Canal locks and the physics of falling water
Doubling water pressure, tight-closing lock gates, and jets from conduit vents
This blue-paper sheet joins hydraulic theory to practical canal engineering. Lettered diagrams analyse how the power of a falling column of water doubles when the column is doubled, and how water issuing from the vents of conduits varies in force with distance from its mouths. Notes describe feeding a navigable canal from the Bisenzio and Ombrone rivers and sending the surplus to ordinary mills, and insist that the gate of a lock must close in tight contact. Small mechanical sketches of the gate and channels accompany the text.
On this page
Doubling the column doubles the water's power
The height of water ab is divided into 8 degrees; taking the lowest degree, which is burdened by the 7 above it, and doubling the water upon it loads it with 8 degrees more than before. Working down through the quarter and half of the height, Leonardo tracks how the pressure on each degree is doubled, with a surplus of one, until across the whole height ab the power is doubled with no excess.
Feeding the canal from the Bisenzio and Ombrone
The Bisenzio and the Ombrone are to cross the canal, giving it abundant water as much as its navigation requires. The surplus goes to the ordinary mills, which will lack exactly as much water as is needed to make up what the locks consume.
The lock gate must close in tight contact
A terse instruction beside the central mechanism: the gate of the lock (conca) must be in contact, that is, must seal tight against its jamb.
Jets from the vents (spiraculi) of the conduits
Of the water that issues from the vents of its conduits, the proportion from power to power is the same as that from distance to distance which they have from their mouths. A related note observes that water pouring through a straight vent of continuous width loses its intended course at top and bottom, the upper end gaining in power as much as the lower loses.
Where two vents redirect the falling stream (a, b, c, d, e)
If the vent a throws its water into e and the vent b throws it into d, then when the two vents are continued through the whole space ab, all the water will be thrown into c. The part that first went from b to d is burdened by the weight ab that bends it to c, while the water ac that first fell into e is sustained by the motion ab.