fluid behavior is where is the shear stress exerted by the fluid ("drag"), is the fluid viscosity—a constant of proportionality, and is the velocity gradient perpendicular to the direction of shear. For a Newtonian fluid, the viscosity, by definition, depends only on temperature, not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress (in Cartesian coordinates) is where is the shear stress on the face of a fluid element in the direction is the velocity in the direction is the direction coordinate. If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is where is the second viscosity coefficient (or bulk viscosity). If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic. In some applications, another rough broad division among fluids is made: ideal and non-ideal fluids. An ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. One example of this is the flow far from solid surfaces. In many cases, the viscous effects are concentrated near the solid boundaries (such as in boundary layers) while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid (ideal flow). When the viscosity is neglected, the term containing the viscous stress tensor in the Navier–Stokes equation vanishes. The equation reduced in this form is called the Euler equation. See also Transport phenomena Aerodynamics Applied mechanics Bernoulli's principle Communicating vessels Computational fluid dynamics Compressor map Secondary flow Different types of boundary conditions in fluid dynamics References Further reading External links Free Fluid Mechanics books Annual Review of Fluid Mechanics CFDWiki – the Computational Fluid Dynamics reference wiki. Educational Particle Image Velocimetry – resources and demonstrations Civil engineering