---
title: "Population 2030 AD by three methods, with fire demand"
subject: "Water Supply Engineering"
chapter: 3
key: "semester_5/water_supply_engineering:pop-as67"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-as67
site: BCT Engineering
---

# Population 2030 AD by three methods, with fire demand

Water Supply Engineering · Chapter 3: Quantity of Water

- Asked in: 2067 Asar (old course)
- 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-as67
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-3

## Question

Estimate the population of a town for design year 2030 AD by any three methods and calculate the design quantity of water in litres/day. The census data are as follows:

| Year (AD) | 1970 | 1980 | 1990 | 2000 |
|---|---|---|---|---|
| Population | 40000 | 45000 | 55000 | 62000 |

Also consider fire demand and losses and wastage.

## Short answer

Design population for 2030 (mean of three methods): 90,033. Design water demand: 18,756,464 l/day (18.76 million l/day) including domestic, losses, and 2-hour fire demand.

## Answer

The last census is 2000, so for 2030, $n = 3$ decades. Three methods are used.

**Arithmetical increase method**

Average increase per decade: $\bar x = \dfrac{62{,}000-40{,}000}{3} = 7{,}333.3$

$$
P_{2030} = P_n + n\bar x = 62{,}000 + 3\times 7{,}333.3 = 84{,}000
$$

**Geometrical increase method**

Average growth rate per decade (geometric mean): $r = \left(\dfrac{62{,}000}{40{,}000}\right)^{1/3}-1 = 15.729\%$

$$
P_{2030} = P_n(1+r)^n = 62{,}000\times(1+0.15729)^{3} = 96{,}100
$$

**Incremental increase method**

Increase per decade: 5,000, 10,000, 7,000; incremental increase: 5,000, -3,000.
$\bar x = 7{,}333.33$, $\bar y = 1{,}000.00$

$$
P_{2030} = P_n + n\bar x + \frac{n(n+1)}{2}\bar y = 62{,}000 + 3(7{,}333.33) + \frac{3(4)}{2}(1{,}000.00) = 90{,}000
$$


| Method | Population (2030) |
|---|---|
| Arithmetical increase | 84,000 |
| Geometrical increase | 96,100 |
| Incremental increase | 90,000 |

The mean of the three is adopted as the design population:
$P_{2030} = 90{,}033$.

#### Design quantity of water
Assumptions: domestic and public demand 135 lpcd (IS 1172), losses and wastage 15% of the domestic demand, fire demand by the National Board of Fire Underwriters formula for a duration of 2 hours.

$$
\begin{aligned}
\text{Domestic} &= 90{,}033\times135 = 12{,}154{,}455\ \text{l/day}\\
\text{Losses} &= 0.15\times12{,}154{,}455 = 1{,}823{,}168\ \text{l/day}\\
Q_f &= 4637\sqrt{P}\,(1-0.01\sqrt{P}),\ P = 90.03\ \text{(thousand)}\\
&= 39{,}823.7\ \text{l/min}\\
\text{Fire volume (2 h)} &= 39{,}823.7\times120 = 4{,}778{,}841\ \text{l}
\end{aligned}
$$

$$
Q_{total} = 12{,}154{,}455+1{,}823{,}168+4{,}778{,}841 = 18{,}756{,}464\ \text{l/day}
$$

**Answer: Design population (2030) = 90,033; design quantity of water = 18,756,464 l/day (18.76 million l/day), including losses and a 2-hour fire demand.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is the average increase (62,000-40,000)/3?
   A. Four census years give 4 intervals
   B. Four census years give 3 decade intervals
   C. The design period is 3 decades
   D. It is the geometric mean
   Answer: B. The average is over the 3 decades. (Key point: Arithmetic increase)

2. How is the design population 90,033 chosen?
   A. The geometric value
   B. The arithmetic value
   C. Mean of the arithmetic, geometric and incremental values
   D. The incremental value only
   Answer: C. (84,000+96,100+90,000)/3 = 90,033. (Key point: Adopted population)

3. Fire demand by the NBFU formula, Q = 4637 sqrt(P)(1-0.01 sqrt(P)), uses P in what unit and gives what unit?
   A. P in thousands; Q in l/min
   B. P in persons; Q in l/s
   C. P in thousands; Q in m^3/day
   D. P in lakhs; Q in l/s
   Answer: A. With P = 90.03 thousand, Q = 39,824 l/min; for 2 h multiply by 120. (Key point: Fire demand)

4. How is the total design quantity formed?
   A. Domestic only
   B. Domestic + 15% losses of domestic + 2-hour fire volume
   C. Domestic + fire flow in l/min
   D. Domestic x 1.15 x 1.5
   Answer: B. 12,154,500+1,823,175+4,778,849 = 18,756,524 l/day. (Key point: Total quantity)

## Related in Water Supply Engineering

- [Water demand 2030, fully plumbed town](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-a74) — Water Supply Engineering, chapter 3
- [Population 2088 by three methods, design year demand](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apop-k72) — Water Supply Engineering, chapter 3
- [Population forecast 2021 census, 2024 base year](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apop-b81) — Water Supply Engineering, chapter 3
- [Rural area demand 2025 AD, incremental increase](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-bk68) — Water Supply Engineering, chapter 3
- [Population in survey year from design demand 800 m3](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apop-s73) — Water Supply Engineering, chapter 3, asked 2×
- [Population 2070 by three methods, demand 2080](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apop-bk80) — Water Supply Engineering, chapter 3, asked 2×

## Related in other subjects

- [Log-Pearson III 50-year flood, 1990-2006](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Alog-pearson-50yr-1990-2006) — Engineering Hydrology, chapter 6
- [Maximum demand and need to calculate it](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Amaximum-demand-need) — Industrial Power Distribution and Illumination, chapter 1
- [TCTO numerical: seven activities, Rs 2000/day](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Atcto-2079-shrawan) — Construction Management, chapter 2
- [Preliminary estimate: office, 2000 m², Rs 20000](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aprelim-est-office-2000-g) — Estimating and Costing, chapter 3