‘Duct’ comes from ‘ducere’, meaning ‘to lead’, the same source as in ‘duke’ and the title for that name nobody could spell in connection with Cheetos, ‘Il Duce’ Mussolini. It also has the connotation ‘to draw’ (as in ductile metals)
Romans handled inverted siphons (cased in lead, I believe) so there was not a problem with their knowing how to handle pressure; the issue is that aqueducts carry water from significant distances, further than it would be economical to enclose them if their channels can be graded for correct average ‘fall’ per mile to give the desired throughput in congii or whatever.
This specifically implies that constant-grade accommodation needs to be made over even comparatively small features in the terrain. For more than relatively small embankments the mass that needs to be excavated and moved for fills begins to add up, and you have all the fun of leaks and settlement with a ready source of liquid ready for even small defects. So you need something that ‘creates’ the appropriate continuous flume across the top, but is supported relative to gravity and buildable with a minimum of falsework and scaffolding. The Roman aqueducts often had multiple levels corresponding to superimposed sets of arches, with only the ‘top’ level having to be graded for flow.
The association with aqueduct and bridges came from the Romans not having any means of piping water under significant pressure, so they put up a bridge to keep the aqueduct near level.
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Perhaps the best explanation might be, if you’re going to be passing over it, it’s a “bridge”, but if you’re going to be passing under it, then it’s a “viaduct”?
Etymologically incorrect: “via” in ‘visaduct’ is Latin for road, not “by way of.” Your “duct” is close enough for this use.
According to the Online Etymological Dictionary, “viaduct” was "apparently coined by English landscape gardener Humphry Repton (1752-1818) for an architectural feature, “a form of bridge adapted to the purposes of passing over, which may unite strength with grace, or use with beauty …”