Sizing a rural piped water scheme: design population, main diameter and ESR staging
A village panchayat of 12,000 people (2021 census) is being given a piped water scheme with a 30-year design period and 1.8% annual geometric growth. The agreed rate is 135 lpcd. The source is a river intake 4 km away, pumping to a ground-level sump and then to an overhead service reservoir (ESR) sited on ground at RL 103.00 m; the lowest ground level in the town is RL 98.00 m and the highest served ground level is RL 102.50 m. An existing 150 mm diameter CI gravity main from the ESR already serves the town and the panchayat wants to reuse it for the new demand to save money. Distribution losses from the ESR to the critical point are estimated at 5.5 m; 7.0 m residual pressure is required for three-storey buildings. The financial sanction is ₹4.2 crore and the panchayat insists on a 900 kL ESR tank because 'bigger is better'.
1. Compute the 2051 design population, the average daily demand and the peak hourly demand, and state which peak factor you will adopt for (a) the transmission main from sump to ESR and (b) the distribution network, with reasons.
Read the worked answer
Population: 12,000 × (1.018)^30. ln 1.018 = 0.01784; × 30 = 0.5352; e^0.5352 = 1.708. So P = 20,492, say 20,500.
Average demand: 20,492 × 135 = 2,766,420 L/day ≈ 2.77 MLD, i.e. 0.0320 m³/s (32 L/s).
Peak hourly: with the customary peak factor of 3 for a small town, Q = 0.0961 m³/s (96 L/s).
Choice of factors:
- Distribution network: use 3.0. It must meet the maximum hourly draw, and there is no nearer storage to shave the peak.
- Transmission main (sump to ESR): use about 2.0–2.25, not 3.0. The ESR itself balances the hourly variation; sizing the rising/gravity main for the full hourly peak would inflate the diameter and the pumping head for a condition the tank absorbs. Take 2.25 × 0.0320 = 0.0721 m³/s.
Judgement note: the rate of 135 lpcd should be confirmed as inclusive of losses and cattle/industrial use; if not, add 15% before sizing. A fire-fighting allowance for a town of this size should be checked separately against the local fire demand formula.
2. Check the existing 150 mm main against the design flow, compute the velocity, select a replacement diameter, and comment on permissible velocities.
Read the worked answer
Check of the 150 mm CI main: area = π/4 × 0.15² = 0.01767 m².
- At the transmission design flow 0.0721 m³/s: v = 0.0721/0.01767 = 4.08 m/s.
- At the peak hourly flow 0.0961 m³/s: v = 5.44 m/s.
Both are far above the 1.0–1.5 m/s band used for design and above the 3 m/s scour/erosion limit for CI. Head loss varies roughly with v², so at 4–5 m/s the friction loss over 4 km (plus the distribution loss of 5.5 m) would consume the entire residual pressure and the scheme would fail at the critical point. The existing 150 mm main cannot be reused.
Replacement: required area at a design velocity of 1.0 m/s = 0.0721/1.0 = 0.0721 m² → d = √(4 × 0.0721/π) = 0.303 m. Select a 300 mm nominal bore main (v ≈ 1.02 m/s); a 350 mm main gives v ≈ 0.75 m/s and more future margin if the panchayat expects extension.
Velocity comment: keep 0.6–1.5 m/s for normal design; below about 0.3–0.5 m/s settlement and stagnation occur; above 3 m/s scour and surge problems appear. Specify the pipe class for the maximum static head at the lowest point, and provide air valves and scour valves along the 4 km route.
3. Test the panchayat's 900 kL ESR claim against the storage guideline and compute the minimum staging height needed to satisfy the residual pressure.
Read the worked answer
Storage: the normal guideline is total storage of about one-third of the average daily demand, made up of balancing, breakdown and fire reserve. One-third of 2.77 MLD = 0.92 ML ≈ 900 kL. So the panchayat's figure is, unusually, defensible - but the money question is where it sits. Splitting it as roughly 450 kL at the ESR (balancing) and 450 kL at the ground-level sump/general storage reduces the staging cost and the structural load on the tower.
Staging height (lowest level of water in the tank must satisfy the critical point):
- highest served ground level = RL 102.50
- residual pressure for three storeys = 7.0 m
- distribution loss to the critical point = 5.5 m
- required minimum water level = 102.50 + 7.0 + 5.5 = RL 115.00
With a 4.0 m deep tank, the tank base RL = 115.00 − 4.00 = RL 111.00. Ground at the ESR site is RL 103.00, so the staging height to the tank bottom is 8.0 m.
Checks the answer must carry: confirm the pressure at the lowest point (RL 98.00) - about 17 m head minus losses - against the pipe class; verify that 8 m of staging is adequate structurally and for the future 15% demand; and carry the final figure through a proper hydraulic analysis rather than a single-path estimate.