If this is a Harris County case and you are not doing jail time as a condition of probation, you get 2 for 1. So, your 8 day sentence would require 4 days, less the one day credit, leaving 3 actual days to serve. So, if you go in at 7 pm on one day, you should get one day credit for that day and spend the next day in jail. At midnight on the next day (after 29 hours in jail) you should get credit for the 3rd day and begin to be processed out, probably being released within a few hours.
You are right - Harris County has 2 for 1 plus you get credit for the time you already served (at 2 for 1). Take 8 days divide by 2 so 4 days required less 1 day served is 3 days. Turn yourself in at 7 p.m. gets you one day credit for that day. The next day is a credit day and then just after midnight, you have all the credit required and they begin processing your paperwork. (They used to let people out right after midnight but there were too many problems so they quit doing that.) If you turned yourself in at 7 on Friday, then you would get out in the early morning hours of Sunday.