Rainwater Harvesting, Overflow and a Dripping Tap
A primary school has a roof area of 60 m² and a water tank of 900 litres. On Monday it rained 20 mm; on Tuesday 5 mm; on Wednesday there was no rain. The tank was empty before Monday. A pupil records that the tank was full and overflowing on Monday evening; by Tuesday evening the overflow had carried away all the new rain. The school garden needs 300 litres each day. A tap in the yard drips once every second; each drop is about 0.05 ml. The water committee wants to know whether to enlarge the tank, repair the dripping tap first, or build a cover over the tank to reduce evaporation and dirt. They ask for calculations and a priority order based on evidence. Assume 1 m² of roof collects 0.8 of the rain that falls on it, because of splashing and first flush.
1. Calculate the water collected on Monday and Tuesday, and explain why the tank overflowed.
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Monday: rainfall 20 mm = 0.020 m. Volume on roof = 60 m² × 0.020 m = 1.2 m³ = 1 200 litres. With 0.8 collection efficiency: 1 200 × 0.8 = 960 litres. Tuesday: 5 mm = 0.005 m; volume = 60 × 0.005 = 0.3 m³ = 300 litres; ×0.8 = 240 litres. Total collected = 960 + 240 = 1 200 litres. The tank holds only 900 litres, so on Monday 960 litres would fill it and about 60 litres would overflow. On Tuesday the tank was already full, so all 240 litres overflowed. The pupil's record is reasonable. The school should not simply enlarge the tank: it should first stop the overflow by using the water, and fit a first-flush diverter.
2. Calculate how much water the dripping tap wastes each day. Using your calculations, recommend a priority order for the committee and justify it.
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Drip loss: one drop per second = 86 400 drops per day (60 × 60 × 24). Each drop is 0.05 ml, so loss = 86 400 × 0.05 = 4 320 ml = 4.32 litres per day. In 30 days that is about 130 litres. Compared with the 300 litres the garden needs each day, the drip is small, but it is continuous and clean water is wasted. The overflow on Tuesday lost 240 litres in one day, which is much larger. So the first priority is to use or store the rain that is already collected, for example by filling the garden and repairing the overflow. Repairing the tap is cheap and should be done, but it is not the biggest loss. A cover reduces evaporation and contamination. The committee should rank: stop overflow and use water, repair the tap, then consider a cover and a bigger tank.
3. A parent says, 'Just buy a bigger tank and the water problem is solved.' Evaluate this claim using the rainfall data and the garden's needs.
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A bigger tank would help only if there is enough rain and the school can use the water before it is lost. The data show 960 litres collected on Monday and 240 litres on Tuesday, a total of 1 200 litres. The garden needs 300 litres each day, so it would use 1 200 litres in four days. A bigger tank could store Monday's rain for later, but it would not create more rain. It would also cost money and may still overflow in a heavy storm. The first step is to stop the existing overflow and repair the drip. A cover would reduce evaporation and keep water clean. A bigger tank is sensible only after these steps and after checking how much water the school can actually use between rains.