§1.4 Classification of fluid

1.4.1 Newtonian fluid and non-Newtonian fluid

Newton's law of internal friction is only applicable to the general fluid and not applicable to some special fluids.Generally, the fluids in accordance with the law of Newton internal friction are called“Newtonian fluid”, otherwise the fluids are called“non-Newtonian fluid”.In continuum mechanics, a Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time.While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian fluid for practical calculations under ordinary conditions.

Fig.1-6 shows the curves describing the relationship between shear stress and shear strain rate of fluid.All these curves are called rheological curves.Slope of the curve is the viscosity μ of fluid.The viscosity μ of Newtonian fluid remains unchanged under constant temperature and pressure.The relationship curve between shear stress and shear strain rate of fluid has a fixed slope.

Among non-Newtonian fluids, a typical example of these substances is Bingham plastic fluid which does not exhibit any shear rate (no flow and thus no velocity)until a certain stress is achieved.Slurry, plasma and tooth paste are all Bingham plastic fluid. Another type of non-Newtonian fluids is pseudo-plastic fluid such as nylon, rubber, paper pulp, blood, milk and cement paste, whose viscosity decreases with the increase of shear strain rate.In addition, expansive fluid is also a type of non-Newtonian fluid. The viscosity of expansive fluids including dough and thick starch paste, increases with the enhancement of shear strain rate.This book only discusses Newtonian fluids.

1.4.2 Ideal fluids

Viscosity, i.e.resistance to gradual deformation by shear stress, is a property of all real fluids.Taking into account the viscosity of fluid complicates the fluid problems. In order to simply the fluid problems, the concept“ideal fluid”was introduced.Ideal fluid is a hypothetical fluid with zero viscosity states.Ideal fluid is an idealized fluid, which does not exist.However, fluids in the flow field or flow zone, where effects of viscosity are small, can be considered as ideal fluids.The conclusions drawn on the basis of ideal fluids can be corrected in order that they are applicable in real fluids.

1.4.3 Compressible fluids and incompressible fluids

Fluids can be categorized into compressible and incompressible fluids according to the difference in the volume reduction of liquid under pressure.The variation of fluid density with pressure is very small.The fluid with a constant density can be considered as an incompressible fluid; otherwise it is a compressible fluid.Strictly speaking, there is no completely incompressible fluid.Under normal conditions, the density of liquid can be considered a constant and liquid can be regarded as incompressible fluid.Gas can be considered incompressible fluid when the variation of pressure is relatively small. When high speed flow of air or water vapor pass through long pipes, the pressure drop is very large and the density varies greatly.In this instance, gas must be considered compressible fluid.