Final answer:
A T-tube is the tube used to drain bile from the common bile duct after exploration. It is designed to support bile flow post-surgery and is named for its T-shaped design.
Step-by-step explanation:
The tube used to drain bile from the common bile duct following exploration is a T-tube. This is a specialized drain which is shaped like the letter 'T' and is specifically designed to be inserted into the bile duct during or after surgery to ensure that bile can continue to flow from the liver to the duodenum, or to allow for drainage of bile outside the body as needed for medical reasons. The common bile duct is a structure formed by the union of the common hepatic duct and the gallbladder's cystic duct, which plays a crucial role in the delivery of bile to the small intestine, particularly to the duodenum.