Population forecast 2021 census, 2024 base year

Base year 2024 and design period 20 years give the design year $2024+20 = 2044$. The last census is 2021, so $n = (2044-2021)/10 = 2.3$ decades.

Population forecast

Arithmetical increase method

Average increase per decade: $\bar x = \dfrac{43{,}000-16{,}000}{4} = 6{,}750.0$

$$P_{2044} = P_n + n\bar x = 43{,}000 + 2.3\times 6{,}750.0 = 58{,}525$$

Geometrical increase method

Average growth rate per decade (geometric mean): $r = \left(\dfrac{43{,}000}{16{,}000}\right)^{1/4}-1 = 28.037\%$

$$P_{2044} = P_n(1+r)^n = 43{,}000\times(1+0.28037)^{2.3} = 75{,}918$$

The two methods give 58,525 and 75,918. The data show a fairly steady increase of 6,000 to 8,000 per decade, while the percentage growth rate is falling. The geometric method (constant percentage growth) therefore overestimates, and the arithmetic method (constant increase) slightly underestimates, since the increase is still rising. The mean of the two methods is adopted as the design population.

$$P_{2044} = \frac{58{,}525+75{,}918}{2} = 67{,}221$$

Water demand

Domestic demand $= 67{,}221\times110/1000 = 7{,}394.4\ \mathrm{m^3/day}$.

Industrial demand is 25% and losses are 15% of the total demand $Q$, so the domestic demand is the remaining 60%.

$$\begin{aligned} Q &= \frac{7{,}394.4}{1-0.25-0.15} = \frac{7{,}394.4}{0.60} = 12{,}323.9\ \mathrm{m^3/day}\\ \text{Industrial} &= 0.25Q = 3{,}081.0\ \mathrm{m^3/day}\\ \text{Losses} &= 0.15Q = 1{,}848.6\ \mathrm{m^3/day} \end{aligned}$$

Answer: Design population (2044) = 67,221; total water demand = 12,324 m$^3$/day (142.6 l/s).