Geez lenny, it was intended as a joke. This forum can also be a place where we can have a little fun if we don't take ourselves too seriously.
The next sounds you hear will be my own palm encountering my forehead, accompanied by the requisite "DOH"!
Here's how I was taught to do dimensional analysis. Using the totalizer example, when you multiply the rate (100 gallons per minute) by the sample period (10 seconds) you can write it like this:
100 gallons | 10 seconds
____________|___________
minute |
The result (1000) has units of gallon-seconds per minute. If you take ten samples, you wind up with an accumulated total of 6000. The problem with the answer is 'what the heck is a gallon-second per minute'?
Obviously, we need to apply a unit conversion factor. The one that springs quickly to mind is 60 seconds per minute. Do we multiply by 60 or divide by 60? Let's go back to the way I originally wrote the fornula and see what happens when we multiply by 60.
100 gallons | 10 seconds | 60 seconds
____________|_____________|____________
minute | | minute
This doesn't look to promising. Now we've got 60,000 gallon-seconds squared per minute squared. Let's try dividing by 60.
100 gallons | 10 seconds | minute
____________|____________|__________
minute | | 60 seconds
This time we end up with 16.67 gallons for each sample. That's because the units of seconds in the numerator (top half of the fraction) and the denominator (bottom half of the fraction) cancel each other out. Likewise for the units of minutes. The only other trick is to recognize that since division is the inverse of multiplication, you also invert the units.
Now try it for larger units like MGD (million gallons per day). Lets say the flow meter is calibrated in MGD, and we sample every ten seconds.
100 million gal | 10^6 gallon | day | hour
_________________|_____________|_________|_______
day | million gal |24 hours |3600 sec
So each sample value of 100 MGD over a 10 second span represents 11,574 gallons.