Determining velocity and friction factor for turbulent flow in smooth tubes

The most popular explicit correlations for the friction factor in smooth tubes are reviewed in this paper. The friction factor for the turbulent flow in smooth tubes is required in some correlations when calculating the Nusselt number. To calculate the friction factor, the velocity profile in a turbulent smooth wall-tube must be estimated at first. The radial velocity distribution was determined using either universal velocity profile found experimentally by Reichardt or by integration the momentum equation using the eddy diffusivity model of Reichardt. The friction factor obtained by using the universal velocity profile gives better results than that obtained from the momentum equation when compared with the Prandtl-von Kármán-Nikuradse equation. Based on the velocity profiles proposed by Reichardt the friction factor was calculated as a function of the Reynolds number and subsequently two formulas for the friction were proposed. They have satisfactory accuracy when comparing with the implicit Prandtl-von Kármán-Nikuradse equation. Thus, it was concluded that the universal velocity profile proposed by Reichardt will provide good results when it is taken into account while integrating the energy conservation equation. There is also a considerable number of experimental correlations for the friction factor in smooth tubes. All these relationships were compared with the experimental data and with the implicit Prandtl-von Kármán-Nikuradse equation that is considered as a standard to test the explicit approximations. The Colebrook and Filonienko explicit correlations are widely used when calculating the Nusselt number for the turbulent flow but they have noticeable errors for small Reynolds number ranged from 3000 to 7000 for the Colebrook relation and from 3000 to 30,000 for the Filonienko relation. For this reason, a new simple and accurate correlation for the friction factor for Reynolds numbers between 3000 and 107 is proposed in the paper.