New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts

Abstract

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.

Hybrid Models for Solving the Colebrook–White Equation Using Artificial Neural Networks

“…Furthermore, optimization with the excel program applies different objective functions. The objective function is to minimize E r defined by Equation (19), and two other objective functions including minimizing MRE defined by Equation ( 25) and minimizing MAXRE defined by Equation (26). However, based on the simulation results, the MRE and MAXRE values generated from these three objective functions did not significantly differ in the MRE and the MAXRE values.…”

“…Moreover, the study and development of the approximation of the Colebrook-White equation are still going on today. Some of the latest studies on this can be seen in several kinds of literature [18][19][20][21][22][23].…”

Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation

“…The real evaluation of the presented formulations is not easy to perform because, although universally accepted as an informal standard, it is questionable how accurate the Colebrook equation is, or how reliable data from Nikuradse's experiment are knowing that his data were measured on very rough pipes, compared to modern materials and that they are a little old, and there is also the controversy with unreported corrections he made to the data [56][57][58][59][60][61][62]. In the final instance, the only valuable comparison can come through real measurements, which are relatively rare [63,64].…”