Fluid mechanics
[1]: 3 It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers.
A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach.
Iranian scholar Abu Rayhan Biruni and later Al-Khazini applied experimental scientific methods to fluid mechanics.
[3] Rapid advancement in fluid mechanics began with Leonardo da Vinci (observations and experiments), Evangelista Torricelli (invented the barometer), Isaac Newton (investigated viscosity) and Blaise Pascal (researched hydrostatics, formulated Pascal's law), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in Hydrodynamica (1739).
Inviscid flow was further analyzed by various mathematicians (Jean le Rond d'Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace, Siméon Denis Poisson) and viscous flow was explored by a multitude of engineers including Jean Léonard Marie Poiseuille and Gotthilf Hagen.
Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl, Theodore von Kármán), while various scientists such as Osborne Reynolds, Andrey Kolmogorov, and Geoffrey Ingram Taylor advanced the understanding of fluid viscosity and turbulence.
Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container.
Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids.
Fluid dynamics has a wide range of applications, including calculating forces and movements on aircraft, determining the mass flow rate of petroleum through pipelines, predicting evolving weather patterns, understanding nebulae in interstellar space and modeling explosions.
The assumptions inherent to a fluid mechanical treatment of a physical system can be expressed in terms of mathematical equations.
Under the continuum assumption, macroscopic (observed/measurable) properties such as density, pressure, temperature, and bulk velocity are taken to be well-defined at "infinitesimal" volume elements—small in comparison to the characteristic length scale of the system, but large in comparison to molecular length scale.
To determine whether or not the continuum hypothesis applies, the Knudsen number, defined as the ratio of the molecular mean free path to the characteristic length scale, is evaluated.
These cases generally involve non-turbulent, steady flow in which the Reynolds number is small.
For more complex cases, especially those involving turbulence, such as global weather systems, aerodynamics, hydrodynamics and many more, solutions of the Navier–Stokes equations can currently only be found with the help of computers.
In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then matching its solution onto that for a thin laminar boundary layer.
[11]: 145 The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity.
An ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force.
