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Modern fluid mechanics examines understanding, predicting and directing of fluids in the fluid structures. But new computational methods need to find out the optimal solution of each hydraulic system because of minimization of power losses. Consequently, this article looks through the shape optimization of hydraulic parts using adjoint optimization method. It is most used gradient-based method. This approach enables to calculate the objective function sensitivities in consideration of the design variables (Kyriakos and Papadimitriou, 2008). Many producers talk about the optimized solutions, but only small part from them use all possibilities for finding the best one. It is motivation why in this paper the shape optimization of the hydraulic valve component with respect to minimization of pressure losses is presented.

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We present a simulation tool for transient events in complex hydraulic networks. The code includes modelling of the transport of suspended cuttings in near-vertical wells. An unstructured finite volume formulation with implicit time integration has been chosen. The unconditional stability of the integrator makes the method suitable for the simulation of transient events over a wide range of characteristic timescales. It handles both very fast transients (e.g. fluid hammer events) and the long-term evolution of the well (e.g. hole cleaning operations). The software has been developed to address the need of the oil industry for a robust and efficient predictive tool allowing effective well control in managed pressure drilling operations. The physical modelling follows the standard practices accepted by the industry (e.g. mud rheology computations). The mathematical foundation of the algorithm is described followed by validation cases that illustrate its capabilities and accuracy. Finally, a practical industrial application example is provided to demonstrate the real-world performance of the software.

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An example of hydraulic design project for teaching purpose is presented. Students’ task is to develop a looped distribution network for water (i.e. to determinate node consumptions, disposal of pipes, and finally to calculate flow rates in the network’s pipes and their optimal diameters). This can be accomplished by using the original Hardy Cross method, the improved Hardy Cross method, the node-loop method, etc. For the improved Hardy Cross method and the node-loop method, use of matrix calculation is mandatory. Because the analysis of water distribution networks is an essential component of civil engineering water resources curricula, the adequate technique better than the hand-oriented one is desired in order to increase students’ understanding of this kind of engineering systems and of relevant design issues in more concise and effective way. The described use of spreadsheet solvers is more than suitable for the purpose, especially knowing that spreadsheet solvers are much more matrix friendly compared with the hand-orientated calculation. Although matrix calculation is not mandatory for the original Hardy Cross method, even in that case it is preferred for better understanding of the problem. The application of commonly available spreadsheet software (Microsoft Excel) including two real classroom tasks is presented.

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Current paper focuses on the analysis of radial gated spillways, which are analyzed by the solution of a numerical model. The Oliana Dam study case is considered and the discharge capacity is predicted both by the application of a level-set based free-surface solver and by the use of traditional empirical formulations The results of the analysis are then used in training an Artificial Neural Network so to allow real-time predictions of the discharge in any situation of energy head and gate opening within the operation range of the reservoir. The comparison of the results obtained with the different methods shows that numerical models can be useful as a predictive tool for the analysis of the hydraulic performance of radial-gated spillways, and highlights some drawbacks regarding the application of the empirical formulas.

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The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental functions, such as logarithmic, exponential, non-integer power, Lambert W and WrightΩ functions. Conversely, we herein present several computationally cheap explicit approximations of the Colebrook equation that require only one logarithmic function in the initial stage, whilst for the remaining iterations the cheap Padé approximant of the first order is used instead. Moreover, symbolic regression was used for the development of a novel starting point, which significantly reduces the error of internal iterations compared with the fixed value staring point. Despite the starting point using a simple rational function, it reduces the relative error of the approximation with one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the relative error of the approximation with two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). This error analysis uses a sample with 2 million quasi-Monte Carlo points and the Sobol sequence.