Re: [Phys-l] Energy divided by power can be a residence time

[John Denker <jsd@av8n.com>]

On 12/22/2009 08:54 AM, Jeff Radtke wrote:
> Residence time is not just for molecules.
>
> Energy flowing through a vehicle resides for a time as kinetic energy  
> in its mass.  This residence time can be calculated easily.  It turns  
> out that the average residence time of an infinitesimal fuel energy  
> element in the driver of an automobile at constant highway speed is  
> about 400 ms.  As explained in my Knol, this time is also a measure of  
> vehicle performance that is proportional to deviation from the  
> Gabrielli-von Karman limit line.
> http://knol.google.com/k/speed-costs-power#
>
> Although there is much discussion about modeling power as a flow, I  
> have not found references to this idea in the literature.  Has anyone  
> seen this before?

The name is not in the literature, but the idea is there,
to the extent that it deserves to be.  At the level of
dimensional analysis, pretty much everybody is aware that
energy divided by power has dimensions of time.

However, there is more to life than dimensional analysis.
A torque and a Lagrangian have the same dimensions, but
that does not mean they are the same thing, or even 
analogous things.

For that matter, drawing an analogy between one thing and
another (energy efficiency versus residence in a flow
reactor) does not guarantee that the analogy is apt.

Also, just because a certain quantity shows up in the
algebra does not mean it has any physical significance
to the problem at hand.  If I may be permitted an
analogy of my own, in the context of wings, *depending*
on the problem at hand, I might be interested in the
span, or the chord, or the area (span*chord) or the
aspect ratio (span/chord).  Given any two of the four
I can calculate the others algebraically ... but just
because I can calculate it doesn't mean I need to
calculate it, or that it has any relevance to the
problem at hand.

Specifically:  Defining an "efficiency number" is at
best a tricky business, because efficiency is not really 
a number at all, but rather a function of many, many
variables.  I have yet to see any evidence that
expressing the "efficiency number" in terms of a
"residence time" tells us anything we didn't already
know.

Even more specifically:  Emphasizing the "residence
time" suggests that it should scale like some other
timescale in the problem, and that changing the
timescale should produce a proportional change in
the "efficiency number" ... which is not generally
the case.

There's more to life than dimensional analysis.