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Academic year
Didactic period
Secondo Semestre

Training objectives

The module represents the connection between the basic fluid mechanics and Hydraulic Engineering, addressing the study of the hydraulics currents. It also deals with some typical technical problems, albeit with an essentially basic approach.
The main objective of this module is to apply the mechanical concepts (ability to manage mass, momentum, energy balances), acquired in the fluid mechanics module, to hydraulic problems of technical interest, mainly the hydraulics of currents, as well as the main cases of groundwater flows. A good ability in computing simple pipe networks and free surface profiles in open channels (including the presence of localized obstacles) is also considered a fundamental objective of the module.
The main knowledge that should be acquired are:
• Fundamental equations governing steady and unsteady flow in pipe networks.
• Fundamental equations governing uniform, steady and unsteady flow in open channels.
• Essential basis of groundwater flows.
• Computing methods for pipe networks and open channels (uniform, steady and unsteady flows).
The main skills (i.e. the ability to apply the knowledge acquired) that should be gained are:
• Evaluate the flow resistance in internal flows, both laminar and turbulent, with particular regard to the latter.
• Designing and verifying simple pipe networks in steady and unsteady flow.
• Designing and verifying open channels in uniform and steady flow.
• Correctly set unsteady flow problems in open channels.


The fundamental importance of a thorough attention to this aspect is emphasized.
As regards the mastery of the necessary physical-mathematical tools, please refer to what is reported in the Fluid Mechanics module syllabus. Learning the Applied Hydraulics module requires mastering the concepts and applications of the Fluid Mechanics module. Taking the exams in the MF-IA order is highly recommended.

Course programme

Le tematiche affrontate nel modulo sono le seguenti.
The module includes 60 hours of teaching, which consist of 52 hours of theoretical lessons and application and / or numerical examples, as well as 8 hours of support for carrying out exercises, strictly similar to those proposed in the exams, with numerical examples and a deep attention to the practical aspects.
The issues addressed in the module are the following.
Buckingham’s Pi theorem. Non dimensional numbers in fluid mechanics. Resistance to flow as a dimensional analysis problem.
Cross-section variations. Localized energy dissipation. Pipes in series and pipes in parallel. Siphons. Pipe networks. Distributed releases of discharge. Practical examples. Pumping and turbine plants.
Continuity and momentum equations. Unsteady uniform flow. Water hammer in elastic ducts. Simplified equations. General solution. Initial and boundary conditions. Fast and slow valve closure. Computation of maximum pressure. Allievi’s equations. Graphical method. The method of Characteristics. Boundary conditions.
Specifica energy and critical depth. Subcritical and supercritical flows. Critical slope. Flow resistance computation. Stage-discharge curves. Compound channels.
Prismatic channels. Free surface profiles. Boundary conditions. Bresse solution. Non prismatic channels. Hydraulic jump and its position. Obstacles, weirs.
Small undulations propagation without resistance. Method of characteristics. Boundary conditions.
Fluid and grains properties. Darcy law. One dimensional seepage in phreatic and artesian aquifers. Phreatic and artesian wells.

Didactic methods

The course is organized as follows:
• lectures on the contents of the course;
• examples aimed at illustrating the practical applications of the concepts imparted;
• support for the development (including numerical calculations) of simulation exercises for the exam tests.

Learning assessment procedures

The objective of the exam is to verify the level of achievement of the previously indicated training objectives. It is highly recommended to take the Applied Hydraulics exam after successfully passing the Fluid Mechanics exam.
The exam consists of a single written test, divided into a practical part lasting two hours and fifteen minutes and a theoretical part lasting forty-five minutes. During the practical part it is possible to consult the notes, provided on the Classroom platform, on the steady flow in open channels, as well as the formulary on the flow resistance in pipes, that will be provided directly by the professor. During the theoretical part no type of material can be consulted.
• The practical part, lasting two hours and fifteen minutes, consists in carrying out two exercises (including numerical calculation), of identical weight in the evaluation, concerning: 1) the hydraulic calculation of steady flow in simple pipe networks; 2) the hydraulic calculation of free surface profiles in wide rectangular channels.
• The theoretical part, lasting forty-five minutes, consists of an open-ended question, which focuses mainly on the topics of the module not addressed in the practical part. In particular, the calculation (formal, i.e. not inclusive of the numerical calculation) of high pressures in water hammer problems, further problems inherent to steady and unsteady free surface flows, seepage flows or other theoretical topics.
• The final evaluation consists of a mark, expressed out of thirty, formulated on the basis of an overall judgment on the three answers (in any case not less than the sum of the three disjoint evaluations, expressed in tenths, of the three answers).
• If the practical part is sufficient but the overall evaluation is insufficient, the candidate can ask to repeat only the theoretical part (single test lasting forty-five minutes).
• The candidate who obtains very good evaluations (higher than 27) can ask to take an integrative oral interview, aimed at a possible improvement of the final evaluation itself.

Reference texts

Reference text: Lecture Notes.
Examples of written tests: Classroom internet site of the course.
In-depth textbooks:
• MARCHI E., RUBATTA A., Meccanica dei fluidi. Principi ed applicazioni idrauliche. UTET, 1981.
• MOSSA M., PETRILLO A. F., Idraulica, CEA, Milano, 2013.
• MONTEFUSCO L., Lezioni di Idraulica. Pitagora Editrice, Bologna, 2005.
• CITRINI D., NOSEDA G., Idraulica. CEA, 1987.
• GHETTI A., Idraulica, Ed. Cortina, Padova, Ultima ediz. .
• LIGGET J.A., CAUGHEY D. A., Fluid Mechanics. An Interactive Text. ASCE Press, Reston, VA, 1998.
• WHITE F. M., Fluid Mechanics, Mc Graw Hill Intern. Student Ed., 1979.
• CENGEL Y.A., CIMBALA J. M., Meccanica dei fluidi, IV edizione, McGraw-Hill Education, Milano, 2020 (italian translation edited by G. Cozzo e C. Santoro).