Thanks to Wikipedia for this summary of our river:
The Aire rises at Malham Tarn then flows underground to Aire Head, near Malham, in North Yorkshire, and then flows through Gargrave and Skipton. After Cononley, the river enters West Yorkshire where it passes through the former industrial areas of Keighley, Bingley, Saltaire and Shipley. It then passes through Leeds and on to the villages of Swillington and Woodlesford. At Castleford is the confluence of the Aire and Calder; just downstream of the confluence was the ford where the ancient British road, used by the Romans, crossed on its way north to York. The river re-enters North Yorkshire near Knottingley and in its lower reaches forms part of the boundary between North Yorkshire and the East Riding of Yorkshire.
The River Aire empties into the River Ouse at Airmyn, ‘myn’ being an old English word for ‘river mouth’. The name possibly derived from Common Brittonic *Isara, meaning “strong river”. The Aire could have been the winwœd or winwæd written about in Old English, from the Old English elements winnan or win (“strife”, “fight”) and wæd (“shallow water”, “ford”), however others have proposed that it is actually the Went (also called the “wynt” in Old English) or the Cock Beck (see Battle of the Winwaed). Still others have claimed that it is actually the name of the battle and not the body of water itself.