Sink the Bismarck! (1960) on Netflix

In 1941 Captain Jonathan Shepard takes over as Director of Operations at naval headquarters in London just as they receive reports that the Bismarck, the pride of the German navy, is going out to sea in the North Atlantic. Shepard argues in favor of moving as many ships as possible to the area to find her. In their first encounter with the Bismarck, the Royal Navy loses HMS Hood, the largest ship in the fleet while HMS Prince of Wales is severely damaged. Shepard then transfers ships from the Mediterranean fleet to go after Bismarck; they include the aircraft carrier Ark Royal on which his son Tom is serving as an aircraft gunner. Damaged in a second encounter, the Bismarck heads for Brest on the French coast and the safety of German coastal defenses and air cover. The only ship in range is the Ark Royal but in their first air sortie, they inadvertently attack HMS Sheffield when they mistake it for the Bismarck. In the second air sortie, they damage the Bismarck sufficiently to allow the surface fleet to catch up to her and sink her.