Population forecasting for water supply design
Arithmetic, geometric and incremental increase methods with a worked example, and how per capita demand turns population into flow.
Water supply schemes are designed for about 30 years ahead, so we need the population at the end of the design period, not today's.
Arithmetic increase method
Assumes the population grows by the same number each decade. Suits old, settled cities.
Pn = P₀ + n x̄
x̄ is the average increase per decade and n the number of decades.
Geometric increase method
Assumes a constant percentage growth each decade. Suits young, fast-growing towns.
Pn = P₀ ( 1 + r100 )^n
r is the geometric mean growth rate per decade.
Incremental increase method
Takes the average increase x̄ and the average change in increase ȳ:
Pn = P₀ + n x̄ + n (n + 1)2 ȳ
It usually falls between the other two.
Worked example
| Year | Population | Increase | Change in increase |
|---|---|---|---|
| 1991 | 40,000 | ||
| 2001 | 46,000 | 6,000 | |
| 2011 | 53,000 | 7,000 | +1,000 |
| 2021 | 61,000 | 8,000 | +1,000 |
x̄ = 7,000, ȳ = 1,000. Forecast for 2051 (n = 3):
Arithmetic: P = 61,000 + 3 × 7,000 = 82,000
Incremental: P = 61,000 + 3 × 7,000 + 3 × 42 × 1,000 = 88,000
Growth rates are 15.0%, 15.2% and 15.1%, geometric mean ≈ 15.1%:
Geometric: P = 61,000 × 1.151³ = 93,000
From population to demand
Multiply by per capita supply. CPHEEO recommends 135 litres per capita per day for towns with sewerage and 150 lpcd for metro cities, plus allowance for losses. Pipes and treatment are then sized for peak flows, using a peak factor of 2 to 3 on the average daily demand for distribution mains.
Quick check
Which method usually gives the highest population forecast for a fast-growing young city?