The other day I was looking at some car fuel consumption numbers which were expressed in both the British Miles per Gallon and the European Litres per 100km. As I looked at the latter my mind went off at a tangent (as it is wont to do) and observed that "l/100km" could also be expressed in "cubic metres per metre" (a volume divided by a distance), and that dimensionally this could be further reduced to just square metres (a volume divided by a length gives an area). For ease of visualisation this could also be expressed as the diameter of a circle

In dimensional analysis the minimised dimensional form of a parameter does actually represent something physical, so I pondered what this diameter might actually represent and the penny dropped - it is the diameter of an imaginary tube which contains the fuel burned by the car.

So for example 56mp(UK)g is 5x10^-7 cubic metres per metre (or square metres). That equates to the area of a circle of 2.5mm diameter.

So the fuel burned by a car doing a constant 56mpg for 100metres would fill a 2.5mm diameter and 100m long.

I found that way of looking at it quite interesting.

If anyone is interested the actual equation boils down to a simple (to 3sig fig) expression. For a fuel consumption of x miles per gallon, the diameter D of the "fuel cylinder" is given by:

D = √(360/x)

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