How long does the effect of a 8 oz. Glass of wine remain in a persons urine

Assuming the wine is 12% abv an 8 oz glass (1.6 US standard drink) time for metabolism should be right at 3 hours. Alcohol in urine, of course, remains until you void. So at that time ethanol should not be detected in blood or urine.*

If you mean by "effect" how long alcohol consumption might be detected, by testing for the metabolites EtG or EtS detection might be extended to 10-36 hours (see Wojcik & Hawthorne (http://alcalc.oxfordjournals.org/content/42/4/317.full#T1))
*based on population average