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Population forecast to 2040, geometric method

Short answer

By geometrical increase method (r = 29.36% per decade), population in 2040 is 68,493. Domestic demand plus 20% industrial and 15% losses gives total water demand 12,645 m³/day (146.4 L/s).

Population of a town in Nepal as obtained from the census report is as follows:

Year (AD)19811991200120112021
Population1500021000270003400042000

Forecast the population of the town in the year 2040 by geometrical increase method and calculate the design year total water demand assuming per capita demand of 120 lpcd. Take industrial demand as 20% of total demand and losses wastage as 15% of total demand. Neglect demands other than domestic, industrial and losses.

The last census is 2021; for 2040, n=(2040−2021)/10=1.9n = (2040-2021)/10 = 1.9 decades.

Population by geometrical increase method

Average growth rate per decade (geometric mean): r=(42,00015,000)1/4−1=29.357%r = \left(\dfrac{42{,}000}{15{,}000}\right)^{1/4}-1 = 29.357\%

P2040=Pn(1+r)n=42,000×(1+0.29357)1.9=68,493P_{2040} = P_n(1+r)^n = 42{,}000\times(1+0.29357)^{1.9} = 68{,}493

Water demand in 2040

Domestic demand =68,493×120/1000=8,219.2 m3/day= 68{,}493\times120/1000 = 8{,}219.2\ \mathrm{m^3/day}.

Industrial demand (20%) and losses (15%) are fractions of the total demand QQ, so the domestic demand is 65% of QQ.

Q=8,219.21−0.20−0.15=8,219.20.65=12,645.0 m3/dayIndustrial=0.20Q=2,529.0 m3/day,Losses=0.15Q=1,896.7 m3/day\begin{aligned} Q &= \frac{8{,}219.2}{1-0.20-0.15} = \frac{8{,}219.2}{0.65} = 12{,}645.0\ \mathrm{m^3/day}\\ \text{Industrial} &= 0.20Q = 2{,}529.0\ \mathrm{m^3/day},\quad \text{Losses} = 0.15Q = 1{,}896.7\ \mathrm{m^3/day} \end{aligned}

Answer: Population in 2040 = 68,493; total water demand = 12,645 m3^3/day (146.4 l/s).

✓ Answer checked by Claude Opus 5.5 (high effort)

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