Newtonian and Non-Newtonian Fluids: Velocity Profiles, Viscosity Data, and Laminar Flow Friction Factor Equations for Flow in a Circular Duct

2008 ◽  
Author(s):  
Melissa M. Simpson ◽  
William S. Janna
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Newtonian Fluid ◽  
Velocity Profiles ◽  
Newtonian Fluids ◽  
Viscosity Data ◽  
Circular Duct ◽  
Flow Friction

Newtonian fluid flow in a duct has been studied extensively, and velocity profiles for both laminar and turbulent flows can be found in countless references. Non-Newtonian fluids have also been studied extensively, however, but are not given the same attention in the Mechanical Engineering curriculum. Because of a perceived need for the study of such fluids, data were collected and analyzed for various common non-Newtonian fluids in order to make the topic more compelling for study. The viscosity and apparent viscosity of non-Newtonian fluids are both defined in this paper. A comparison is made between these fluids and Newtonian fluids. Velocity profiles for Newtonian and non-Newtonian fluid flow in a circular duct are described and sketched. Included are profiles for dilatant, pseudoplastic and Bingham fluids. Only laminar flow is considered, because the differences for turbulent flow are less distinct. Also included is a procedure for determining the laminar flow friction factor which allows for calculating pressure drop. The laminar flow friction factor in classical non-Newtonian fluid studies is the Fanning friction factor. The equations developed in this study involve the Darcy-Weisbach friction factor which is preferred for Newtonian fluids. Also presented in this paper are viscosity data of Heinz Ketchup, Kroger Honey, Jif Creamy Peanut Butter, and Kraft Mayonnaise. These data were obtained with a TA viscometer. The results of this study will thus provide the student with the following for non-Newtonian fluids: • Viscosity data and how it is measured for several common non-Newtonian fluids; • A knowledge of velocity profiles for laminar flow in a circular duct for both Newtonian and non-Newtonian fluids; • A procedure for determining friction factor and calculating pressure drop for non-Newtonian flow in a duct.

Dispersion of matter in non-Newtonian laminar flow through a circular tube

1966 ◽  
Vol 292 (1429) ◽  
pp. 203-208 ◽  
Keyword(s):  
Laminar Flow ◽  
Newtonian Fluid ◽  
Circular Tube ◽  
Newtonian Fluids ◽  
Parallel Plane ◽  
Bingham Plastic ◽  
Ellis Model ◽  
Model Fluid ◽  
Flow Through

Taylor’s analyses of the dispersion of Newtonian fluids in laminar flow in a circular tube are extended to the flow of the Bingham plastic and Ellis model fluid. The previous results for the Newtonian fluid and power-low fluid can be deduced from the results of this work. It is indicated that Aris’s modification of Taylor’s analyses can be naturally applied to the non-Newtonian fluid. Results obtained for laminar flow between two parallel plane walls are given in the appendix.

scholarly journals Fluctuations of the non-Newtonian fluid flow in a Kenics static mixer: An experimental study

2008 ◽  
Vol 10 (3) ◽  
pp. 35-37 ◽  
Author(s):  
Sylwia Peryt-Stawiarska ◽  
Zdzisław Jaworski
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Strong Dependence ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Test Fluid ◽  
Static Mixer ◽  
Flow Fluctuations

Fluctuations of the non-Newtonian fluid flow in a Kenics static mixer: An experimental study The measurements for a Kenics static mixer were carried out using Laser Doppler Anemometer (LDA). The test fluid was non-Newtonian solution of CMC, Blanose type 9H4. The velocity data inside the 5th Kenics insert were collected for the axial components at five levels of Reynolds number, Re = 20 ÷ 120. Velocity fluctuations were also analyzed in the frequency domain, after processing them with the help of the Fast Fourier Transform (FFT) procedure. The spectra of fluctuations provided information about level of the fluctuations in the observed range of Reynolds number. The obtained data were then also used to plot the velocity profiles for the fifth insert of the Kenics mixer. It was concluded that in the investigated range of Reynolds numbers (Re = 20 ÷ 120) a strong dependence of the velocity profiles and the flow fluctuations on Reynolds number was observed.

scholarly journals solutions of the CW equation for flow friction

2017 ◽  
Author(s):  
Dejan Brkić
Keyword(s):  
Fluid Flow ◽  
Friction Factor ◽  
Explicit Form ◽  
Iterative Procedure ◽  
Lambert W Function ◽  
Explicit Formulas ◽  
Flow Friction ◽  
Transcendental Functions ◽  
Flow Through

The empirical Colebrook–White (CW) equation belongs to the group of transcendental functions. The CW function is used for the determination of hydraulic resistances associated with fluid flow through pipes, flow of rivers, etc. Since the CW equation is implicit in fluid flow friction factor, it has to be approximately solved using iterative procedure or using some of the approximate explicit formulas developed by many authors. Alternate mathematical equivalents to the original expression of the CW equation, but now in the explicit form developed using the Lambert W-function, are shown (with related solutions). The W-function is also transcendental, but it is used more general compared with the CW function. Hence, the solution to the W-function developed by mathematicians can be used effectively for the CW function which is of interest only for hydraulics.

A Critical Examination of Correlation Methodology Widely Used in Heat Transfer and Fluid Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
Eugene F. Adiutori
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Power Laws ◽  
Critical Examination ◽  
Highly Nonlinear ◽  
Flow Pressure ◽  
The Impact

The correlation methodology widely used in heat transfer and fluid flow is based on fitting power laws to data. Because all power laws of positive exponent include the point (0,0), this methodology includes the tacit assumption that phenomena are best described by correlations that include the point (0,0). • If a phenomenon occurs near (0,0), the assumption is obviously valid. For example, laminar flow occurs near (0,0), and therefore the assumption is valid for laminar flow pressure drop correlations. • If a phenomenon does not occur near (0,0), the assumption is obviously invalid. For example, turbulent flow does not occur near (0,0)—it occurs only after a critical Reynolds number is reached. Therefore the assumption is invalid for turbulent flow pressure drop correlations. When the assumption is invalid, the correlation methodology widely used in heat transfer and fluid flow is lacking in rigor. The impact of the lack of rigor is evidenced by examples that demonstrate that, when this methodology is applied to phenomena that do not occur in the vicinity of (0,0), highly nonlinear power laws oftentimes result from data that exhibit highly linear behavior. Because the widely used methodology lacks rigor when applied to phenomena that do not occur near (0,0), power laws based on this methodology are suspect if they purport to describe phenomena that do not occur near (0,0). Data cited in support of such power laws should be recorrelated using rigorous correlation methodology. Rigorous correlation methodology is also used in heat transfer and fluid flow. It is described in the text, and should become the methodology in general use.

Fluid flow and convection heat transfer in concentric and eccentric cylindrical annuli of different radii ratios for Taylor-Couette-Poiseuille flow

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110407
Author(s):  
Hosny Abou-Ziyan ◽  
Reda Ameen ◽  
Khairy Elsayed
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Friction Factor ◽  
Rotational Speed ◽  
Convection Heat Transfer ◽  
Tangential Velocity ◽  
Convection Heat ◽  
Eccentric Annuli

This paper presents the results of fluid flow and convection heat transfer in concentric and eccentric annuli between two cylinders using a three-dimensional computational fluid dynamics model. Effects of rotational speed ( n = 0, 150, 300, and 400 rpm) and eccentricity (ε = 0, 0.15, 0.3, 0.45, and 0.6) on axial and tangential velocity distribution, pressure drop and forced convection heat transfer are investigated for radii ratios (η) of 0.2, 0.4, 0.6, and 0.8, Reynolds number 2.0 × 103–1.236 × 105, Taylor number 1.47 × 106–1.6 × 1010, and Prandtl number 3.71–6.94. The parameters cover many applications, including rotary heat exchangers, mixers, agitators, etc. Nusselt numbers and friction factors for stationary and rotated concentric and eccentric annuli are correlated with four dimensionless numbers. The results revealed that when the speed of the inner cylinder increases from 0 to 400 rpm, the friction factor increases by 7.7%–103% for concentric and 8.2%–148% for eccentric annuli, whereas Nusselt number enhances by 37%–333% for concentric and 44%–340% for eccentric annuli. The radius ratio has a substantial effect on the heat transfer and pressure drop in annuli. The eccentricity enhances the heat transfer up to 12%, whereas its effect on the friction factor is not monotonic as it depends on Reynolds number, radii ratios, and rotational speed.

The Effect of Twisted-Tape Width on Heat Transfer and Pressure Drop for Fully Developed Laminar Flow

1996 ◽  
Vol 118 (3) ◽  
pp. 584-589 ◽  
Author(s):  
W. M. Chakroun ◽  
S. F. Al-Fahed
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Twisted Tape ◽  
Constant Wall Temperature ◽  
Low Reynolds Number Flows ◽  
Temperature Boundary ◽  
Series Of Experiments

A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wavelengths, each with five different widths, have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 to 15 percent for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but has a more pronounced effect on heat transfer at the higher range of Reynolds number. It is recommended to use loose-fit tapes for low Reynolds number flows instead of tight-fit in the design of heat exchangers because they are easier to install and remove for cleaning purposes.

scholarly journals Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media

1979 ◽  
Vol 19 (03) ◽  
pp. 164-174 ◽  
Author(s):  
Chi U. Ikoku ◽  
Henry J. Ramey
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Oil Recovery ◽  
Transient Flow ◽  
Polymer Solutions ◽  
Newtonian Fluids ◽  
Petroleum Engineering ◽  
Published Data ◽  
Well Test

Abstract The transient flow behavior of non-Newtonian fluids in petroleum reservoirs is studied. A new partial differential equation is derived. The diffusivity equation is a special case of the new equation. The new equation describes the flow of a slightly compressible, non-Newtonian, power-law fluid in a homogeneous porous medium. This equation should govern the flow of most non-Newtonian oil-displacement agents used in secondary and tertiary oil-recovery projects, such as polymer solutions, micellar projects, such as polymer solutions, micellar solutions, and surfactant solutions. Analytical solutions of the new partial differential equation are obtained that introduce new methods of well-test analysis for non-Newtonian fluids. An example is presented for using the new techniques to analyze injection well-test data in a polymer injection project. project. Graphs of the dimensionless pressure function also are presented. These may be used to investigate the error when using Newtonian fluid-flow equations to model the flow of non-Newtonian fluids in porous media. Introduction Non-Newtonian fluids, especially polymer solutions, microemulsions, and macroemulsions, often are injected into the reservoir in various enhanced oil-recovery processes. In addition, foams sometimes are circulated during drilling. Thermal recovery of oil by steam and air injection may lead to the flow of natural emulsions and foams through porous media. Some enhanced oil-recovery projects involving the injection of non-Newtonian fluids have been successful, but most of these projects either failed or performed below expectation. These results suggest the need for a thorough study of the stability of non-Newtonian fluids at reservoir conditions, and also a new look at the flow of non-Newtonian fluids in porous media. porous media. Many studies of the rheology of non-Newtonian fluids in porous media exist in the chemical engineering, rheology, and petroleum engineering literature. In 1969, Savins presented an important survey on the flow of non-Newtonian fluids through porous media. In some cases, he interpreted porous media. In some cases, he interpreted published data further and compared results of published data further and compared results of different investigators. van Poollen and Jargon presented a numerical study of the flow of presented a numerical study of the flow of non-Newtonian fluids in homogeneous porous media using finite-difference techniques. They considered steady-state and unsteady-state flows and used the Newtonian fluid-flow equation. They considered non-Newtonian behavior by using a viscosity that varied with position. No general method was developed for analyzing flow data. Bondor et al. presented a numerical simulation of polymer presented a numerical simulation of polymer flooding. Much useful information on polymer flow was presented, but transient flow was not considered.At present, there is no standard method in the petroleum engineering literature for analyzing petroleum engineering literature for analyzing welltest data obtained during injection of non-Newtonian fluids into petroleum reservoirs. However, injection of several non-Newtonian oil-displacement agents is an important oilfield operation. Interpretation of well-test data for these operations should also be important. Obviously, procedures developed for Newtonian fluid flow are not appropriate. SPEJ P. 164

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