The history of fluid mechanics is a fundamental strand of the history of physics and engineering. The study of the movement of fluids (liquids and gases) and the forces that act upon them dates back to pre-history. The field has undergone a continuous evolution, driven by human dependence on water, meteorological conditions, and internal biological processes.

The success of early civilizations, can be attributed to developments in the understanding of water dynamics, allowing for the construction of canals and aqueducts for water distribution and farm irrigation, as well as maritime transport. Due to its conceptual complexity, most discoveries in this field relied almost entirely on experiments, at least until the development of advanced understanding of differential equations and computational methods. Significant theoretical contributions were made by notables figures like Archimedes, Johann Bernoulli and his son Daniel Bernoulli, Leonhard Euler, Claude-Louis Navier and George Stokes, who developed the fundamental equations to describe fluid mechanics. Advancements in experimentation and computational methods have further propelled the field, leading to practical applications in more specialized industries ranging from aerospace to environmental engineering. Fluid mechanics has also been important for the study of astronomical bodies and the dynamics of galaxies.

A pragmatic, if not scientific, knowledge of fluid flow was exhibited by ancient civilizations, such as in the design of arrows, spears, boats, and particularly hydraulic engineering projects for flood protection, irrigation, drainage, and water supply. The earliest human civilizations began near the shores of rivers, and consequently coincided with the dawn of hydrology, hydraulics, and hydraulic engineering.

Observations of specific gravity and buoyancy were recorded by ancient Chinese philosophers. In the 4th century BCE Mencius describes the weight of the gold is equivalent to the feathers. In 3rd century CE, Cao Chong describes the story of weighing the elephant by observing displacement of the boats loaded with different weights.

The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work On Floating Bodies (Ancient Greek: Περὶ τῶν ὀχουμένων), around 250 BC. In it, Archimedes develops the law of buoyancy, also known as Archimedes' principle. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.

In the Greek school at Alexandria, which flourished under the auspices of the Ptolemies, attempts were made at the construction of hydraulic machinery, and about 120 BC the fountain of compression, the siphon, and the forcing-pump were invented by Ctesibius and Hero. The siphon is a simple instrument; but the forcing-pump is a complicated invention, which could scarcely have been expected in the infancy of hydraulics. It was probably suggested to Ctesibius by the Egyptian wheel or Noria, which was common at that time, and which was a kind of chain pump, consisting of a number of earthen pots carried round by a wheel. In some of these machines the pots have a valve in the bottom which enables them to descend without much resistance, and diminishes greatly the load upon the wheel; and, if we suppose that this valve was introduced so early as the time of Ctesibius, it is not difficult to perceive how such a machine might have led to the invention of the forcing-pump.

Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids; and the first attempt to investigate this subject was made by Sextus Julius Frontinus, inspector of the public fountains at Rome in the reigns of Nerva and Trajan. In his work De aquaeductibus urbis Romae commentarius, he considers the methods which were at that time employed for ascertaining the quantity of water discharged from ajutages (tubes), and the mode of distributing the waters of an aqueduct or a fountain. He remarked that the flow of water from an orifice depends not only on the magnitude of the orifice itself, but also on the height of the water in the reservoir; and that a pipe employed to carry off a portion of water from an aqueduct should, as circumstances required, have a position more or less inclined to the original direction of the current. But as he was unacquainted with the law of the velocities of running water as depending upon the depth of the orifice, the want of precision which appears in his results is not surprising.

Islamicate scientists, particularly Abu Rayhan Biruni (973–1048) and later Al-Khazini (fl. 1115–1130), were the first to apply experimental scientific methods to fluid mechanics, especially in the field of fluid statics, such as for determining specific weights. They applied the mathematical theories of ratios and infinitesimal techniques, and introduced algebraic and fine calculation techniques into the field of fluid statics. Al-Khazini, in The Book of the Balance of Wisdom (1121), invented a hydrostatic balance.