The shape of a pendant drop is studied by employing free energy minimization. This free energy includes the gravitational potential energy and the interfacial surface energy. We employed the Lagrange multipliers method to minimize free energy while maintaining drop volume as constant. The differential equation for the shape of any pendant drop was established as a function of one dimensionless parameter only. This novel dimensionless parameter is defined as the shape factor. Around the origin of the chosen coordinate axis, an analytical solution to the differential equation was found. For a general solution, a numerical approach was followed to estimate drop shape. Furthermore, we calculated the detached volume from the bulk pendant drop. Comparison of the results with the experimental findings shows good agreements. A new Axisymmetric Drop Shape Analysis method is suggested, which can help users estimate any unknown of the problem if one geometrical data of the drop is known.

This study aims to search for optimum design parameters for a slurry pipeline problem and optimum operation parameters for a multi-reservoir scheduling problem by using Bi-Attempted Base Optimization Algorithm (ABaOA), which has been recently developed as a numerical bidirectional search algorithm. The slurry pipeline problem is a constrained non-linear cost minimization problem with constraints on facility capacities. It has two separate cost terms that behave differently with changes in decision variables. The problem includes several decision variables in addition to the fact that the objective function is highly non-linear. On the other hand, the multi-reservoir problem is a well-known problem in Hydraulics that aims to maximize benefit by optimizing the releases of each reservoir. The problem has a known global optimum, which is used to test the abilities of the ABaOA. The ABaOA is developed from Base Optimization Algorithm (BaOA) by transforming its operators with the aim to diversify the search paths to reach the global optimum. Its applications in hydrosystems show that it converges to the optimum solutions in reasonable times. The results from the first application are compared to the ones obtained from Genetic Algorithms (GA) application. It is observed that ABaOA outperformed GA in terms of speed of convergence and finding a better alternative solution. The ABaOA reaches the global optimum in the second application. In addition, alternatives with better benefit functions, including some penalties have been determined.