says “A while back, Mike noted to me that, given how little I drive my car, I should probably add fuel stabilizer to the tank. I bought some Sea Foam (a brand that he had noted particularly). It wasnt until yester-day that I actually refueled my car. (And, even then, I had about a third of a tank left.) “That got me thinking about a math problem. “Like most people, I dont completely drain my tank before refilling it. (In fact, most car engines are damaged if run until out of fuel!) So there will be some amount of additive still in the fuel when next I refill. If I pour the same amount of additive into the tank each time, could I in theory reach some point at which the tank contained nothing but additive? “Well, not really. “At the extreme, if I refilled the tank after every time that it were down by a pint, and added a pint of additive, then basically Id never again put any gasoline in the car. In that case, if the car could somehow keep going, then the tank _might_ ultimately have nothing but additive, because its contents are not continously divisible and perfectly homogenized, &c. Then again, maybe a bit of gasoline would stay at the bottom, or at the top, depending upon specific gravities. “But Im not going to do that. A more realistic scenario would have me refilling the tank whenever it were about half full, and it holds about 10 gallons. So about half of the previous quantity of additive would remain as I added more. If _exactly_ half remained each time, and I added the same quantity each time, then the amount of additive would grow, but at an ever shrinking rate, and thered be an upper bound to the growth. Id never have quite double the original amount of additive. If instead of refilling when the engine were half full, I refilled when it were a third full, then Id never have quite 1½ times as much. The ceiling is 1/(1-f) times the amount of additive used each time, where f is the fraction (1/2, 1/3, 1/4, 9/10, or whatever) of a tank that I have left at each refilling.”
Posted on: Wed, 10 Sep 2014 09:14:47 +0000