Correlation of the Friction Factor for Turbulent Pipe Flow of Dilute Polymer Solutions

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

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Discussion: “Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow” (Haaland, S. E., 1983, ASME J. Fluids Eng., 105, pp. 89–90)

Journal of Fluids Engineering ◽

10.1115/1.3240975 ◽

1983 ◽

Vol 105 (2) ◽

pp. 242-243 ◽

Cited By ~ 1

Author(s):

Don J. Wood

Keyword(s):

Friction Factor ◽

Pipe Flow ◽

Turbulent Pipe Flow ◽

Explicit Formulas

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Pressure drop and mass transfer in dilute polymer solutions in turbulent drag-reducing pipe flow

International Journal of Heat and Mass Transfer ◽

10.1016/0017-9310(82)90109-0 ◽

1982 ◽

Vol 25 (12) ◽

pp. 1869-1878 ◽

Cited By ~ 6

Author(s):

R. Smith ◽

M.F. Edwards ◽

H.Z. Wang

Keyword(s):

Mass Transfer ◽

Pressure Drop ◽

Pipe Flow ◽

Polymer Solutions ◽

Dilute Polymer Solutions ◽

Turbulent Drag

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A Review of Explicit Friction Factor Equations

Journal of Energy Resources Technology ◽

10.1115/1.3231190 ◽

1985 ◽

Vol 107 (2) ◽

pp. 280-283 ◽

Cited By ~ 45

Author(s):

D. J. Zigrang ◽

N. D. Sylvester

Keyword(s):

Friction Factor ◽

Pipe Flow ◽

Turbulent Pipe Flow ◽

Explicit Equation ◽

Flow Friction ◽

Friction Factors ◽

High Degree ◽

Very High

A review of the explicit friction factor equations developed to replace the Colebrook equation is presented. Explicit friction factor equations are developed which yield a very high degree of precision compared to the Colebrook equation. A new explicit equation, which offers a reasonable compromise between complexity and accuracy, is presented and recommended for the calculation of all turbulent pipe flow friction factors for all roughness ratios and Reynold’s numbers.

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