Fractional entropy-based models of one-dimensional velocity distributions in partially filled and fully filled pipe flows

The entropy concept has been applied for one-dimensional (1D) velocity modeling in partially and fully filled pipe flows. The 1D velocity distribution models for partially and fully filled pipes are derived using fractional entropy by employing the entropy maximization concept and dividing the whole flow depth into two regions. For a partially filled pipe flow, two regions are distinguished using the dip-position whereas, for the fully filled pipe flow, it is decided using the pipe centerline. The entropy approaches have been applied individually in each region to derive the velocity distributions. Finally, using the asymptotic matching method, single velocity distribution laws are proposed which apply to the entire flow depth. Both the proposed velocity models for partially and fully filled pipes are validated with different sets of experimental data and satisfactory results are achieved. Proposed fractional entropy-based velocity models in partially filled and fully filled pipes are compared with the Tsallis wavelet entropy-based velocity distribution model (for partially filled pipes), and Guo and Julien’s modified log-wake law and Guo’s second log-wake law respectively. Comparison results show that the proposed models are comparable with existing models and give better results when quantitatively analyzed. First entropy-based eddy viscosity model is proposed for fully filled pipe flows and compared with experimental data. Results show that the eddy viscosity model produces good agreement with the data (near pipe invert and obvert) except in the core region of the pipe comprising 40% of the radius.