scholarly journals 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)

1983 ◽  
Vol 105 (2) ◽  
pp. 242-243 ◽  
Author(s):  
Don J. Wood
Keyword(s):  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Explicit Formulas

Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow

1983 ◽  
Vol 105 (1) ◽  
pp. 89-90 ◽  
Author(s):  
S. E. Haaland
Keyword(s):  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Explicit Formulas

Explicit, but accurate formulas for the friction factor are given as a substitute for the more inconvenient implicit formulas which are at present considered to be the most accurate.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

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.

A Review of Explicit Friction Factor Equations

1985 ◽  
Vol 107 (2) ◽  
pp. 280-283 ◽  
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.

Pressure Drop and Heat Transfer of Nanofluid in Turbulent Pipe Flow Considering Particle Coagulation and Breakage

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Jian-Zhong Lin ◽  
Yi Xia ◽  
Xiao-Ke Ku
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Volume Concentration ◽  
Particle Diameter ◽  
Turbulent Pipe Flow ◽  
Particle Volume ◽  
Friction Factors

Numerical simulations of Al2O3/water nanofluid in turbulent pipe flow are performed with considering the particle convection, diffusion, coagulation, and breakage. The distributions of particle volume concentration, the friction factor, and heat transfer characteristics are obtained. The results show that the initial uniform distributions of particle volume concentration become nonuniform, and increase from the pipe wall to the center. The nonuniformity becomes significant along the flow direction from the entrance and attains a steady state gradually. Friction factors increase with the increase of particle volume concentrations and particle diameter, and with the decrease of Reynolds number. The friction factors increase remarkably at lower volume concentration, while slightly at higher volume concentration. The presence of nanoparticles provides higher heat transfer than pure water. The Nusselt number of nanofluids increases with increasing Reynolds number, particle volume concentration, and particle diameter. The rate increase in Nusselt number at lower particle volume concentration is more than that at higher concentration. For a fixed particle volume concentration, the friction factor is smaller while the Nusselt number is larger for the case with uniform distribution of particle volume concentration than that with nonuniform distribution. In order to effectively enhance the heat transfer using nanofluid and simultaneously save energy, it is necessary to make the particle distribution more uniform. Finally, the expressions of friction factor and Nusselt number as a function of particle volume concentration, particle diameter and Reynolds number are derived based on the numerical data.

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