The Paugh Number

Bear with me, those who completely are not into this type of thing. Something came to me at work a few days ago, and I knew it needed to be addressed here.

In the world of mechanical engineering, particularly in fluid dynamics and heat transfer, dimensionless constants come up all the time. These constants have names like the Nusselt number, the Rayleigh number, and the ubiquitous Reynolds number. These numbers are dimensionless because they describe the ratio of two values with the same dimensions. For example, the Reynolds number is the ratio of inertial force to viscous force in a fluid, so fluid flow with a high Reynolds number is dominated by inertia and fluid flow with a low Reynolds number is dominated by viscosity. The lack of dimensionality means that the Reynolds number (and all of these dimensionless constants) is normalized across all situations. In other words, I can compare the Reynolds number of slow moving oil in a small pipeline to the Reynolds number of fast moving air in a large wind tunnel. They are just raw numbers.

So how is this relevant? Well, it recently became obvious to me that the study of paugh could benefit from the use of dimensionless constants, in much the same way that the study of fluids does. All things can be described as the ratio of two paugh-related values with the same dimensions. Thus, the paugh qualities of all things can be described with one raw number.

I give you...

...the Paugh number.

I'm defining the Paugh number as the ratio of exhaustion to normalcy. Both exhaustion and normalcy can be described in units of force, so the ratio, as long as the two are expressed in the same units, is dimensionless. Let's look at some examples from the paughrcives.

High Paugh number (exhaustion outweighs normalcy):


Low Paugh number (normalcy outweighs exhaustion):


Paugh number close to 1 (exhaustion and normalcy roughly equal):


Remember: the normalcy is the picture's, but the exhaustion is the beholder's. It goes back to the definition of paugh: excessively ordinary, causing physical exhaustion in the observer.

Obviously, the existence of a Paugh number opens up virtually endless further opportunities for study. Why not invert the Paugh number? How could a given paugh situation have its Paugh number inverted? Can there be a negative Paugh number? I exhale slowly at the paughssibilities.

Finally, it is very important to note that the Paugh number is NOT a measure of overall paugh, only a measure of the specific type of paugh involved. A low Paugh number in no way implies a low level of paugh; instead, it describes paugh where normalcy outweighs exhaustion. Both must be present for there to be paugh. I reiterate: both exhaustion and normalcy must be present for there to be paugh. Another way to state this fundamental fact is that in order for a situation to be paugh, the Paugh number can neither be zero nor infinity. I leave that for the interested party to digest.

I feel much better now.