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Population from spring yield of 5 L/s

Short answer

Spring yield 5 l/s = 432000 l/d; at 65 lpcd it serves design population 6646. Current population = 6646/(1.017)^20 = 4744.

Safe yield of a proposed spring is 5 liter per second and per capita water demand is 65 lpcd. Calculate the current population that can be taken under the scheme if design period is 20 years and population growth rate is 1.7% per annum.

The spring yield must supply the demand of the population at the end of the design period, so work backwards from the design year population.

Step 1: daily yield

Q=5 l/s×86400=432,000 l/dayQ = 5\ \text{l/s}\times86400 = 432{,}000\ \text{l/day}

Step 2: design population that can be served

Pd=Qq=432,00065=6,646P_{d} = \frac{Q}{q} = \frac{432{,}000}{65} = 6{,}646

Step 3: population today

Pd=P0(1+r)n⇒P0=6,646(1.017)20=4,744P_{d} = P_0(1+r)^n \Rightarrow P_0 = \frac{6{,}646}{(1.017)^{20}} = 4{,}744

Answer: Current population that can be served = 4,744 (about 4,740 persons); design population after 20 years = 6,646.

✓ Answer checked by Claude Opus 5.5 (high effort)

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