Hydraulics

The course aims to provide students with the fundamental knowledge required to address engineering problems involving fluids at rest and/or in motion. In particular, the course covers the design and verification of reservoirs, pressurized pipelines, and natural and artificial open-channel systems.

This knowledge will enable students to approach topics related to the management of hydraulic systems, hydraulic risk mitigation, and electricity generation from renewable energy sources.

The acquired knowledge will be applicable to the design and management of products and systems aimed at improving quality of life, in accordance with Goals 2, 3, 6, 7, 8, 9, 11, 12, 13, 14, and 15 of the 2030 Agenda.

Knowledge and Understanding

Students will learn the properties of fluids and understand the principles of hydrostatics, the fundamental equations governing ideal fluid dynamics, and the physical laws governing the motion of real fluids, together with their respective fields of applicability. They will also understand the operation of hydraulic machines and the physics of open-channel flows.

Applying Knowledge and Understanding

Through practical exercises, students will learn how to determine pressure distributions and hydrostatic forces, and how to apply the fundamental equations of ideal and real fluid dynamics. They will also be able to address simple design and verification problems involving pumping and hydropower systems. For open-channel flows, students will be able to determine critical depth and normal depth, and to draw and interpret gradually varied flow profiles under steady-flow conditions.

Making Judgements

Students will be able to identify the most appropriate calculation schemes and governing equations for the hydraulic problem under consideration and justify the assumptions adopted. They will critically evaluate results by checking the consistency of pressures, flow rates, and energy heads with the physical and operating conditions of the hydraulic system considered. They will be able to distinguish situations in which the ideal fluid assumption is appropriate from those requiring consideration of head losses. In the study of open-channel flows, they will be able to identify the flow regime and determine the boundary conditions required for profile computation.

Communication Skills

Students will be able to describe hydraulic phenomena and illustrate calculation procedures using appropriate technical language. The graphical and written responses required in the written examinations will help students develop and demonstrate their ability to clearly represent hydraulic schemes and flow profiles, explicitly state assumptions and calculation steps, and interpret the results obtained. Any oral examination will also provide an opportunity to demonstrate the ability to explain theoretical concepts and justify proposed solutions.

Learning Skills

Students will develop an independent study method based on the critical use of textbooks and teaching materials, on making connections between theory and applications, and on the ability to identify calculation errors. These skills will provide the foundation for further study in subsequent courses and for the continuous updating of professional competencies.

The course combines theoretical lectures and numerical applications to promote a gradual understanding of the topics and active student participation. The following activities are planned:

• Lectures conducted in a participatory format to maximize student engagement and facilitate the development of course content;
• Guided classroom exercises aimed at the numerical application of concepts and of the analytical and modelling methods most commonly used in hydraulics;
• Midterm assessments designed to evaluate students' understanding of course content and the development of competencies throughout the semester;
• A visit to the DICAr Hydraulics Laboratory, focusing on physical modelling methodologies and on comparing theoretical schematizations with observable phenomena;
• Technical visits to construction sites, operating agencies, and other organizations involved in hydraulic engineering works, subject to organizational feasibility during the semester.

Should it become necessary to conduct activities in blended or remote mode, methods and tools will be adapted while maintaining the learning objectives and course content.

Students with specific needs or with a status officially recognized by the University may agree with the instructor on support measures and a personalized learning pathway, in accordance with applicable University regulations.

Attendance is strongly recommended. Participation in lectures and exercises promotes gradual learning, discussion of solution procedures, and verification of understanding.

• • Introduction to the course
  • Fluids and their properties
  • Fluid statics
  • Fluid kinematics
  • Fundamental equations of hydraulics
  • Bernoulli's theorem
  • Equations governing the motion of real fluids
  • Pressurized flows
  • Practical problems involving long pipelines and systems with pumps and turbines
  • Open-channel flows: uniform flow, critical flow conditions, and steady flow
  • Drawing and interpretation of steady-flow profiles

1. M. Mossa, A.F. Petrillo: “Idraulica”, CEA Milano, 2024.
2. D. Citrini, D. Noseda: “Idraulica”, CEA-Milano, 1987 .
3. G. Alfonsi, E. Orsi: “Problemi di Idraulica e Meccanica dei Fluidi”, CEA Milano, 1984.

Assessment Methods

Learning is assessed through either three optional midterm tests or a single final written examination. Each assessment typically lasts two hours. Students who successfully pass the midterm examinations may choose to have the resulting grade officially recorded. The oral examination is optional and may be taken at the student's discretion.

The assessments verify understanding of the principles and the ability to apply them to proposed problems. The clarity of graphical representations and any oral presentation contributes to the evaluation of communication skills. Connections between topics and the application of methods to problems with data different from those encountered in worked examples provide evidence of students' ability for independent learning.

Registration for examinations is carried out through the University online portal. Examination sessions are scheduled in accordance with University Academic Regulations: two examination dates for each of the three examination sessions, one examination date during each of the two teaching breaks, and two examination dates reserved for students repeating the course and/or belonging to the categories specified in Article 30 of the University Academic Regulations.

During periods permitted by the academic calendar, and in addition to regular office hours, students may arrange further meetings for clarification by contacting the instructor via e-mail.

Midterm tests

The three midterm examinations follow the progression of the course syllabus and are normally held during the teaching period. Their content is approximately as follows:

• First test: hydrostatics, pressure distribution, and forces acting on plane and curved surfaces.
• Second test: motion of ideal and real fluids, applications of Bernoulli's theorem, evaluation of dynamic forces, and analysis of hydraulic systems with pumps and turbines.
• Third test: open-channel flows, uniform flow, critical flow conditions, and drawing of steady-flow profiles.

All questions require open-ended answers. Each test is graded on a scale of 30 points. Students may take all tests regardless of their performance in previous ones. The overall grade is the average of the three scores; an average grade of at least 18/30 constitutes a passing mark.

The validity of the midterm assessment results extends throughout the relevant academic year.

Students achieving an overall grade higher than 15/30 in the midterm examinations may choose to take an oral examination, even if they have already obtained a passing grade. The oral examination is held during the official examination sessions (see Final Written Examination), for which students must register in any case in order to record the final grade.

Final Written Examination

As an alternative to the midterm examinations, students may sit a single two-hour written examination. The examination assesses the same competencies and covers all the topics listed for the midterm examinations.

The results of the written examination are communicated within one week; a grade of at least 18/30 constitutes a passing mark.

Students achieving a grade higher than 15/30 in the written examination may choose to take an oral examination, even if they have already obtained a passing grade. The interview takes place within one week of the written examination and explores all course topics, including applications to pressurized flows, hydraulic machinery systems, and open-channel flows. The oral examination is intended to assess mastery of the subject matter, connections among topics, reasoning ability, and proper use of technical language. In this case, the final grade also takes into account the outcome of the oral examination.

Criteria for Evaluating Written Examinations

Each written examination consists of 10 questions requiring numerical and graphical answers. Up to 3 points are assigned to each answer:

• 3 points for a correct solution;
• 2 points for minor calculation errors;
• 1 point for moderately significant theoretical errors;
• 0 points for an incorrect answer.

The total score is expressed on a scale of 30 points.

Criteria for Awarding the Final Grade

The following ranges describe the level of preparation associated with each grade. For written examinations, the scoring system described above applies; in the optional oral examination, clarity of presentation, independence of reasoning, and ability to establish connections among topics are also considered.

During the periods permitted by the academic calendar, in addition to scheduled weekly office hours, students may arrange further meetings to seek clarification by contacting the professor via email.

Assessments may also be conducted online, should circumstances require it.

• Determine the pressure distribution in a fluid at rest and represent it graphically.
• Calculate the resultant hydrostatic force acting on a plane or curved surface.
• Apply Bernoulli's theorem, specifying assumptions and the meaning of each term.
• Determine the dynamic force exerted by a flow.
• Draw and interpret the hydraulic grade line and the energy grade line.
• Evaluate head losses along a pipeline.
• Calculate the power required by a pump or delivered by a turbine.
• Determine the critical depth and normal depth in a channel.
• Identify the flow regime in an open-channel flow.
• Draw and interpret gradually varied flow profiles under steady-flow conditions, specifying the relevant boundary conditions.