Dimensionless Numbers in Chemical Engineering

Are Cup Final questions eligible for the Armadillo Award?

I have often spoken (or written) in favour of science questions being taken more seriously in the Quiz League, but this one seems almost wilfully obscure.

As I've said before, I had a scientific education; I did chemistry to 'A' Level. But this question left me dumbfounded; I'd never heard of the Reynolds, Prandtl or Sherwood numbers, so what chance did I have of saying what type of numbers they were?

I think the same went for the rest of my team, and I suspect the other team as well. In fact I'd be surprised if anyone in the room (that was maybe about fifty people) knew the answer – unless the person who set it was there. If they were, they weren't letting on.

When we heard the answer, its banality was almost as mind–boggling as the obscurity of the question. So they're dimensionless, are they? How fascinating.

I had actually heard the term 'dimensionless number' before, and I knew what it meant; but it would have taken me a lot more than twenty seconds to think of it as a possible answer to this question. So long, in fact, that I'd probably have lost the will to live.

Most measurements, in order to be meaningful, need to be defined in terms of a particular unit. For example: length can be measured in terms of metres, centimetres, or feet and inches; time can be measured in seconds, minutes, hours, days (etc.). Weight can be measured in pounds and ounces, kilograms, or grams.

Dimensionless numbers are simply measurements that are not defined by any unit. They're typically (at least, the ones I understand are) defined as the ratio between two quantities that have the same units. The best–known example is probably pi – the ratio between the diameter and circumference of a circle.

Wikipedia lists some 70 dimensionless numbers that are used in fluid dynamics, including the Reynolds, Prandtl and Sherwood numbers. The only one that I've ever heard of (not counting these three) is the Mach number. According to Wikipedia, the Reynolds and Mach numbers are "common examples" of dimensionless numbers in fluid dynamics.

I would have said that what I know about fluid dynamics you could write on the back of a postage stamp, but apparently when we talk about the Mach number in terms of aircraft speeds (the ratio between the speed of the aircraft and the speed of sound in air), this is fluid dynamics. Don't ask me what the Reynolds number is, though – I've looked it up on Wikipedia and it might as well be double Dutch.

I would love to know who set this question, and what made them think it was suitable for a general knowledge quiz.

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