Advanced Hydraulics is a course aimed at giving a deep knowledge on incompressible fluids motion and on their Mathematical modelling. The course is also aimed at developing the skills necessary to formulate and use basic numerical models for solving the most common mathematical models of applied Hydraulics: the method of characteristics and the finite difference method.

The course belongs to the master of Civil Engineering for the Protection from Natural Hazards, which is aimed at preparing a highly qualified Civil Engineer in the field of the protection of the territory and civil infrastructures from hydrogeological and seismic hazards.
In this framework, the course defines conceptual hydraulic models of increasing complexity, with particular reference to the most common ones: the 1D and 2D hydraulic model.

At the end of the course the student:
1) will own a deep knowledge of Fluid Mechanics;
2) will be able to formulate a model able to simulate a considered phenomenon, starting from the theories dealt during the course;
3) will be able to solve computationally the model using basic numerical methodologies;
4) will be able to interpret critically the results obtained from numerical models.

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Flow kinematics. Deformation. Vorticity. Decomposition of the flow field into a solenoidal and irrotational component. Dynamics. Mass, momentum and energy budget. Dimensionless form of the equations. Low Reynolds motions. Moderate Reynolds motions: boundary layer. High Reynolds motions: instability and transition to turbulence. Turbulence. Ideal flows and their applications. 1D scheme and its application in Hydraulics: pipe and open channel flows. The method of characteristics and finite differences for the integration of the motion equations. Applications to water hammer, dam-break and unsteady open channel flows. The 2D shallow water equations.

Core Documentation

Lecture notes written by the teacher.

Bruce R. Munson, Donald F. Young, Theodore H. Okiishi, “Fundamentals of Fluid Mechanics”, John Wiley & sons;

Yunus A. Cengel, John M. Cimbala, “Fluid Mechanics: Fundamentals and Applications” Mc Graw Hill.

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