For non-Newtonian fluids in pipe

Corresponding expressions for the friction loss in laminar and turbulent flow for non-Newtonian fluids in pipes, for the two simplest (two-parameter) models—the power law and Bingham plastic—can be evaluated in a similar manner. The power law model is very popular for representing the viscosity of a wide variety of non-Newtonian fluids because of its simplicity and versatility. However, extreme care should be exercised in its application, because any application involving extrapolation beyond the range of shear stress (or shear rate) represented by the data used to determine the model parameters can lead to misleading or erroneous results. 

Garcia, E. J. and Steffe, J. F. 1987. Comparison of friction factor equations for non-Newtonian fluids in pipe flow. J. Food Process Eng. 9 93-120. 

S. S. Yoo, Heat Transfer and Friction Factors for Non-Newtonian Fluids in TUrbulent Pipe Flow, Ph.D. thesis, University of Illinois at Chicago, 1974. 

S. S. Yoo and J. P. Hartnett, Thermal Entrance Lengths for non-Newtonian Fluid in Turbulent Pipe Flow, Lett. Heat Mass Transfer (2) 189,1975. 

W. A. Meyer, A Correlation of the Friction Characteristics for TUrbulent Flow of Dilute Viscoelastic non-Newtonian Fluids in Pipes, AIChE J. (12) 522,1966. 

Gottifredi JC. Flores AF. Extended Leveque solution for heat transfer to non-Newtonian fluids in pipes and flat ducts. International Journal of Heat and Mass Transfer 1985 28 903-908. 

The second part of the book covers two important flow fields of outstanding interest in petroleum industry. On the one hand, chapter 7, by Fester et al. deals explicitly with pipe flows. In particular, they review the loss coefficient data for laminar flow on non-Newtonian fluids in pipe fittings. Chapter 8, by Sun et al. focuses on enhanced oil recovery methods and explores the flow behavior of polymer solutions through a porous media. 

For steady, uniform, fully developed flow in a pipe (or any conduit), the conservation of mass, energy, and momentum equations can be arranged in specific forms that are most useful for the analysis of such problems. These general expressions are valid for both Newtonian and non-Newtonian fluids in either laminar or turbulent flow. 

The most important case of this transition for chemical engineers is the transition from laminar to turbulent flow, which occurs in straight bounded ducts. In the case of Newtonian fluid rheology, this occurs in straight pipes when Re = 2100. A similar phenomenon occurs in pipes of other cross sections, as well and also for non-Newtonian fluids. However, just as the friction factor relations for these other cases are more complex than for simple Newtonian pipe flow, so the criteria for transition to turbulence cannot be expressed as a simple critical value of a Reynolds number. 

The parameter B is called a dampening parameter, as its physical significance is associated with dampening turbulent fluctuations in the vicinity of a wall. For Newtonian pipe flow ithas the numerical value 22. For non-Newtonian fluids it has been found to be a function of various rheological parameters as follows ... 

Steffe and Morgan (1986) discussed in detail the selection of pumps and the sizing of pipes for non-Newtonian fluids. Preliminary selection of a pump is based on the volumetric pumping capacity only from data provided by the manufacturers of pumps. 

For non-Newtonian fluids, the viscosity in the above equations must be replaced by an appropriate apparent viscosity. In pipe-flow applications, as shown in Chapter 3, the pipe-flow apparent viscosity (%p) based on the diameter D and the average axial velocity in the tube (1 can be used in deriving the appropriate dimensionless numbers ... 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

Dodge and Metzner (16) presented an extensive theoretical and experimental study on the turbulent flow of non-Newtonian fluids in smooth pipes. They extended von Karman s (17) work on turbulent flow friction factors to include the power law non-Newtonian fluids. The following implicit expression for the friction factor was derived in terms of the Metzner-Reed modified Reynolds number and the power law index ... 

Solve the flow of a non-Newtonian fluid in a pipe, following the example, for pressure drops of 10, 10, 10, and 10 Pa. The parameters are tjq = 0.492 Pa s, A = 0.1 and n = 0.8. Plot the shear rate as a function of radial position. Calculate the average velocity. Plot the shear stress as a function of radial position. How do these curves change as the pressure drop is increased ... 

There are insnfficient data in the literatnre to provide a reliable estimate of the effect of roughness on friction loss for non-Newtonian flnids in tnrbnlent flow. However, the influence of roughness is normally neglected, since the laminar bonndary layer thickness for such fluids is typically much larger than for Newtonian fluids (i.e., the flow conditions most often fall in the hydraulically smooth range for common pipe materials). An expression by Darby et al. (1992) for / for the power law flnid, which applies to both laminar and turbulent flow, is... 

Even when the plug flow assumption is not valid, transportation processes usually can be modeled approximately by the transfer function for a time delay given in Eq. 6-28. For liquid flow in a pipe, the plug flow assumption is most nearly satisfied when the radial velocity profile is nearly flat, a condition that occurs for Newtonian fluids in turbulent flow. For non-Newtonian fluids and/or laminar flow, the fluid transport process still might be modeled by a time delay based on the average fluid... 

HARTNETT and KOSTIC 26 have recently examined the published correlations for turbulent flow of shear-thinning power-law fluids in pipes and in non-circular ducts, and have concluded that, for smooth pipes, Dodge and Metzner S(27) modification of equation 3.11 (to which it reduces for Newtonian fluids) is the most satisfactory. 

Heywood, N. 1. and Cheng, D. C.-H. Trans Inst. Measurement and Control 6 (1984) 33. Comparison of methods for predicting head loss in turbulent pipe flow of non-Newtonian fluids. 

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