i already have the 4-8 trays and everything i as just wondering if a 50 reservoir can hold enough water for a 4-8 tray without changing the water every day or two
Should be more than sufficient.
I'm running four 1200mm sq (close to 4' sq) trays, each with 125L (33 gal) tanks; only requires topping with water & pH adjustment once a week. I dump & clean tanks every 2 weeks.
Used to run them on 100L tanks; the smaller tanks required topping more than 1x a week (top when 1/3 of water is gone). With the 125L tanks, water consumption is fairly closely matched to nutrient consumption as the nute ppm remains steady over the week, but drops when the tank is topped with plain water, the loss owing to what nutes the plants have eaten.
I use rockwool floc in 8" tall x 8" dia plastic pots, which hold about 2L of water each. The plants suck a fair bit of water but I suspect that there's a fair bit of evaporation from the rockwool as well. A system using expanded clay pellets may not use as much water. Pellets don't hold as much water, so less is left in the media to evaporate under warm lights. If you're using pellets, you may be able to use a smaller tank with no worries.
Your tank can be as small as about double the volume of a flooded tray, but more tank volume means less maintenance and greater ppm stability. On the other hand, it costs more in nutes to mix up a tank.