Estimation of the Velocity Distribution in Circular Pipe with Velocity Measurement at Two Points Using the Renyi Entropy

In most practical hydraulic engineering problems, accurate flow measurements are required. Understanding flow quantities is an important point in water resources management. Therefore, providing the most appropriate velocity distribution estimation relation that is consistent with the measurement data has always been of interest to researchers. With the development of entropy theory, these methods have been used in a wide range of engineering sciences, including hydraulics and fluid mechanics. In the present study, using the Renyi entropy method, the effective parameter "m" on the Renyi entropy parameter "G" was investigated and the velocity distribution in a circular pipe in the conditions that 36.2, 50, and 70% of the circular pipe fills. It was estimated at two points by measuring the velocity at depths (0.1D-0.9D), (0.2D-0.8D), and (0.3D-0.7D) relative to the water level. In order to determine the accuracy of estimating the velocity distribution using the Renyi method, the correlation coefficient and the root mean square error was used and also to determine the accuracy of entropy parameters, normalized root mean square error was used. The results showed that the Renyi entropy method has high accuracy with observational data. Also, velocity measurement at depth (0.9D-0.1D) from the water surface for 36.2, 50, and 70% of the circular pipe, with the normalized root mean square error to 0.2325, 2.36, and 0.51 respectively, has higher accuracy.