Thursday, June 2, 2011

If I change my transmission fluid by replacing 3.5 quarts at a time, how long until all the fluid is new?

It holds 8 quarts total. With my car I can remove the transmission drain plug to drain 3.5 quarts easily. The torque converter holds lots of fluid though.If I change my transmission fluid by replacing 3.5 quarts at a time, how long until all the fluid is new?
Since everything mixes together again, the answer is theoreticlly never. However, allowing a little bit of old fluid, say 1%, then this is the calculation. Let QO(t) be the quarts of old fluid at time t and QN(t) the quarts of new fluid at time t, then QN(t) = 8 - QO(t)



Q(0) = 8, QN = 0

Q(1) = 8 - 3.5 =4.5, QN = 3.5



The next draining is not all old fluid and is expected to be made up of the same proportions as the entire supply 4.5:3.5



Q(2) = 4.5 - 3.5(4.5/8) = 2.53125, QN = 3.5 - 3.5(3.5/8) + 3.5 = 5.46875



Here is an Excel calculation, showing that it takes 12 refills. Of course all of this ignores the new fluid getting dirty!



8 0

4.5 3.5

2.53125 5.46875

1.423828125 6.576171875

0.80090332 7.19909668

0.450508118 7.549491882

0.253410816 7.746589184

0.142543584 7.857456416

0.080180766 7.919819234

0.045101681 7.954898319

0.025369696 7.974630304

0.014270454 7.985729546

0.00802713 7.99197287