Fluid Mechanics -- from Eric Weisstein's World of Physics

Fluid mechanics is the study of the flow of fluids, and is sometimes known as hydrodynamics. Properties normally ascribed to fluids include density

, compressibility

(sometimes specified in terms of the so-called second viscosity coefficient

), and dynamic viscosity

. In general, the motion of fluids is extremely complicated, including highly nonlinear phenomena like turbulence, and cannot be described exactly. However, in simple geometries and when certain simplifying properties hold, some fluid mechanical systems are amenable to exact solutions.

The Navier-Stokes equations are the fundamental partial differential equations that describe the fluid of incompressible fluids. For low Reynolds number (an important dimensionless parameter depending on flow speed, size of the fluid system, and viscosity that characterized the qualitative type of fluid motion that will occur), the inertia term in these equations is smaller than the viscous term and can therefore be ignored, leaving the so-called equation of creeping motion. In this regime, viscous interactions have an influence over large distances from an obstacle. For low Reynolds number flow at low pressure, the Navier-Stokes equation becomes a diffusion equation. The flow of a fluid at low Reynolds number, where the viscous forces are much larger than the inertial forces is known as Stokes flow, and its equations are the Navier-Stokes equations with the inertia (left sides of equations 2-4) and body force terms equal to zero. For high Reynolds number flow, the viscous force is small compared to the inertia force, so it can be neglected, leaving Euler's equation of inviscid motion.

The boundary conditions of fluid mechanics include the no-slip condition, which requires that the fluid in contact with a container's walls be at rest

where U is the velocity of the wall, n is the normal vector, and

is the unit normal vector. The no-transfer condition requires that no fluid can be transferred through walls

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