Zone-wise Water Supply: Aggregate Surplus Against Zonal Deficit
A district water review note lists five zones: A - 80,000 persons, 12.0 MLD supplied; B - 45,000 persons, 8.1 MLD; C - 1,20,000 persons, 15.0 MLD; D - 30,000 persons, 6.0 MLD; E - 20,000 persons, 2.0 MLD. The district norm is 135 litres per capita per day. The board's draft press note names Zone C as the worst-served zone, citing its size; the councillor from Zone E protests that her zone is worse. The finance wing counters that the district as a whole is in surplus, so no new source is needed this year. Zone C's distribution system is separately reported to lose 8 per cent of its input as non-revenue water, a figure the board has so far treated as an accounting detail rather than a supply problem.
1. Compute the per-capita supply of each zone, identify those below the norm, and quantify the shortfall in MLD.
Read the worked answer
Per-capita supply = MLD × 1,000,000 ÷ population:
- A: 12,000,000/80,000 = 150 lpcd
- B: 8,100,000/45,000 = 180 lpcd
- C: 15,000,000/120,000 = 125 lpcd
- D: 6,000,000/30,000 = 200 lpcd
- E: 2,000,000/20,000 = 100 lpcd
Against 135 lpcd, zones A, B and D are above the norm; C and E are below it.
Shortfall in volume:
- C: (135 − 125) × 120,000 = 1,200,000 L = 1.2 MLD
- E: (135 − 100) × 20,000 = 700,000 L = 0.7 MLD
Total = 1.9 MLD.
Note the two ways of reading 'worst': C is worst by absolute volume (1.2 MLD, and 1,20,000 people affected), while E is worst by relative service (100/135 = 74 per cent of the norm, a 26 per cent shortfall against C's 7 per cent). Both members are right in their own metric, which is why the metric has to be stated before the ranking is argued.
2. The finance wing argues that a district-level surplus means no new source is needed. Evaluate that argument.
Read the worked answer
District demand at the norm = 295,000 × 135 = 39.825 MLD. District supply = 12.0 + 8.1 + 15.0 + 6.0 + 2.0 = 43.1 MLD. Surplus = 3.275 MLD, about 8 per cent.
The arithmetic is right and the conclusion is wrong. The surplus sits entirely in A (1.2 MLD above norm), B (2.025 MLD) and D (1.5 MLD) - zones already over-supplied - while C and E are 1.9 MLD short. Water is not fungible across a district without transmission mains, storage and pressure; an aggregate figure is a bookkeeping statement, not a service level.
There is one useful inference in the numbers: the aggregate surplus (3.275 MLD) exceeds the aggregate deficit (1.9 MLD), so the binding constraint is conveyance and storage, not the source.
Answer: reject 'no new source needed'. The district needs a transfer main (or a local source for E), plus a leakage programme, and the press note should report C and E by name rather than a district average that no consumer experiences.
3. Zone C loses 8 per cent of its input as non-revenue water. What gross supply must it receive to deliver 135 lpcd at the tap, and how does that change the 1.2 MLD figure?
Read the worked answer
Required at the tap = 135 × 120,000 = 16.2 MLD. Gross input = 16.2/0.92 = 17.61 MLD, i.e. an additional 17.61 − 15.0 = 2.61 MLD of gross supply, not the 1.2 MLD implied by the norm gap.
Check the present position properly: 15.0 × 0.92 = 13.8 MLD at the tap = 115 lpcd, not 125. Zone C is 20 lpcd worse than the headline figure suggests.
Leakage control alone cannot close it. To deliver 16.2 MLD from a 15.0 MLD input you would need zero losses. A realistic cut to 4 per cent gives 15.0 × 0.96 = 14.4 MLD = 120 lpcd - still 15 lpcd short. With losses at 4 per cent, the gross requirement becomes 16.2/0.96 = 16.875 MLD, an addition of about 1.88 MLD.
Answer: C needs both measures. The scheme brief should quote roughly 2.6 MLD of additional gross supply at the present 8 per cent loss, or about 1.9 MLD if losses are first brought down to 4 per cent. Using the 1.2 MLD at-the-tap figure for the brief would under-provide the scheme from the day it is commissioned.