Perhaps spurious, but I'll say it anyway.
According to many opinions, one is required to wait six hours between eating milk and meat. This is either so that the meat can be digested and its taste dissipate, or for fragments of meat in your mouth to disintegrate and disappear.
On Erev Pesach we are Biblically forbidden to eat chametz for six hours, starting at midday. (Later on, the rabbis added another hour or two to these six.) Perhaps the reason for these six hours is like the reason for the above six hours. In each case, the food could require six hours to be digested and/or disappear. Before eating dairy we must make sure that no meat remains in our digestive system, and similarly, before beginning Pesach we must make sure that no chametz remains in our digestive system.