Fifteen muhurtas divide the daytime and fifteen the night, so they are 48 minutes long only at the equinoxes. The 8th daytime muhurta is also called Abhijit; the 29th, Brahma muhurta, is the traditional hour before dawn for study and prayer.
In traditional Indian timekeeping the day (ahoratra, अहोरात्र) begins at sunrise. It is divided into 60 ghati (घटी, also nadi or danda), each ghati into 60 pal (पल, also vinadi) and each pal into 60 vipal (विपल). One ghati is 24 minutes, one pal 24 seconds and one vipal 0.4 seconds. The time elapsed since sunrise, counted this way, is the ishtakala used in almanacs and horoscopes, for example "born at 23 ghati 14 pal".
This clock counts fixed 24-minute ghatis from local sunrise. Because sunrise moves from day to day, a sunrise-to-sunrise day is not exactly 24 hours, so the count at the next sunrise is 60 ghati give or take a fraction of a pal or two. Daytime (dinamana) and night (ratrimana) in ghati change with the season and latitude.
The day and the night are each split into 15 muhurtas (मुहूर्त) and into four praharas or yamas (प्रहर, याम) of roughly three hours. These are proportional ("temporal") hours: in summer the daytime ones are longer. The muhurta names follow the list commonly given in panchang practice (as tabulated, for example, in the Wikipedia article on muhurta); other lists exist and spellings vary.
Sunrise is computed with the astronomy-engine library for the place and time zone chosen, to within a minute or so; local hills and haze shift what you actually see.