In analysis of flow through rockfill media, due to high velocity and Reynolds number, the flow is transformed to non-Darcy state. In a Darcian flow, due to the linear relationship between velocity and hydraulic gradient, analysis is made more easily. However, by increasing the flow velocity, the regime is diverted from Darcy law and becomes turbulent where its analysis is more complicated. At the present stage, there are no exact criteria to distinguish between Darcy and non-Darcy flow. Since the Manning equation has a wide application in open channel flow, in the present paper the concept of Darcy's friction factor has been combined with Manning's equation and a new form of equation has been obtained for analysis of flow through a rockfill media. In the process of investigation, two sets of laboratory data from the tests conducted on flow through unconfined and confined rockfill media were obtained and the analytical relationships were calibrated accordingly. Based on the analytical solution and laboratory data, for determination of Manning's roughness coefficient (n), new relationships were developed. For this purpose, more than 150 laboratory data from flow through confined and unconfined flumes filled with rockfill materials were used. The results of the investigation have proved the validity of application of the Manning equation in a fully rough flow.

Exponential partial Bell polynomials are a main tool for computing explicit formula for a large family of numbers and polynomials. Using these polynomials, we review most of the polynomials already studied in the book of Djordjevic-Milovanovic (2014). This study allows to unify the writing of these polynomials and obtain other extensions. Consequently the obtained results find their application in Number Theory,notably for the arithmetical properties of power products, Fermat numbers, Mersenne numbers and Fermat Last Theorem.

Curved weirs in plan due to their special hydraulic conditions as well as long crest, have suitable capability in effective water surface regulation in irrigation canals and networks. Also, these weirs have high turbulence intensity in downstream and make better conditions for rivers, in environmental point of view. There are few studies regarding calculation of curved weirs’ discharge coefficient and their head-discharge equation. In this study, using new optimization method of genetic programming, a dimensionless equation for discharge coefficient has been proposed based on two non-dimensional parameters of weir angel and ratio of water head to weir height. For training and testing of the proposed equation, experimental data of Kumar et al, have been used.Comparison of results obtained from this equation with the experimental data reveals high accuracy of the new equation of genetic programming. Mean absolute errors of the proposed equation for discharge coefficient have been calculated as 1.36 and 1.65 percent, for training and testing phases, respectively. This error for non-linear equation of Kumar et al, is nearly 9.4 percent.

In this paper, we give some distance formulas for 3-dimensional maximum space. We study in 3-dimensional analytical space furnishing with maximum metric, and in this space we give distance formulas between a point and a line, a point and a plane and between two lines in terms of maximum metric.