Estimation of hydraulic resistance coefficient in smooth pipes

A comparative analysis of the most widespread analytical relations used for estimation of coefficient in smooth pipes is made. A new simple relation that contains a minimum number of empirical parameters and allows evaluation of the hydraulic resistance coefficient in an explicit form is proposed. The effectiveness of the relation has been verified, and the obtained data have been compared with the results of experiments performed at Princeton and Oregon universities and published in 2004. The compatibility between the calculated and experimental results is analyzed in terms of average, median and maximum absolute values of their relative deflections. Simulations have shown that in spite of the fact that the data obtained during these experiments are close, the difference between the relations constructed using these results is significant. So, if the arithmetic means or medians of relative deflections are taken as the efficiency factor of these relations, the best coincidence with the experimental results from the Oregon experiment is ensured by the relation proposed by G. Barenblatt. Our relation gives slightly larger deflections. At the same time, a comparison with the results from the Princeton experiment indicates that it provides the lowest deflections for both the average and median values and the maximum values of absolute deviations among all the considered relations.