# Fluid Mechanics

A fluid is a substance that deforms continuously when subjected to a tangential or shear stress, however small the shear stress may be. Such a continuous deformation under the stress constitutes a flow. Fluid mechanics is therefore the study of mechanics of such matter. As such, it pertains mostly to the study of liquids and gases, however the general theories may be applied to the study of amorphous solids, colloidal suspensions and gelatinous materials.

Fluid mechanics is a subdivision of continuum mechanics. Consequentially, fluids are considered continuous media for analysis, and their discrete nature is of no consequence for most applications. This assumption is valid mostly on length scales much larger than intramolecular distances. The departure from continuum is characterised by a dimensionless parameter, the Knudsen Number, defined by ${\displaystyle K_{n}=\lambda /L}$, where L is a characteristic length scale of the flow. The continuum hypothesis holds good if Kn < 0.01. However, recent applications in nanotechnology and biotechnology are demonstrating that the governing equations are still relevant on smaller scales, specifically when they are modified to include the effects of electrostatic, magnetic, colloidal and surface-tension driven forces.

Some fluid mechanics problems can be solved by applying conservation laws (mass, momentum, energy) of mechanics to a finite control volume. However, in general, it is necessary to apply those laws to an infinitesimal control volume, then use the resulting differential equations. Additionally, boundary values, initial conditions and thermodynamic state equations are generally necessary to obtain numeric or analytic solutions.