Before Heron, no correct notion of the discharge of a canal, pipe, or river had been correctly formulated. Indeed, the notion of velocity was essentially unknown in Greek mechanics. The quantity of water delivered by an aqueduct or canal was quantified uniquely by a measure of the flow area. It was Heron who formulated for the first time the notion that the volumetric discharge, i. e. the volume of water delivered in a unit of time, is the product of the flow area and the velocity. One finds the following in his work Dioptra:
“It is to be noted that in order to know how much water the spring supplies it does not suffice to find the area of the cross section of the flow… It is necessary also to find the speed of the flow, as the swifter the flow is, the more water the spring supplies.”[201]
The importance of the current velocity in calculating the discharge is thus established, but Heron did not have any means of measuring this velocity. So he also proposed another means of calculating the quantity of water delivered in a day:
“One should therefore dig a reservoir below the stream and note with the help of a sundial how much water flows into the reservoir in a given time, and thus calculate how much will flow in a day. The amount of water will be clear from the measure of the time.”
Coming too late to be useful to the Romans, who were the great constructors of this period, the concept is destined to be gradually forgotten over time. It is only in the West during the Renaissance that it will once again be formulated.
