raising the tank: high cost, about 10 per cent gain, and added risk to the old main. The order follows two rules: diagnose before building, and buy the largest effect per rupee first.
3. A villager argues that the spring is drying up because the tank now empties faster. Test that claim with the numbers given.
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Convert the spring yield: 1.5 L/s × 3600 s = 5,400 litres per hour. A 2,000-litre tank would refill in 2,000 ÷ 5,400 h ≈ 0.37 h, about 22 minutes, if all the flow went into it. Over 24 hours the spring yields about 5,400 × 24 ≈ 129,600 litres, far more than 23 households can use for drinking, cooking and washing.
So the tank emptying faster is explained by increased draw - five extra households on the branch - not by a failing spring. The complaint and the physical evidence point in different directions, and the evidence wins.
One caution before closing the case: April is the dry season, and 1.5 L/s may already be the pre-monsoon minimum. Measure the spring yield again in the driest week, keep a weekly log, and compare it with total household demand. If it ever falls below demand, then storage and source capacity become the real constraint and pipe size no longer matters.