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Demand 2074 BS, geometric and decreasing rate

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.

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.20342044205420642074
Population (Nos)45,50049,00053,00057,00059,500

Survey year 2074 BS; base period 5 years and design period 30 years, so the design year is 2074+5+30=21092074+5+30 = 2109 BS. The last census is 2074, so n=35/10=3.5n = 35/10 = 3.5 decades.

Population forecast

Geometrical increase method

Average growth rate per decade (geometric mean): r=(59,50045,500)1/4−1=6.937%r = \left(\dfrac{59{,}500}{45{,}500}\right)^{1/4}-1 = 6.937\%

P2109=Pn(1+r)n=59,500×(1+0.06937)3.5=75,242P_{2109} = P_n(1+r)^n = 59{,}500\times(1+0.06937)^{3.5} = 75{,}242

Decreasing rate of growth method

DecadeIncreaseGrowth rate (%)Decrease in rate (%)
2034-20443,5007.69-
2044-20544,0008.16-0.47
2054-20644,0007.550.62
2064-20742,5004.393.16

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

YearGrowth rate (%)Population
20843.2861,454
20942.1862,795
21041.0863,473
2114-0.0263,458

Population at 2109 is obtained by linear interpolation between the decade values: P2109=63,465P_{2109} = 63{,}465.

Water demand (q=110q = 110 lpcd)

Q=P×110 l/dayQ = P\times110\ \text{l/day}
MethodPopulation (2109)Demand (m3^3/day)Demand (l/s)
(a) Geometrical increase75,2428,27795.8
(b) Decreasing rate of growth63,4656,98180.8

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 m3^3/day. (b) Decreasing rate: P = 63,465, Q = 6,981 m3^3/day.

✓ Answer checked by Claude Opus 5.5 (high effort)

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