Rainwater tank: how far does one storm go?
A family in Hamilton wants to cut their water bill by installing a 2,000-litre rainwater tank. Their garage roof is a rectangle 9.6 m long and 6.4 m wide. Only one downpipe can be connected, and it collects from the 60% of the roof that slopes toward it. The tank is fitted with a first-flush diverter that discards the first 10% of every rainfall event. The family plans to use the tank only for the vegetable garden, which needs about 180 litres per day in summer. Local rainfall in a typical summer storm is 25 mm. The tank costs $1,450 installed, and mains water costs $1.85 per cubic metre (1 m³ = 1,000 L). The family wants to know how much water one 25 mm storm delivers, how many days that lasts, and whether the tank will ever pay for itself from garden use alone.
1. Calculate how many litres from a 25 mm storm reach the tank. Show the catchment area used, the unit conversion, and the effect of the first-flush diverter. State whether the tank overflows.
Read the worked answer
Catchment area = 9.6 × 6.4 = 61.44 m². Only 60% drains to the downpipe: 61.44 × 0.60 = 36.864 m².
Rainfall of 25 mm = 0.025 m. Volume = area × depth = 36.864 × 0.025 = 0.9216 m³. Since 1 m³ = 1,000 L, that is 921.6 L gross.
The first-flush diverter discards 10%: 921.6 × 0.90 = 829.4 L reaching the tank.
The tank holds 2,000 L, so 829 L fits with no overflow (about 41% full). The calculation assumes all the rain is captured and none splashes or evaporates, so 829 L is an upper estimate.
2. How many days of garden watering does one such storm provide? Compare this with a full week's demand.
Read the worked answer
Daily garden use = 180 L. Days of supply = 829.4 ÷ 180 = 4.61 days, so about 4.6 days, or 4 full days plus part of a fifth.
In a week the garden needs 7 × 180 = 1,260 L, so one storm supplies 829.4 ÷ 1,260 = 66% of a week's need. The garden would need roughly 1,260 ÷ 829.4 = 1.5 storms per week to keep up. That matters because a single 25 mm storm is not a typical weekly event; longer dry spells would empty the tank and the garden would switch back to mains water.
3. The family wants the tank to pay for itself from water savings. Calculate the value of one storm's water and the number of storms needed to recover the $1,450 cost. Give a recommendation.
Read the worked answer
Value of one storm's water = 0.8294 m³ × $1.85 = $1.53. The tank cost $1,450. Number of storms to repay = 1,450 ÷ 1.53 = 948 storms (about 945).
If a storm like this happened once a week for the 12 weeks of summer, that is 12 storms a year: 948 ÷ 12 = 79 years. That is far longer than the tank's life, so the tank will not pay for itself from garden water savings alone.
Judgement: the payback argument fails, but the tank may still be reasonable for other reasons such as reducing stormwater runoff, having water during restrictions, or convenience. If the family's main goal is saving money, a smaller tank or a mains timer may be better value.