Heat oven to 350 degrees F.
Place turkey wings, celery, onion and carrot in roasting pan. Roast in 350 degree oven for 1 hour, stirring twice, or until nicely browned.
Place ingredients from roasting pan in 8-quart stockpot. Add the water. Simmer, partially covered, 2 hours, skimming fat from time to time. Strain. Add more water if needed to make 4 cups broth. (Can be made day ahead; refrigerate.)
On day of dinner, remove cooked turkey from roasting pan; pour off fat. Add broth to pan (reserving 1/2 cup); cook over low heat, scraping up browned bits.
Stir flour and reserved 1/2 cup broth in small bowl. Whisk into pan along with salt and pepper. Cook over low heat, whisking, until thickened. Strain into gravy boat. Makes 4-1/2 cups.