I have my tomatoes in a SWC this year. They are doing well, using 2 gallons of water a day. When planting I put a cup of timed release fertilizer in the mix, the type claimed to last up to 9 months, 18-6-12. Because I have some fertilizer made in stick form to be used in a "root fertilizer tool" which I threw away years ago, I am dropping one stick a month down the filler pipe. I am not sure it is helping, but it has not hurt. Al

i do it all the time but it is for the micro nutrients. my fert strip only has the NPK.

When I had SWCs, I added FP to the water reservoir whenever the leaves looked like they needed a hit. Worked well.

I originally put so much dang fertilizer (about 1.5 cups)in my tomato (Rutgers) 5 gal SWC, I couldn't see adding ANY to the water. I used MG Shake and Feed originally which had some micros in it. The thing grew like crazy, and was darker green than any other plant I grew in the ground or container. It also flowered and fruited really well.

"darker green than any other plant ... flowered and fruited really well"

Yes. Some books say if you put in too much nitrogen fertilizer it will stunt the fruiting. I have never, ever seen this. The greener the leaves the more fruit has always been my experience.