Cry Me An Illogical River

"Cry me a river!" urged Julie London in the famous song from 1955. Let us consider the mechanics of complying with her suggestion...

The largest river in the world, the Amazon, is 2976 miles long with a drainage of 219,000 cubic metres per second, while the smallest is the Roe in Montana, 201 feet in length with a drainage of 156,000,000 gallons per day. A gallon is 4.546 litres and a litre is one cubic decimetre, so we can work out that the Amazon is seventy-eight thousand times as long as the Roe and discharges two hundred and seventy times as much water every single second.

Clearly a “river” is a fairly vague concept. To be on the safe side, let us take the average of these two extremes and consider the result to be the archetypal river of the song. This hypothetical river will be 1489 miles long and drain 109,000 cubic metres of water per second.

How is it possible for a human being to cry such an amount of liquid? A human being is approximately 60% water, so that a man weighing 70 kilograms will contain about 40 litres, or twenty seven thousand times less than the amount drained by our hypothetical river every second. In order to cry a river, a human eye would have to be scaled up until it was 685 metres in diameter!

Julie London was asking for the impossible!