Pressure Loss Equations for Laminar and Turbulent Non-Newtonian Pipe Flow
Publication: Journal of Hydraulic Engineering
Volume 124, Issue 5
Abstract
The equations that define Newtonian pipe flow are well established and used routinely by engineers and scientists throughout the world. The same cannot be said for non-Newtonian flows, which have a higher degree of complexity. This paper presents a coherent set of equations for the laminar and turbulent flow of Herschel-Bulkley fluids. These equations are consistent with those used for Newtonian fluids and previous work on the behavior of generalized non-Newtonian fluids. A numerical model for non-Newtonian flows is discussed and has been compared with experimental measurements from different sources. This model has been used to run a series of simulations to find the coefficients required for a new turbulent friction factor correlation. A new Reynolds number has been defined that represents the conditions in turbulent flows more realistically than the existing Metzner-Reed Reynolds number.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ackers, P., and Allen, M. C.(1980). “The laminar flow of sewage sludge through pipelines.”Public Health Engr., 8, 88–106.
2.
Buckingham, E.(1921). “Plastic flow through capillary tubes.”Proc., ASTM, 21, 1154.
3.
Chilton, R. A., Stainsby, R., and Thompson, S. L.(1996). “The design of sewage sludge pumping systems.”J. Hydr. Res., Delft, The Netherlands, 34, 395–407.
4.
Clapp, R. M. (1961). “Turbulent heat transfer in pseudo-plastic non-Newtonian fluids.”Proc., Conf. Int. Devel. in Heat Transfer, University of Colorado, Boulder, Colo., Part III, Sec. A, 652–661.
5.
Cross, M. M.(1965). “Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems.”J. Colloid Sci., 20, 417–437.
6.
Dodge, D. W., and Metzner, A. B.(1959). “Turbulent flow of non-Newtonian systems.”AIChE J., 5, 189–204.
7.
Govier, G. W., and Aziz, K. (1972). The flow of complex mixtures. Von Nostrand-Reinhold, New York, N.Y.
8.
Herschel, W. H., and Bulkley, R.(1928). “Measurement of consistency as applied to rubber-benzene solutions.”Proc., ASTM, Kolloid Z, 26, 621.
9.
Kozicki, W., and Kuang, P. Q.(1993). “Prediction of lower/upper limiting viscosities.”Can. J. Chem. Engrg., 71, 329–331.
10.
Launder, B. E., and Sharma, B. I.(1974). “Application of the energy dissipation model to the calculation of flow near a spinning disc.”Lett. Heat and Mass Transfer, 1, 131–138.
11.
Lazarus, J. H., and Slatter, P. T.(1988). “A method for the rheological characterisation of tube viscometer data.”J. Pipelines, 7, 165–176.
12.
Meter, D. M., and Bird, R. B.(1964). “Tube flow of non-Newtonian polymer solutions: Part 1 laminar flow and rheological models.”AIChEJ., 10, 878–881.
13.
Metzner, A. B.(1957). “Non-Newtonian fluid flow—relationships between recent pressure drop correlations.”Ind. Engrg. Chem., 49, 1429–1433.
14.
Metzner, A. B., and Reed, J. C.(1955). “Flow of non-Newtonian fluids—correlation of the laminar, transition, and turbulent-flow regions.”AIChEJ., 1(4), 434–440.
15.
Mooney, M. J.(1931). “Explicit formulas for slip and fluidity.”J. Rheology, 2, 210–222.
16.
Rabinowitsch, B.(1929). “Ueber die viskositat und elastizitat von solen.”Z Phisik Chem Ser A, 145, 1–26.
17.
Sisko, A. W.(1958). “The flow of lubricating greases.”Ind. Engrg. Chem., 50, 1789–1792.
18.
Stainsby, R., Chilton, R. A., and Thompson, S. L. (1994). “Prediction of the head losses in non-Newtonian sludge using CFD.”Proc., 2nd CFDS Int. User Conf., CFX Int., AEA Technol., Didcot, Oxfordshire, U.K., 259–272.
19.
Thomas, A. D., and Wilson, K. C.(1987). “New analysis of non-Newtonian turbulent flow—yield-power-law fluids.”Can. J. Chem. Engrg., 65, 335–338.
20.
Tomita, Y.(1959). “A study of non-Newtonian flow in pipelines.”Bull. JSME, 2, 469.
21.
Torrance, B. M.(1963). “Friction factors for turbulent non-Newtonian fluid flow in circular pipe.”J. South African Mech. Engrg., 13, 89–91.
22.
Wilson, K. C., and Thomas, A. D.(1985). “A new analysis of the turbulent flow of non-Newtonian fluids.”Can. J. Chem. Engrg., 63, 539–546.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 124 • Issue 5 • May 1998
Pages: 522 - 529
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: May 1, 1998
Published in print: May 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.