[From Rick Marken (2001.11.17.1000)]
I said:
Maybe we just have a notation problem. If Q is a flow (rate of change
with respect to time) then why divide by t (which usually denotes time,
not time _unit_)? If Q is a flow then Q/t is like dividing a car's speed
(Q in miles/hr) by the time since the start of the trip. So if Q/t were
plotted as a function of time (t), Q/t would fluctuate as the speed of
the car changes over time but it would also be getting generally smaller
as time goes on (as t, the numerator, increases).
That should of course, be "(as t, the denominator, increases)"
I should add, by the way, that if you use t to represent a constant
_unit_ measure of time (like hours, i.e.. t = 1 hr) so that Q/t is a
rate like miles/hr, then Q must be a measure of the _change_ in Q during
the unit time, t. In this case. Q/t is a measure of rate (flow). By
choosing a convenient unit (t = 1 unit), t can be eliminated from the
formulae. Then you can just write Q to represent the rate (or flow). But
it seems like this could get confusing. If Q represents the flow (rate
of change) of Q over time then what represents the value of Q over time?
I think it would be much clearer to go with the mathematical convention
and have Q represent the value of Q with respect to time and have dQ/dt
represent the flow of Q with respect to time.
Best regards
Rick
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Richard S. Marken
MindReadings.com
marken@mindreadings.com
310 474-0313