Question

The annual precipitation recorded in a town is 400 mm. Rainwater is being collected from the flat roof of a building, and then treated to potable standards, and stored. Water loss due to evaporation, transmission and treatment is 40 percent of the total harvested volume. The roof area is 500 sq.m. There are 3 occupants, with average daily water demand as 200 lpcd. The stored rainwater will be adequate for the household's daily use for \underline{\hspace{1cm}} days [in integer].

Hint:

Always convert rainfall depth (mm) → volume using catchment area, then apply loss factor, and divide by demand to get days.

Answer 1

Step 1: Calculate total rainfall volume harvested.
\nAnnual rainfall = 400 mm = 0.4 m
\nRoof area = 500 m\(^2\)
\n\[\n\text{Total volume harvested} = 0.4 \times 500 = 200 \; \text{m}^3\n\] \n\n

Step 2: Convert to liters.
\n\[\n200 \; \text{m}^3 = 200 \times 1000 = 200{,}000 \; \text{liters}\n\] \n\n

Step 3: Account for 40% losses.
\n\[\n\text{Effective stored volume} = 200{,}000 \times (1 - 0.40) = 120{,}000 \; \text{liters}\n\] \n\n

Step 4: Daily water demand.
\nPopulation = 3 persons, Demand = 200 lpcd
\n\[\n\text{Daily demand} = 3 \times 200 = 600 \; \text{liters/day}\n\] \n\n

Step 5: Calculate days of sufficiency.
\n\[\n\text{No. of days} = \frac{120{,}000}{600} = 200 \; \text{days}\n\] \n\n \n

Final Answer: \n\[\n\boxed{200 \; \text{days}}\n\]