Newtonian fluid definition

Wikipedia, Non-Newtonian fluid definition, available http //en.wikipedia.org/wiki/Non-Newtonian fluid. 

The flow of compressible and non-compressible liquids, gases, vapors, suspensions, slurries and many other fluid systems has received sufficient study to allow definite evaluation of conditions for a variety of process situations for Newtonian fluids. For the non-Newtonian fluids, considerable data is available. However, its correlation is not as broad in application, due to the significant influence of physical and rheological properties. This presentation is limited to Newtonian systems, except where noted. 

As indicated in Section 3.7.9, this definition of ReMR may be used to determine the limit of stable streamline flow. The transition value (R ur)c is approximately the same as for a Newtonian fluid, but there is some evidence that, for moderately shear-thinning fluids, streamline flow may persist to somewhat higher values. Putting n = 1 in equation 3,140 leads to the standard definition of the Reynolds number. 

The usual approach for non-Newtonian fluids is to start with known results for Newtonian fluids and modify them to account for the non-Newtonian properties. For example, the definition of the Reynolds number for a power law fluid can be obtained by replacing the viscosity in the Newtonian definition by an appropriate shear rate dependent viscosity function. If the characteristic shear rate for flow over a sphere is taken to be V/d, for example, then the power law viscosity function becomes... 

In the case of non-Newtonian flow, it is necessary to use an appropriate apparent viscosity. Although the apparent viscosity (ia is defined by equation 1.71 in the same way as for a Newtonian fluid, it no longer has the same fundamental significance and other, equally valid, definitions of apparent viscosities may be made. In flow in a pipe, where the shear stress varies with radial location, the value of fxa varies. As pointed out in Example 3.1, it is the conditions near the pipe wall that are most important. The value of /j.a evaluated at the wall is given by... 

This value is one-fourth of the friction factor used in Section 6.3. For the sake of consistency with the literature, the definition of Eq. (6.50) will be used with non-Newtonian fluids in the present section. 

Figure H1.1.5 Empirical models that are used to predict the complete flow curve of non-Newtonian fluids or portions of the complete curve. In the full-curve models, K is a constant with time as its dimension and m is a dimensionless constant. See text for definition of other variables in equations.

For simple fluids, also known as Newtonian fluids, it is easy to predict the ease with which they will be poured, pumped, or mixed in either an industrial or end-use situation. This is because the shear viscosity or resistance to flow is a constant at any given temperature and pressure. The fluids that fall into this category are few and far between, because they are of necessity simple in structure. Examples are water, oils, and sugar solutions (e.g., honey unit hi.3), which have no dispersed phases and no molecular interactions. All other fluids are by definition non-Newtonian, so the viscosity is a variable, not a constant. Non-Newtonian fluids are of great interest as they encompass almost all fluids of industrial value. In the food industry, even natural products such as milk or polysaccharide solutions are non-Newtonian. 

API Recommended Practice 520 Part I, Sizing and Selection This API design manual includes basic definitions and information about the operational characteristics and applications of various pressure relief devices. It also includes sizing procedures and methods based on steady state flow of Newtonian fluids. This RP covers equipment that has a maximum allowable pressure of 15 psig (1.03 barg) or greater. 

The dynamic response of a particle in gas-solid flows may be characterized by the settling or terminal velocity at which the drag force balances the gravitational force. The dynamic diameter is thus defined as the diameter of a sphere having the same density and the same terminal velocity as the particle in a fluid of the same density and viscosity. This definition leads to a mathematical expression of the dynamic diameter of a particle in a Newtonian fluid as... 

The ambiguity of definition of Re encountered in the concentric annulus case is compounded here because of the fact that no viscosity is definable for non-Newtonian fluids. Thus, in the literature one encounters a bewildering array of definitions of Re-like parameters. We now present friction factor results for the non-Newtonian constitutive relations used above that are common and consistent. Many others are possible. 

As per the definition of a Newtonian fluid, the shear stress, ct, and the shear rate, y, are proportional to each other, and a single parameter, t], the viscosity. 

M. van den Tempel. Surface Rheology, in Journal of Non-Newtonian Fluid Mechanics 2 (1977) 205-19. (Review with a phenomenological emphasis operational definitions and coupling to bulk rheology.)... 

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