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Second Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/72]  CIVIL ENGINEERING [72/00 - Ord. 2013]  PERCORSO COMUNE 10 100


- Knowledge and understanding of physical processes taking place in a still or moving fluid, with emphasis on steady incompressible flow in pipes or open channels;
- Applying knowledge and understanding to the solution of practical problems related to the design of hydraulic infrastructures and facilities of interest to the civil engineer.
- Acquiring capability of autonomous critical judgement on possible design alternatives;
- Acquiring communication skills related to information, ideas, problems and related solutions;
- Learning skills provided by the physical-mathematical background offered in the course will enable further self-learning in the field of hydraulics..


Knowledge of fundamental concepts and methods of general Physics, Mechanics, Mathematical Analysis, Algebra, and Geometry.
According to the Teaching Rule of the Degree Course, credits for the following (or equivalent) courses must be acquired before the exam of Hydraulics:
- Analisi matematica 1 (Mathematical Analysis 1);
- Geometria e algebra (Geometry and Algebra);
- Fisica 1 (Physics 1)


1. Introduction: Continuum approximation. Definition of fluid. Physical properties of fluids. (3 h)

2. Hydrostatics: Stresses at a point. Local and integral equations of hydrostatics. Homogeneous and incompressible fluids: Stevin law; pressure distribution; water table; relative and absolute pressure; Pascal law. Immiscible stratified fluids. Gases. Manometers. Forces exerted on planar surfaces. Forces exterted on surfaces of any shape: method of integral equation; direct computation of force components. Forces on immersed bodies. Capillarity. (10+9 h)

3. Fluid kinematics: velocity fields and pathlines. Eulerian and Lagrangian approaches; Lagrangian derivative. Local analysis of motion. Classification of flows. Stream lines and streak lines. Fluxes across surfaces; streamtubes. Transport theorem. Local and integral forms of continuity equation. (5 h)

4. Fundamental equations of fluid dynamics: stresses; Cauchy theorem; stress tensor; Local form of the linear momentum equation. Constitutive law of Newtonian flows; Navier-Stokes equation. Integral form of linear momentum equation: general form and form for a viscous fluid. Pressure head distribution in a plane normal to a pathline; Bernoulli theorem; viscous losses; inviscid fluid schematization. Extension to compressible fluids. (6 h)

5. Discharge flows: orifices. Weirs. Transients. (3+3 h)

6. Dimensional analysis: dimensional omogeneity; dimensionless quantities; Pi-theorem. (1 h)

7. Irrotational flows: vorticity, velocity potential. Bernoulli theorem. Incompressible homogeneous flows: Laplace equation; boundary conditions. Two-dimensional potential flows; stream function; flow net; Examples of potential flows: theories of wave motion; flow in porous media. (2 h)

8. Turbulence: laminar flow and turbulent flow; Reynolds number. Statistical analysis of turbulence; equations for averaged quantities; turbulent stresses. (3 h)

9. One-dimensional flows: gradually varied flows: regular cross sections; axial stress approximation; pressure line. Continuity equation. Flow power in a cross section. Bernoulli Theorem: average total head; energy line and pressure line; head losses. Measuring instruments. (4 h)

10. Flow in pipes: uniform flow in circular pipe: velocity profile; logarithmic velocity profile; shear stresses; distributed head losses. Nikuradse diagram and Moody diagram. Roughness. Prandt-Von Karman, Prandtl-Nikuradse and Colebrook formulas. Practical formulas: Chezy formula. Local head losses. Hydraulic analysis of a pipeline. Long pipelines: design and verification methods. Depression flows. Momentum equation for unsteady flows. (11+13 h)

11. Hydraulic machinery: Pumps: total head rise, pressure head rise, geodetic rise, net and gross power inputs. Verification problem: computation of flow rate; cavitation; maximum depression allowed; NPSH; maximum flow rate. Design problem: total costs; maximum benefit diameter. Turbines. (2+4 h)

12. Free surface flows: uniform flow: stage-discharge curves; composite cross sections. Specific head. Critical state. Celerity of small amplitude perturbations. Classification of flows and channels. Steady, non-uniform flow profiles. Perturbing factors and boundary conditions. Control sections. Hydraulic jump: total force. Flow over a bottom rise; section narrowing; intake from a reservoir. Broad crested weir. (12+9 h)

Teaching Methods

Duration: 10 weeks, 10 hours per week; total 100 hours
Theory: 62 hours; practice exercise: 38 hours.

Because of the current emrgency related to COVID-19 pandemy, until new directives are issued classes are to be held in a mixed mode, i.e. both in presence and online. However, dealing with a course to be tought in the second semester, in the following the normal, in presence, teaching mode is presented as well, for the case that the present emergency is overcome by the start of the course.
After exercitation classes, students are given homework on the same subjects, which can be solved as group work, about the solution of practical problems. The related results are sent to the teacher anonymously via a Google form and then discussed in the classroom. Both classroom and homework exercises are further explained and discussed during tutoring activities.
lectures and exercitations are developed making in the form of Power Point presentations, integrated with instant notes by the teacher, either on the Power Point slides or on electronic chalkboard, for better explaination of concepts or on request of clarifications by the students
During the course, students are subjected to two intermediate tests on the solution of practical problems. After passing the tests successfully, students are enabled to complete the exam passing the oral examination, provided this latter is given during the summer session following the end of the course
Depending on the classroom available, lectures and exercitations are developed at the chalkboard, using colored chalks/pens for graphical schemes, or on electronic chalkboard.

Verification of learning

The assessment is expressed in a scale in the range 0 to 30, with 18 being a minimum for positive outcome.
Until the current emergency related to COVID-19 pandemy is overcome, exams are held in oral, online form only. However, dealing with a course to be tought in the second semester, in the following the normal, in presence, procedure for exams is presented as well, for the case that the present emergency is overcome by the end of the course.
Verifiable abilities required to successfully pass the exam: addressing and solving practical problems about still fluids (pressure distribution, forces on surfaces), steady incompressible flows in pipes (design and verification calculations; dynamic forces; pressure and flow rate measurement) and in open channels (normal depth and flow rate calculations; flow rate measurement; calculation of steady free surface profiles). Ascertaining the abilities above implies knowledge and understanding of underlaying physical processes, critical reasoning in the analysis of problems at hand and autonomous judgement when choosing between design alternatives. Communication skills both in written and oral forms are appreciated during the corresponding parts of the exam. Self-learning skills are best ascertained in the oral examination on assessment of theoretical concepts.
In oral online exams a practical problem is proposed to the student for solution in qualitative form, followed by two questions on theoretical concepts. Solution in qualitative form is meant to be as detailed presentation of the correct methods of solution of the problem, with omission of numerical calculations only. The student is assigned a score in the range 0 to 30 based on: i) ) correctness in analyzing and addressing solutions for the proposed problem; ii) mastery of theoretical concepts; iii) critical reasoning, awareness of relations between different topics and related synthesis skills; iv) use of proper terminology
Normally, the exam develops as follows:
- a written task consisting in numerical solution of three practical problems (essentially on statics of fluids, pressurized flows and free surface flows). The student is assigned a score in the range 0 to 30. Assessment is based on: i) completeness of answers to the proposed queries; ii) correctness in analyzing problems and addressing solutions; iii) correctness of computations; iv) clarity of presentation of the methods of solution. Textbooks and handbooks can be referenced; but not collections of exercises;
- an oral examination, provided a minimum assessment of 18/30 was achieved in the written task, dealing with the outcome of the written task and theoretical topics. The student is assigned a score in the range 0 to 30, based on: i) mastery of theoretical concepts; ii) critical reasoning, awareness of relations between different topics and related synthesis skills; iii) use of proper terminology
Final assessment results from the arithmetic average of the scores achieved in the written and oral examinations. Unsuccessful outcome of oral examination implies repeating the written part of the exam as well.
As an exception to the normal procedure, students passing successfully the intermediate classroom tests are asked to pass the oral examination only, provided this latter is given during the summer session following the end of the course (June to September). The score of the intermediate classroom tests is obtained as the arithmetic average of the scores marked in each of the two tests, expressed in the range 0 to 30. The resulting score concurs to the final assessment as for the written task in the normal procedure.


Main reference: Lecture notes (in Italian);

Suggested for further study:
- Idraulica (Citrini-Noseda)
- Meccanica dei Fluidi (Marchi-Rubatta);
- Idraulica (Mossa - Petrillo);
- Meccanica dei Fluidi (Çengel-Cimbala);
- Meccanica dei Fluidi (Cenedese);
- Dispense di Idraulica (Fassò).

- Practical class (download http://people.unica.it/andreabalzano/didatticateaching/idraulica-ordinamento-dm270-corso-1/);
- Problemi di Idraulica e Meccanica dei Fluidi (Alfonsi-Orsi);
- Esercizi di Idraulica e di Meccanica dei Fluidi (Longo-Tanda);
- Idraulica (Citrini-Noseda);
- Meccanica dei Fluidi (Çengel-Cimbala);
- Collection of exercise problems (Fassò) (download http://pcque.unica.it/).
- collection of exam problems (download http://people.unica.it/andreabalzano/didatticateaching/idraulica-ordinamento-dm270-corso-1/)
- collection of miscellaneous exercises (download http://people.unica.it/andreabalzano/didatticateaching/idraulica-ordinamento-dm270-corso-1/)

More Information

At the following web address:
the following items can be accessed:
- location of the teacher's office, e-mail address, phone;
- scheduling of tutoring
- scheduling of exams
- detailed course syllabus
- references (lecture notes, practical problems with hint to solution, other practical problems)

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