2020/2021

2020/2021

DM270

ICAR/01 (HYDRAULICS)

DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE

ENVIRONMENTAL ENGINEERING

PERCORSO COMUNE

1°

1st semester (28/09/2020 - 22/01/2021)

6

48 lesson hours

Italian

WRITTEN AND ORAL TEST

MANENTI SAURO (titolare) - 6 ECTS

Basics of vector and tensor algebra.
Mathematical foundations.
Integral theorems (Stokes and Gauss).

At the end of the Course, the student will acquire the fundamental theoretical concepts and mathematical tools for the computer analysis of relevant problems in the hydraulic engineering field, such as: free surface water waves, filtration flows in porous media, viscous flows.

Review of mathematical foundations: vector, tensor and matrix algebra; coordinate systems; Stokes theorem and Gauss theorem.
The continuum concept.
Analysis of stress: Cauchy stress principle; stress tensor; principal stress; deviator and spherical stress tensors.
Deformation and strain: Lagrangian and Eulerian description; small deformation theory; strain tensor; principal strains; spherical and deviator strain tensors; plane strain; compatibility equations; velocity gradient tensor; rate of deformation tensor; vorticity tensor.
Fundamental laws of continuum mechanics: mass conservation - continuity equation; Reynolds transport theorem; linear momentum conservation - Cauchy equation of motion; angular momentum conservation; energy conservation.
Constitutive equations: Newtonian fluid.
Navier-Stokes equations; special cases: perfect fluid; Euler and Bernoulli equations; Kelvin theorem. Global momentum equation. Filtration flows in porous media. Analogy with heat conduction in solids.
Common non-Newtonian rheological models. Experimental measure of viscosity. Viscous fluid dampers for vibration control.
Small amplitude wave theory: definitions; solution of the linearized boundary value problem (BVP); dispersion equation; relative depth conditions; water particle kinematics and trajectories; pressure field; energy of the wave field; wave propagation on cylindrical bathymetry; mild slope conditions; shoaling and refraction. Outline of spectral wave models and applications.

Lectures on: basics of Continuum Mechanics, development of balance equations, constitutive equations and Navier-Stokes equations.
Practical classes on: solution through computer programs of Navier-Stokes equations for practical problems in the field of Fluid Mechanics; experimental measurement of fluid viscosity.

Aris R. "Vectors, tensors, and the basic equations of fluid mechanics" 1990 Dover pub ISBN-10: 0486661105.
Chou P.C. & Pagano N.J. "Elasticity, tensor, dyadic, and engineering approaches" 1992 Dover pub ISBN-13: 978-0486669588.
Citrini D., Noseda D. "Idraulica" CEA, Milano 1987
Dean R.G. & Darlymple R.A. "Water wave mechanics for engineers and scientists" 1991 World Scientific ISBN: 978-981-02-0421-1.
De Girolamo P., Franco L., Noli A. "Fondamenti di oceanografia e idraulica marittima per ingegneri", dispense del corso (in Italian).
Ghetti A. "Idraulica" Libreria int. Cortina - Padova 2004.
Prager W. "Introduction to mechanics of continua" Ginn and Co. 1961
Wilkinson W.L. "Non-Newtonian fluids" 1960 Pergamon Press.
Young I.R. "Wind Generated Ocean Waves" Volume 2, 1st Edition. Elsevier 1999 - ISBN: 9780080433172

Oral exam on problems proposed during practical classes, with discussion of related theoretical aspects.

Lecture notes can be downloaded from the course page on the platform KIRO (https://elearning2.unipv.it/ingegneria/)