How did the Romans get water up hills using aqua ducts?

Technically, the Romans were not able to get water to move uphill in a general sense. All aqueducts move water from an elevated source (spring-fed streams in the mountains) to end-users at a lower elevation. The water flows almost entirely downhill from the source to the end user. If the water needed to cross a valley, the Romans would build an arched structure with an elevated channel to cross the valley, but even this channel would have a vary slight downhill gradient that allowed water to flow towards the end user. If a large hill was in their way, the Romans would either divert the channel around the hill, dig a trench through the hill, or dig a tunnel through the hill, all while maintaining a fairly constant, slight downhill gradient towards the end user.
The only exception to the rule of a generally constant downhill slope to the water channel is that specific tunnel segments, the Romans could build the tunnel as an inverted siphon (mentioned above) to cross a depression or valley and raise the water level on the downhill side almost to the level of the uphill side. To do this requires a well-sealed tunnel strong enough to withstand the increased water pressure within the siphon. Note, however, that except for gaining a little bit of elevation if you slow down fast-moving water, you normally cannot get water to flow out of the outlet at a higher elevation than the inlet. So technically, even the Romans were not able to get water to flow “up a hill”.

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