Continuum Mechanics

Institution: DICAR (UNIPV)

Major: HYRIS

Term: 1st Semester

Instructor: Sauro Manenti (

CFU: 6


Duration: available here

Schedule: available here

Office hours: Wednesday-Friday 9-13 AM



The course aims at providing the fundamental theoretical concepts and mathematical tools for the analysis of relevant problems in the field of hydraulic engineering. Basic exercises will be discussed in order to implement the relevant concepts of Continuum Mechanics in practical problems.



Review of mathematical foundations: vector and tensor algebra, coordinate systems, Stokes theorem and Gauss theorem.

Analysis of stress: the continuum concept, Cauchy stress principle, stress tensor, principal stress, Mohr circles (introductory notes), 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, angular momentum conservation, energy conservation.

Constitutive equations: Newtonian fluids.

Governing equations of Fluid Mechanics: Navier-Stokes equation. Special cases: perfect fluid; Euler and Bernoulli equations; Laplace equation. Kelvin theorem.

Viscosity of Newtonian fluids: basic concepts; flow curve. Common non-Newtonian rheological models: Bingham, pseudoplastic; dilatant. Experimental measurement of fluid viscosity, principal types of rheometers.

Applications to engineering problems: CFD modeling of annular viscous fluid damper as a passive energy dissipation system.

Numerical solution of the fundamental equations of fluid mechanics and engineering applications: basic concepts and assumptions of Smoothed Particle Hydrodynamics (SPH) method. SPH modeling of landslide generated wave in artificial reservoir.



Basics of vector and tensor algebra.

Foundations of mathematical Physics.



  • Aris R. “Vectors, Tensors, and the Basic Equations of Fluid Mechanics” Dover
  • Chou P.C. & Pagano J. “Elasticity, Tensor, Dyadic, and Engineering Approaches” Dover pub.
  • Kundu P. K., Cohen M., Dowling D. R. “Fluid Mechanics” 6th Ed. 2016 Elsevier A.P.
  • Liu, G-R. and Liu, M.B. “Smoothed Particle Hydrodynamics: a Meshfree Particle Method”. World Scientic, 2003
  • Prager W. “Introduction to Mechanics of Continua” Ginn and Co. 1961
  • Wilkinson W.L. “Non-Newtonian Fluids”. 1960 Pergamon Press.
  • Lecture notes downloadable from



The final examination will consist of an oral discussion on the course’s topics and exercises.