For most of human history, people moved water very skilfully without any theory of how water moves. Irrigation canals in Mesopotamia and Egypt, the aqueducts of Rome, the qanats of Persia and the river works of China were built by trial, by experience passed from master to apprentice, and by careful observation. This chapter looks at what these builders knew, what the philosophers of the ancient world thought about flow, and how Leonardo da Vinci, at the end of the period, began to look at water with the eyes of a scientist.
Everything flows: Greek ideas about motion and the void¶
The phrase panta rhei (“everything flows”) is traditionally linked to Heraclitus of Ephesus (around 500 BCE). The words themselves do not appear in his surviving fragments; they come from later writers summarizing his thought. What survives is the famous river image: you cannot step into the same river twice, because new waters are always flowing past. For Heraclitus, the world was a process of constant change held together by an underlying order.
Other Greek thinkers asked more mechanical questions. The atomists, Leucippus and Democritus, imagined the world as indivisible particles moving through empty space. Aristotle (384–322 BCE) rejected the void. In his physics a vacuum could not exist, because a body moving through nothing would meet no resistance and would move infinitely fast. This idea, later summarized as horror vacui (“nature abhors a vacuum”), would be used for almost two thousand years to explain why water rises in a suction pump or a siphon.
Aristotle also had to explain why a thrown stone keeps moving after it leaves the hand. His answer, called antiperistasis, was that the air displaced at the front of the stone rushes around to push it from behind. The medium was both the cause of motion and the cause of resistance. The idea seems strange now, but it shows that the problem of how a body moves through a fluid was at the center of physics from the beginning. Medieval scholars such as John Buridan (14th century) criticized it and proposed instead that the thrower gives the stone an internal impetus, an early step toward the modern idea of momentum.
Archimedes and the beginning of hydrostatics¶
Archimedes of Syracuse (around 287–212 BCE) produced the first real theory in fluid mechanics. In On Floating Bodies, he started from a few postulates about a fluid at rest and proved, in the style of Euclid’s geometry, what is now called Archimedes’ principle:
He also analyzed the stability of floating bodies, such as a paraboloid floating at an angle, problems that are still the basis of ship stability. The well-known story of Archimedes leaping from his bath and shouting eureka after discovering how to test the gold of King Hiero’s crown is told by the Roman architect Vitruvius two centuries later and may be a legend. The water-lifting screw that carries his name was probably known in Egypt before him.
Hydrostatics, the science of fluids at rest, was therefore founded early and on solid ground. Hydrodynamics, the science of fluids in motion, would have to wait almost two thousand years.
The engineers of Alexandria¶
In Hellenistic Alexandria, a group of engineers built ingenious devices driven by water, air and steam. Ctesibius (3rd century BCE) is credited with the force pump, a water organ and an improved water clock (clepsydra) that kept a constant flow by holding a constant head in the supply tank. Philo of Byzantium described siphons and pneumatic devices. Hero of Alexandria (1st century CE) collected many of these inventions in his Pneumatica, including the aeolipile, a spinning sphere driven by jets of steam, often called the first steam turbine.
Hero also made an important observation about flow. In his Dioptra, he noted that the amount of water a spring delivers cannot be known from the cross-section of the flow alone; one must also take into account how fast it flows, for example by timing how long it takes to fill a vessel. In modern terms, he recognized that discharge depends on both area and velocity. This insight was not widely applied. The Romans, as we shall see, measured water by area alone.
Roman aqueducts and the water commissioner¶
The city of Rome was supplied by eleven aqueducts built over five centuries. They carried water by gravity over distances of up to about 90 km, mostly in covered channels with gentle, carefully surveyed slopes, and crossed valleys on arcades or, occasionally, with inverted siphons made of lead pipes. The engineering was remarkable, and some aqueducts still run today.
Our best source on how the system was managed is De aquaeductu by Sextus Julius Frontinus, who was appointed water commissioner (curator aquarum) of Rome in 97 CE. Frontinus measured water in units called quinariae, based on the cross-section of standard bronze nozzles (calices) through which water was delivered to users. He found large discrepancies between the water entering the system and the water delivered, and he blamed fraud and illegal taps, of which there were certainly many. But part of the discrepancy came from the method itself: a nozzle under a higher head delivers more water than an identical nozzle under a lower head. Without the idea that discharge is area times velocity, the accounts could never balance.
Water engineering beyond the Mediterranean¶
Many civilizations developed sophisticated hydraulic engineering independently.
Qanats in Persia, from the early first millennium BCE, were gently sloping tunnels that tapped groundwater at the foot of mountains and carried it many kilometers to villages and fields, with vertical shafts for access and ventilation. The technique spread across the Middle East, North Africa and Central Asia.
Dujiangyan in Sichuan, China, built around 256 BCE under the governor Li Bing, divides the Min River into an inner and an outer channel with a fish-mouth-shaped levee, controlling floods and irrigating the Chengdu Plain without a dam. It is still in use.
The Grand Canal of China, linked into a single system under the Sui dynasty around 600 CE, carried grain from the south to the northern capitals. The pound lock, with gates at both ends of a chamber, appears in China in the 10th century.
Nilometers in Egypt measured the annual rise of the Nile, which determined the harvest and, therefore, the taxes. They are among the oldest systematic hydrological records (see Chapter 7).
In the medieval Islamic world, engineers translated and extended Greek works. The Banu Musa brothers in 9th-century Baghdad described automatic devices controlled by floats and siphons. Ismail al-Jazari, in his Book of Knowledge of Ingenious Mechanical Devices (1206), described water-raising machines, including a double-acting pump with a crank, and elaborate water clocks. Water wheels (norias) lifted water for irrigation from Spain to Syria. In China, Su Song completed an astronomical clock tower in Kaifeng around 1090, driven by a water wheel with an escapement mechanism.
In medieval Europe, water mills spread so widely that the Domesday Book of 1086 lists more than five thousand of them in England. Tide mills, fulling mills and mills for sawing and forging made water power the main source of mechanical energy before steam.
Leonardo da Vinci: looking at water¶
Leonardo da Vinci (1452–1519) filled thousands of notebook pages with observations of water. The Codex Leicester (written around 1506–1510) is largely about water: rivers, waves, erosion, the shape of the Earth and the circulation of water through it. Leonardo worked as a military and hydraulic engineer, planning canals and river diversions for patrons in Milan and Florence, so his interest was practical as well as artistic.
Three of his observations stand out.
Continuity. Leonardo stated that a river flows faster where it is narrow and slower where it is wide, so that the same amount of water passes every section in the same time. This is the principle of continuity, written today as
where is the discharge, the cross-sectional area and the mean velocity.
Vortices. His drawings of water falling into a pool, flowing past obstacles and curling behind a plate are so accurate that modern fluid dynamicists still use them as illustrations. He distinguished the large-scale motion of the stream from the swirling eddies within it, and compared the curls of water to curls of hair. In a sense, he was the first to draw turbulence.
Flight. In his Codex on the Flight of Birds (1505) and other notes, Leonardo studied how birds use the air, and designed flapping-wing flying machines. He grasped that the air resists the wing as much as the wing pushes on the air, an idea close to the principle of action and reaction.
Leonardo’s notebooks were not published in his lifetime. They were scattered after his death, and most of their ideas had to be rediscovered by others. They show, however, a new attitude: water was something to be watched closely, measured and explained.
The word “revolution”¶
In 1543, the year of his death, Nicolaus Copernicus published De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres). For Copernicus, a revolution was simply a turning, the circular motion of a planet. Over the following two centuries, as his Sun-centered system overturned the old cosmos, the word acquired its modern meaning of a sudden and complete change, first in science and later in politics.
The next problem was obvious once the Earth was set in motion: what carries the planets around the Sun? One of the most influential answers, as Chapter 2 shows, was a giant whirlpool, a vortex in an invisible fluid filling all of space. The history of fluid mechanics and the history of the cosmos were about to become entangled.
Summary¶
Ancient and medieval societies built advanced water systems by experience, not theory.
Archimedes founded hydrostatics; hydrodynamics did not yet exist.
Aristotle’s rejection of the vacuum and his view of the medium as both mover and resister shaped thinking about flow until the 17th century.
Hero saw that discharge depends on velocity as well as area; Frontinus’s accounts show the cost of ignoring this.
Leonardo da Vinci observed continuity, vortices and the mechanics of flight, but his notebooks stayed unpublished.
Further reading¶
Rouse, H., & Ince, S. (1957). History of Hydraulics, chapters 1–4. Iowa Institute of Hydraulic Research.
Mays, L. W. (Ed.) (2010). Ancient Water Technologies. Springer.
Hodge, A. T. (1992). Roman Aqueducts and Water Supply. Duckworth.
Needham, J. (1971). Science and Civilisation in China, Vol. 4, Part 3: Civil Engineering and Nautics. Cambridge University Press.
Gombrich, E. H. (1969). The form of movement in water and air. In C. D. O’Malley (Ed.), Leonardo’s Legacy. University of California Press.