--- title: "Population forecast 2021 census, 2024 base year" subject: "Water Supply Engineering" chapter: 3 key: "semester_5/water_supply_engineering:pop-b81" source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-b81 site: BCT Engineering --- # Population forecast 2021 census, 2024 base year Water Supply Engineering · Chapter 3: Quantity of Water - Asked in: 2081 Bhadra, 8 marks - Video: [population forecasting, Arithmetic increase method with example, water supply engineering numericals](https://www.youtube.com/watch?v=K6sSBXtUFY4) — Civil Engineering Exam - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-b81 - Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-3 ## Question Population of a municipality in Nepal as obtained from census data is as follows: | Year (A.D) | 1981 | 1991 | 2001 | 2011 | 2021 | |---|---|---|---|---|---| | Population | 16000 | 22000 | 28000 | 35000 | 43000 | Forecast the population for the design year using any two methods. Determine the water demand for the municipality at the end of the design year if the base year is taken as 2024 AD and the design period is 20 years. Assume per capita water allowance of 110 lpcd. Take industrial demand as 25% of total demand and water losses wastage as 15% of the total demand. Neglect other demands. ## Short answer Using arithmetical increase method, population in 2044 is 58,525; geometrical increase gives 75,918. Design population adopted as mean 67,221. Total water demand (including 25% industrial and 15% losses) is 12,324 m³/day (142.6 L/s). ## Answer 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).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Base year 2024 and design period 20 years with last census 2021: what is n? A. 2.3 decades B. 2.0 decades C. 2.4 decades D. 4.4 decades Answer: A. Design year 2044; (2044-2021)/10 = 2.3. (Key point: Design year and n) 2. What is the arithmetic forecast formula used? A. P = Pn(1+r)^n B. P = Pn + n x average decadal increase C. P = Pn + n x mean + n(n+1)/2 y D. P = average of last two Answer: B. Arithmetical increase adds n times the average increase per decade (6,750), giving 58,525. (Key point: Arithmetical method) 3. Industrial 25% and losses 15% are fractions of total Q. How is Q found from domestic? A. Q = domestic x 1.40 B. Q = domestic / 0.85 C. Q = domestic / 0.60 D. Q = domestic x 0.60 Answer: C. Domestic is the remaining 60% of Q, so Q = 7,394.4/0.60 = 12,324 m3/day. (Key point: Demand with percentages) 4. Why is the geometric result not adopted alone? A. It is too low B. The data show almost constant increase, so geometric is too high; the mean 67,221 is adopted C. Census data are unreliable D. It has no formula Answer: B. Population increases by roughly constant amounts per decade, so geometric overestimates. 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