It was not the Manchester Ship Canal that the Bridgewater Canal crossed on an arched bridge - the arched aqueduct actually crossed the Mersey and Irwell Navigation, which was there before the ship canal was built.
The swing aqueduct was built at the same time as the ship canal. The stone arches had been high enough to allow the river barges to pass below, but the sea-going vessels that would use the ship canal were too big, so the swing aqueduct was designed - the first and only one of its kind!