---
title: "Demand 2074 BS, geometric and decreasing rate"
subject: "Water Supply Engineering"
chapter: 3
key: "semester_5/water_supply_engineering:demand-a75"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/demand-a75
site: BCT Engineering
---

# Demand 2074 BS, geometric and decreasing rate

Water Supply Engineering · Chapter 3: Quantity of Water

- Asked in: 2075 Asoj, 8 marks
- Video: [FORECAST THE POPULATION OF GIVEN YEAR- WATER SUPPLY ENG. 4TH SEMESTER @Er.dipesh186 NUMERICAL](https://www.youtube.com/watch?v=EsTkhEvqRDg) — Er. Dipesh Bhatt
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/demand-a75
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-3

## Question

The survey is carried out in year 2074 B.S. for a water supply scheme for a new municipality with the per capita water allowance of 110 lpcd. Calculate the total water demand at the service year considering the base and design period of 5 and 30 years respectively if population is forecasted from (a) Geometrical increase method and (b) Decreased rate of growth method. The collected census data of the town is as follows:

| Year B.S. | 2034 | 2044 | 2054 | 2064 | 2074 |
|---|---|---|---|---|---|
| Population (Nos) | 45,500 | 49,000 | 53,000 | 57,000 | 59,500 |

## Short answer

Geometrical method gives population 75,242 and demand 8,277 m3/day. Decreasing rate method gives population 63,465 and demand 6,981 m3/day.

## Answer

Survey year 2074 BS; base period 5 years and design period 30 years, so the design year is $2074+5+30 = 2109$ BS. The last census is 2074, so $n = 35/10 = 3.5$ decades.

#### Population forecast
**Geometrical increase method**

Average growth rate per decade (geometric mean): $r = \left(\dfrac{59{,}500}{45{,}500}\right)^{1/4}-1 = 6.937\%$

$$
P_{2109} = P_n(1+r)^n = 59{,}500\times(1+0.06937)^{3.5} = 75{,}242
$$

**Decreasing rate of growth method**

| Decade | Increase | Growth rate (%) | Decrease in rate (%) |
|---|---|---|---|
| 2034-2044 | 3,500 | 7.69 | - |
| 2044-2054 | 4,000 | 8.16 | -0.47 |
| 2054-2064 | 4,000 | 7.55 | 0.62 |
| 2064-2074 | 2,500 | 4.39 | 3.16 |

Average decrease in rate $= 1.102\%$ per decade.

| Year | Growth rate (%) | Population |
|---|---|---|
| 2084 | 3.28 | 61,454 |
| 2094 | 2.18 | 62,795 |
| 2104 | 1.08 | 63,473 |
| 2114 | -0.02 | 63,458 |

Population at 2109 is obtained by linear interpolation between the decade values: $P_{2109} = 63{,}465$.


#### Water demand ($q = 110$ lpcd)
$$
Q = P\times110\ \text{l/day}
$$

| Method | Population (2109) | Demand (m$^3$/day) | Demand (l/s) |
|---|---|---|---|
| (a) Geometrical increase | 75,242 | 8,277 | 95.8 |
| (b) Decreasing rate of growth | 63,465 | 6,981 | 80.8 |

The per capita allowance of 110 lpcd is taken to cover all domestic and public demands, so no separate losses or institutional demands are added.

**Answer: (a) Geometrical: P = 75,242, Q = 8,277 m$^3$/day. (b) Decreasing rate: P = 63,465, Q = 6,981 m$^3$/day.**

## Check yourself

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

1. Survey 2074 BS, base period 5 and design period 30 years, last census 2074. What n (in decades) is used for the forecast?
   A. 3.5 decades
   B. 3.0 decades
   C. 35 decades
   D. 0.35 decades
   Answer: A. Design year = 2074+5+30 = 2109, so 35 years = 3.5 decades from the last census. (Key point: Design year and n)

2. Why is the exponent 1/4 used in r = (59,500/45,500)^(1/4) - 1?
   A. There are 5 census years
   B. The design period is 4 decades
   C. There are 4 decade intervals between the 5 census years
   D. It gives the arithmetic mean rate
   Answer: C. Five census records span 4 decades; the geometric mean per decade takes the 4th root of the overall ratio. (Key point: Geometric growth rate)

3. How is the 2109 population obtained in the decreasing rate of growth method?
   A. By applying the 2064-2074 growth rate to 2074 population for 3.5 decades
   B. By linear interpolation between the 2104 and 2114 decade populations
   C. By taking the average of 2084 and 2094 values
   D. By using the geometric mean rate
   Answer: B. The method forecasts decade-end populations with a declining rate, then interpolates to the required year. (Key point: Decreasing rate method)

## Related in Water Supply Engineering

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- [Demand of new municipality 2016, 45,000 pop](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-a76) — Water Supply Engineering, chapter 3, asked 2×
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- [Population 2090 by three methods, 110 lpcd](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apop-b79) — Water Supply Engineering, chapter 3, asked 2×

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