This paper was prepared for the Society of Petroleum Engineers Symposium on Mechanics of Rheologically Complex Fluids, to be held in Houston, Tex., Dec. 15–16, 1966. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made.

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.


This paper proposes a friction-factor correlation for turbulent flow of viscoelastic fluids in tubes. The correlation is a generalization of the Blasius form such that


where f is the friction factor and K is a parameter for the particular fluid. N'Re is the Reynolds number generalized from the Oswald-deWaele model


where D is tube diameter, V is bulk velocity, rho is density, K' and n' are the consistency variable and the flow behavior index, respectively. f" is the friction factor predicted from the correlation of Dodge and Metzner for a given value of n' and a modified Reynolds number [1 + NWs] N'Re where NW, is the Weissenberg number. The correlation fits existing viscoelastic data within an average of 8 per cent.


There are many fluids which do not follow Newton's law of viscosity. These fluids are broadly classified as either purely viscous non-Newtonian or viscoelastic. Three approaches are used to develop predictive techniques for the flow of these complex fluids:

  1. the phenomenological approach, where one correlates semi-empirical functions with experimental data;

  2. the molecular or structural approach, where one tries to relate bulk behavior with the detailed dynamics of the structural unit; and

  3. the continuum approach, where one tries to generate models by placing general restrictions on the form of the rheological equations as prescribed by the rules of tensor analysis.

Correlations have been tested for purely viscous non-Newtonian fluids against considerable data for smooth tubes. Three turbulent flow correlations exist for viscoelastic fluids; each correlation has been derived from an independent set of flow data. This paper presents a correlation for friction factors for fluids in turbulent, viscoelastic flow which fits the data as well as or better than the three above-cited correlations. The proposed correlation is a generalization of the Blasius correlation for the turbulent flow of Newtonian fluids.

This content is only available via PDF.