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The History of Fluid Mechanics: A Brief Overview. Fluid mechanics is the branch of applied mathematics that deals with fluids and their interactions with surfaces and free boundaries using techniques such as fluid statics, fluid dynamics, and hydromechanics. The theory of fluid mechanics can be found in the works of Aristotle, Leonardo da Vinci, Huygens and Newton among others. However, it was not until the late 1800s when this field began receiving major attention in academia. It is considered to be one of the most important branches in engineering today due to its role in designing machinery, control systems for power plants or dams, aircraft bodies or wings. In this section we present a brief overview on the history of fluid mechanics.The field of fluid mechanics has a long and complex history dating back to antiquity. In an early work, Leonardo da Vinci discuss some basic ideas about fluids and pressure. In Greek Physika, Aristotle presented his first ideas on the fundamental principles of fluids which were developed by him over many years of research. An important concept from Aristotle is the concept of "absolute density" which is proportional to the amount of matter it contains. In his works, he used this concept as a mathematical limit for how far a fluid can flow or expand under a given pressure difference. Later, in the Middle Ages, John Philoponus and Alhazen developments in classical Greek ideas. In one of his most famous experiments, Alhazen showed that a weight submerged in a fluid experiences a force equal to the weight of the displaced fluid. In this experiment he also noted that the maximum amount of possible displacement occurs when the weight is lowered until it just touches the fluid.During this time period there were some advancements in understanding of fluids and pumps, but most progress was based on empirical observations and not on formal mathematical models. The 17th century brought major advances in understanding fluid dynamics due to the work of key scholars such as Robert Hooke, Evangelista Torricelli, Isaac Newton, Jean Bernoulli, and Daniel Bernoulli. Some important discoveries at this time period include Galileo's law of reflection and the law of conservation of mechanical energy. This last discovery was later called "Newton's bucket rule". During this period, fluid mechanics emerged as a separate branch of mathematics that is now sometimes referred to as "fluid mechanics or hydromechanics". However, there were still major gaps in the mathematical modeling of fluids which required more mathematical developments. Also at this time many experiments concerning fluids were conducted by leading scholars such as Robert Boyle. In the 19th century, Navier and Stokes developed and formalized many of the important concepts of fluid dynamics. At this time, "hydrostatics" began to refer to gravitational phenomena, while "hydrodynamics" dealt with non-gravitational phenomena. The fluid statics equations were developed by Duhamel which provided a mathematical model for hydrostatic pressure distribution. Fluid dynamics was dealt with using Navier's method in space in which he was able to formally derive the equation for motion in a viscous incompressible fluid in steady state. It was not until much later in the century when Stokes developed an important equation named after him called the "Stokes' law".

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