*Newtonian vs non-Newtonian fluids**Sir*

*Isaac Newton*

*showed how*

*stress*

*and the rate of*

*strain*

*are very close to linearly related for many familiar fluids, such as*

*water*

*and*

*air*

*. These*

*Newtonian fluids*

*are modeled by a coefficient called*

*viscosity*

*, which depends on the specific fluid.*

*However, some of the other materials, such as emulsions and slurries and some visco-elastic materials (eg.*

*blood*

*, some*

*polymers*

*), have more complicated*

*non-Newtonian*

*stress-strain behaviours. These materials include sticky liquids such as*

*latex*

*,*

*honey*

*, and lubricants which are studied in the sub-discipline of*

*rheology*

*.*

*Magnetohydrodynamics**Main article:*

*Magnetohydrodynamics*

*Magnetohydrodynamics*

*is the multi-disciplinary study of the flow of*

*electrically conducting*

*fluids in*

*electromagnetic*

*fields. Examples of such fluids include*

*plasmas*

*, liquid metals, and*

*salt water*

*. The fluid flow equations are solved simultaneously with*

*Maxwell's equations*

*of electromagnetism.*

*Other approximations**There are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below.*

*The**Boussinesq approximation**neglects variations in density except to calculate**buoyancy**forces. It is often used in free**convection**problems where density changes are small.**Lubrication theory**exploits the large**aspect ratio**of the domain to show that certain terms in the equations are small and so can be neglected.**Slender-body theory**is a methodology used in**Stokes flow**problems to estimate the force on, or flow field around, a long slender object in a viscous fluid.**The**shallow-water equations**can be used to describe a layer of relatively inviscid fluid with a**free surface**, in which surface**gradients**are small.**The**Boussinesq equations**are applicable to**surface waves**on thicker layers of fluid and with steeper surface**slopes**.**Darcy's law**is used for flow in**porous media**, and works with variables averaged over several pore-widths.**In rotating systems, the**quasi-geostrophic approximation**assumes an almost perfect balance between**pressure gradients**and the**Coriolis force**. It is useful in the study of**atmospheric dynamics**.*

*Terminology in fluid dynamics**The concept of*

*pressure*

*is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be*

*measured*

*using an aneroid, Bourdon tube, mercury column, or various other methods.*

*Some of the terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in*

*fluid statics*

*.*

*Terminology in incompressible fluid dynamics**The concepts of total pressure (also known as*

*stagnation pressure*

*) and*

*dynamic pressure*

*arise from*

*Bernoulli's equation*

*and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense - they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to*

*pressure*

*in fluid dynamics, many authors use the term*

*static pressure*

*to distinguish it from total pressure and dynamic pressure.*

*Static pressure*

*is identical to*

*pressure*

*and can be identified for every point in a fluid flow field.*

*In Aerodynamics,*

*L.J. Clancy*

*writes (page 21): "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure."*

*A point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special name - a*

*stagnation point*

*. The*

*pressure*

*at the stagnation point is also of special significance and is given its own name -*

*stagnation pressure*

*.*

*Terminology in compressible fluid dynamics**In a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid. In addition to the concept of total pressure (also known as*

*stagnation pressure*

*), the concepts of total (or stagnation) temperature and total (or stagnation) density are also essential in any study of compressible fluid flows. To avoid potential ambiguity when referring to temperature and density, many authors use the terms static temperature and static density. Static temperature is identical to temperature; and static density is identical to density; and both can be identified for every point in a fluid flow field.*

*The temperature and density at a*

*stagnation point*

*are called stagnation temperature and stagnation density.*

*Readers might wonder if there are such concepts as dynamic temperature or dynamic density. There aren't.*

*A similar approach is also taken with the thermodynamic properties of compressible fluids. Many authors use the terms total (or stagnation)*

*enthalpy*

*and total (or stagnation)*

*entropy*

*. The terms static enthalpy and static entropy appear to be less common, but where they are used they mean nothing more than enthalpy and entropy respectively, and the prefix 'static' is being used to avoid ambiguity with their 'total' or 'stagnation' counterparts.*