Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2022/2023
Scuola Scuola di Ingegneria Civile, Ambientale e Territoriale
Insegnamento 056795 - HYDRAULICS
Cfu 10.00 Tipo insegnamento Monodisciplinare
Docenti: Titolare (Co-titolari) Messa Gianandrea Vittorio

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing - Civ (1 liv.)(ord. 270) - MI (503) INGEGNERIA CIVILEOAEAZZZZ056795 - HYDRAULICS

Obiettivi dell'insegnamento

Several applications in Civil Engineering involve fluids in static or dynamic conditions. The course provides the theoretical background and some application-oriented skills of Hydraulics and Fluid Mechanics, developed in the framework of continuum mechanics. The course is focused on the mathematical modelling of Hydraulics processes for Civil Engineering, both in a general fashion and referring to simplified case-specific formulations to handle processes of interest for the study program. Particular attention will be given to the 1D modelling of pressurized pipe systems and open channel flows, which requires also exploring the fundamentals of dimensional analysis and the development of empirical laws. The models are critically discussed in the light of their theoretical ground and their engineering effectiveness. Students will be able to solve technical problems related with the design and verification of hydraulic systems in steady-state conditions, and they will briefly explore simple yet relevant unsteady-state processes. More generally, students will know the theoretical basis of Hydraulics and Fluid Mechanics, and they will be able to make qualitative and quantitative judgments regarding different phenomena.

Risultati di apprendimento attesi

Knowledge and ability in understanding:

After passing the exam, students will

  • know the principles, the parameters, and the basic theories of Hydraulics and Fluid Mechanics
  • know the basic approaches for the engineering handling of hydraulic processes
  • understand the basic functioning of a pipeline system
  • understand the basics aspects of open channel flow

Ability in applying knowledge and understanding:

After passing the exam, students will be able to

  • calculate the force exerted by fluids in static conditions on a surface
  • perform the preliminary design and verification of a pipeline system
  • set up and analyze simple open channel flow problems in steady-state conditions

Argomenti trattati
  • Basic concepts of continuum mechanics. Mass forces and surface forces; stress and stresses tensor.
  • Classification of fluid flows. Compressible vs incompressible; laminar vs turbulent; steady vs unsteady; 1D, 2D, 3D.
  • Physical properties of fluids. Density; vapor tension and cavitation; coefficient of compressibility; viscosity and rheology; surface tension and capillary effect.
  • Fluid statics. Basic equation of fluid statics (differential and integral formulations); instruments for measuring pressure; Stevin’s law and its application; calculation of the force produced by a quiescent fluid on flat and curved surfaces.
  • Fluid kinematics. Eulerian and Lagrangian frameworks; material derivative; streamlines and pathlines.
  • The fluid mechanics problem. Fundamental equations in the differential and integral formulations: mass conservation, momentum conservation, equation of state. The need for constitutive models.
  • Inviscid flows. The constitutive model for inviscid flow. The Euler equation in the differential and integral formulations. The Bernoulli equation. 
  • 1D modelling of quasi 1D flows. Quasi 1D flows and their 1D description. Formulations of the mass conservation equation, the Euler equation and the Bernoulli equation for quasi 1D flows. Gradually-varied flow. The Coriolis coefficients.
  • 1D modelling of pressurized pipe flows. Energy balance for pressurized pipe systems. Hydraulic grade line and piezometric line. Major losses: the Darcy-Weisbach equation and the Moody chart. Minor losses: sudden enlargment, diffuser, entrance and exit losses, other pipe fittings. Interaction between pipe flow and hydraulic machinery (pumps and turbines). Notes on water hammer.
  • 1D modelling of open channel flow. Key parameters in the 1D modelling of open channel flow. Specific energy of open channel flow in a cross-section: the critical depth, sub-critical flow and super-critical flow. Specific force of open channel flow in a cross-section. Uniform open channel flow: the Chezy-Strickler equation. Mild slope and steep slope channel flows. Steady-state open channel flow with no lateral inflows/outflows: differential equation of fluid flow in cylindrical channels and reference solutions (M1, M2, M3, S1, S2, S3). Change of slope and roughness. The hydraulic jump. Flow from a reservoir located upstream, and discharge into a reservoir located downstream. Flow over a hump.
  • Discharge through orifices and weirs.


Fundamentals of calculus and continuum mechanics.

Modalità di valutazione

The exam consists of a written test and of an oral colloquium, which must take place in the same call.

The written test, in turn, consists of three exercises, to be solved in a symbolic manner. The first exercise concerns fluid statics, and its goal is to verify the capability of the students in evaluating the pressure distribution in a system of fluids at rest, and calculate the force acting on flat and curved surface. The second exercise concerns the 1D modelling of pressurized pipe flows, pipe flows, and its goal is to verify the capability of the students in modelling pipeline systems, expressing the results both through mathematical formulas and graphically (hydraulic gradient line and piezometric line). The third exercise concerns the 1D modelling of open channel flow, and its goal is to verify the capability of the students in setting up the problem and qualitatively obtaining the possible free surface profiles.

Upon positive evaluation at the written test, students are eligible to undertake the oral examination, which will cover all topics of the course, and it might consist of either open questions of theoretical nature (including derivation) or simple exercise to be solved in a symbolic manner. In relation to specific organizational needs, the students might be asked to answer the questions in written form, and their work will be subject of discussion with the teacher. Goal of the oral examination is verifying that the students know the main principles and models of Hydraulics, and that they are able to apply them to solve relevant technical problems in Civil Engineering. At the same time, it is assessed the capability of the students to explore links between the topics of the course.

Risorsa bibliografica facoltativaB.R. Munson, T.H. Ohiishi, W.W. Huebsch, A.P. Rothmayer, Fundamentals of Fluid Mechanics (7th Edition), Editore: John Wiley and Sons, Anno edizione: 2013, ISBN: 9781118318676
Risorsa bibliografica facoltativaH. Chanson, The hydraulics of open channel flow: An introduction, Editore: Elsevier, Anno edizione: 2004, ISBN: 0750659785
Risorsa bibliografica facoltativaA.W. Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, Editore: CRC Press, Anno edizione: 2021, ISBN: 9870429423116

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Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

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