Water outlets of different shapes and their discharge
Square, circular and triangular orifices compared by contact and by flow
Leonardo studies how the shape of an outlet set below the surface of a reservoir governs how much water it discharges in a given time. He argues that less contact between the water and the outlet's edge means less resistance, so a circular hole (with a shorter perimeter than a square of equal area) lets water pass more freely. A series of marginal figures compares square, circular and triangular outlets, and a row of four shapes at the foot ranks them by how much they pour.
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Less contact at the outlet means freer passage of water
Among outlets set at equal depth below the surface of a reservoir, the one whose edge has the least contact with the water passing through it least impedes that water. The rule turns the question of discharge into a question of the outlet's shape and perimeter.
Square versus circle compared by perimeter (a, b)
Let a be a square outlet and b a circular one of equal area. Because the line encircling the square is longer than that encircling the round, the water through b has less contact and flows more freely. The reasoning rests on comparing the perimeters of equal-area figures.
How the water's bulk lies above or below the outlet
Of equal outlets at equal height, the one that pours more in equal time is the one that has the greater 'sum of itself' toward its lower part rather than its upper part. Leonardo relates discharge to where the mass of the passing water is concentrated relative to the opening.
Four outlets ranked by how much they pour (a, b, c, d)
The four outlets a, b, c and d are equal and set at equal height: a pours less from the middle downward than b, and c less than d. Here the round hole discharges less water than the square one.