Water from a cistern: fall, weirs and orifices
Hydraulic questions on falling water, flow over a weir, and moderating the Canal's sluices
A densely written hydraulics sheet posing questions about water issuing from a cistern (bottino): whether a longer fall draws more water behind it, and whether water falls more powerfully through a pipe than freely through air. Further passages state that velocity over a weir grows with the head of water above the mouth, and compare the discharge of triangular versus circular orifices of equal capacity, each illustrated by a small figure. A final column argues a dispute over regulating the sluice-mouths of a navigation canal (Navilio) and the losses caused by moderating them. Small diagrams of a stepped weir, a channel that is partly wide and partly narrow, and a triangular-and-circular orifice accompany the text.
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Does falling water draw more water behind it?
It is asked whether water issuing from the cistern into the air draws behind it the more water from the cistern the greater the length of its fall, and whether such water is more powerful falling through a pipe than falling freely through the air. The adversary answers that a given thickness of water is swifter the less it touches the lips of the mouth from which it pours.
Velocity over a weir grows with the head of water
If a weir passes 2 inches of water and a third inch is added, the lower inch doubles its power, velocity and quantity, because in uniform slopes velocity is proportional to height. Conversely, if the head above the mouth is halved, the discharge falls in the same proportion, so water that poured in one hour then pours in two.
Triangular versus circular orifice of equal capacity
When the centre of the circle is at the same height as the centre of an equal-capacity triangular orifice, the triangle pours more water than the circle. But if the centre of natural gravity of the triangle equals the height of the circle's centre, the two discharge equally.
Regulating the sluice-mouths of the Canal
The argument is not whether it harms the treasury, since the gift was made conditional, but whether it harms a third party, harm caused by the moderations. The mouths should have been moderated from above, toward where the Canal comes in, and not from below, because the recovered water rose much higher above the lower mouths.