In a recent BBC news article about the Toddbrook Reservoir in Derbyshire, it was reported that, following storm damage, the dam was in danger of collapse with the potential of releasing 300 million gallons of water onto the nearby town of Whaley Bridge.
In 2019, readers could be forgiven for having no idea what 300 million gallons of water looks like.
To visualise large volumes it is often useful to calculate the length of a side of a cube with an equivalent volume.
Using imperial units, this is something that has always been difficult to do, due to the fact that liquid volumes are traditionally measured in units that don’t relate easily to length units. For example, in this instance we would want to know how many cubic feet, or cubic yards, there are in 300 million gallons. Without knowing the conversion factor for gallons to cubic feet, this would require the use of a search engine and calculator. We would also need to make an assumption as to which gallon is being used. Is it the imperial gallon which hasn’t been used for trade for at least 30 years, or is it the US gallon, which is sometimes reported in parentheses for American readers.
If we are given the value in metric units (litres or cubic metres), the exercise is straight forward, and requires practically no arithmetic. Converting litres (cubic decimetres) to cubic metres is simply a matter of dividing by 1000. A cubic metre is quite easy to visualise and is the standard unit used on all water utility bills.
The volume of water is approximately 1.3 million cubic metres. For visualisation purposes, we can approximate this to a cube of 1 million cubic metres. Such a cube has a side of length 100 metres, or one hectometre. Therefore, with little effort, it is possible to visualise the enormous volume of water reported as being slightly more than one cubic hectometre, or a cube with a side as long as a 100 metre running track.
The report continues, and mixes units when it quotes the metric units being used by the emergency services: The fire services are quoted as “pumping out 7,000 litres of water a minute”, in a bid to bring down the water level, and the police were quoted as having plans for scenarios including the dam collapsing “which holds back 1.3 million tonnes of water”.
At the time of writing, the emergency services are still in a race against time to prevent further deterioration of the dam from more heavy rain. We wish everyone involved well.