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For a compressible fluid in a tube the volumetric flow rate Q(x) and the axial velocity are not constant along the tube; but the mass flow rate is constant along the tube length. The volumetric flow rate is usually expressed at the outlet pressure. As fluid is compressed or expanded, work is done and the fluid is heated or cooled.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
In continuum mechanics, time-dependent viscosity is a property of fluids whose viscosity changes as a function of time. The most common type of this is thixotropy , in which the viscosity of fluids under continuous shear decreases with time; the opposite is rheopecty , in which viscosity increases with time.
By introducing the tensors (matrices) , and (where e is a scalar called dilation, and is the identity tensor), which describes crude shear flow (i.e. the strain rate tensor), pure shear flow (i.e. the deviatoric part of the strain rate tensor, i.e. the shear rate tensor [14]) and compression flow (i.e. the isotropic dilation tensor), respectively,
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
Chengwei and Linqing [12] used an analysis of the surface height probability distribution to remove one of the more complex terms from the average Reynolds equation, ¯ / and replace it with a flow factor referred to as contact flow factor, . Knoll et al. calculated flow factors, taking into account the elastic deformation of the surfaces.
Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate). Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow .
where η is the dynamic viscosity of the fluid, N is the entrainment speed of the fluid and P is the normal load per length of the tribological contact. Hersey's original formula uses the rotational speed (revolutions per unit time) for N and the load per projected area (i.e. the product of a journal bearing's length and diameter) for P.