Water Instruments: Flow Through Pipes
How the width and length of a pipe change the speed and quantity of the water it carries
Under the running heading 'Water instruments,' the page treats water carried through screws and pipes, illustrated by several small sketches in the right margin of channels and pipes drawing water from a river (labelled 4 4 and 2 2). Leonardo states rules relating pipe width and length to flow: water falling straight down a uniform pipe is faster the longer the pipe, and among pipes of equal length the wider ones flow faster because the water's central line lies farther from the pipe's friction. He also notes that water in a level pipe runs thicker than in an open channel, especially when the pipe takes in and lets out the water perpendicularly. The right margin carries stepped diagrams of pipes at intakes and outlets.
On this page
Width and length govern the speed of water in a pipe
Water descending straight through a pipe of uniform width is faster the longer the pipe. Among pipes of equal length, the wider ones give faster motion because the central line of the water is more remote from the pipe's friction and so is less impeded. Water in a level pipe runs thicker than in an open channel, above all when the pipe receives and discharges the water perpendicularly.
The water-screw and the width of its pipe
Among simple water-screws of equal thickness, length and obliquity, the one whose pipe is wider carries a smaller quantity of water in proportion to that pipe. Leonardo refers the proof to the third proposition of the book, 'Of the screws.'
Pipes drawing water from a river
A marginal sketch shows two pipes taking water from a river, with the numeral labels 4 4, and a companion figure labelled 2 2. These accompany the heading 'Of the waters that move through pipes.'