Combine rhubarb and water in a large saucepan. Bring to a boil; cook 10 minutes. Remove from heat; strain mixture through a sieve into a bowl, pressing rhubarb with the back of a spoon to remove as much liquid as possible. Discard rhubarb. Add granulated sugar, brown sugar, and juice; stir until sugars dissolve. Cover and chill.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 1 hour or until firm. Remove sorbet from freezer 10 minutes before serving.
MyRecipes is working with Let's Move!, the Partnership for a Healthier America, and USDA's MyPlate to give anyone looking for healthier options access to a trove of recipes that will help them create healthy, tasty plates. For more information about creating a healthy plate, visit www.choosemyplate.gov.