## Learning objectives

Knowledge and understanding:

During the course the student will learn the fundamentals of fluid mechanics and will develop the ability to understand and critically analyze the physical reason of phenomena concerning fluids at rest or in motion in natural or artificial systems. The method of investigation is that of mathematical modeling.

Skills:

The student will develop the ability to apply the basic notions of Hydraulics to elementary problems typical of civil and environmental engineering.

Autonomy of judgment:

The student will acquire the basic tools and develop a critical skills useful for analyzing and dealing with autonomous elementary problems of Hydraulics.

Communication skills:

At the end of the course the student will be able to expose the acquired knowledge with adequate mastery and good language skills.

Learning ability:

At the end of the course the student will have consolidated knowledge and basic skills in the field of hydraulic matter that will allow him to deepen later the theoretical and technical knowledge useful for the design and verification of simple hydraulic engineering works.

## Prerequisites

It is useful to have previously attended the courses of Mathematical Analysis, Geometry, General Physics and Rational Mechanics.

## Course unit content

Introduction to hydraulics, Fluid statics, Fluid kinematics, Fluid dynamics, Dimensional analysis and similitude, Pressure currents, Free surface currents.

Detailed program of lessons available on Elly.

During the course will be carried out numerical exercises aimed at consolidating the mastery of the fundamental principles of the subject and to acquire the ability to quantify the characteristics of a problem.

## Full programme

Chapter 1. Introduction to hydraulics

Lesson No 1: 1.1 General information on fluids, 1.2 The concept of fluid as continuous, 1.3 Dimensions, units of measurement and fundamental and derived quantities

Lesson No 2: 1.4 Tensions in a fluid, 1.4.1 The Cauchy tetrahedron theorem, 1.4.2 Considerations on the Cauchy tetrahedron theorem, 1.4.3 Rotation of the Cauchy tetrahedron, 1.4.4 Corollary of the tetrahedron theorem of Cauchy for isotropic system.

Lesson No 3: 1.5 Compressibility, density and thermal expansion, 1.6 Surface tension, 1.7 Viscosity, 1.8 Other fluid properties.

Chapter 2. Fluid statics

Lesson No 4: 2.1 Undefined equation of the fluid statics, 2.2 Global equation of the fluid statics.

Lesson No 5: 2.3 Stevino's Law and Pressure Considerations, 2.4 On Pressure Distribution.

Lesson No 6: 2.6 Pushes on flat surfaces, 2.7 Pushes on curved surfaces, 2.8 Floating, 2.9 Hydrostatic paradox.

Lesson No 7: 2.10 Measurement of pressure, 2.11 Small specific gravity fluids (outline), 2.12 Mariotte's formula, 2.12 Relative balance (outline)

Chapter 3. Fluid kinematics

Lesson No 8: 3.1 Motion patterns, 3.2 Speed and acceleration.

Lesson No 9: 3.3 The visualization of a field of motion, 3.4 Flow tubes, 3.5 Types of motion, 3.6 Comparison of regimes and types of motion.

Lesson No 10: Appendix C. Reynolds transport theorem and handouts, 3.9 Undefined continuity equation, 3.10 Global continuity equation for fixed control volumes in space, 3.11 Continuity equation applied to currents.

Chapter 4. Fluid dynamics

Lesson No 11: 4.1 Undefined equation of motion, 4.2 Stokes viscosity law (overview), 4.3 Euler and Navier Stokes equation.

Lesson No 12: 4.4 Typical flow conditions, 4.5 Global equation of the dynamic equilibrium, 4.6 Coefficient of the quantity of momentum.

Lesson no 13: 4.7 Bernoulli's theorem, 4.8 Pressure distribution and gradually varied currents, 4.9 Geometric and energetic significance of the Bernoulli theorem.

Lesson no 14: 4.11 Outflow processes, 4.12 Other applications of the Bernoulli theorem, 4.14 Extension to the currents of the Bernoulli theorem and power of a current, 4.15 Some applications of the extensions of the Bernoulli theorem to the various motions and currents (Venturimeter), 4.16 Extension to real fluids.

Lesson no 15: 4.17 Energy exchange between a current and a machine, 4.18 Applications.

Chapter 5. Dimensional analysis and similarity

Lesson No 16: 5.1 The principle of dimensional homogeneity, 5.2 Some classical engineering equations (overview), 5.3 Theorem Π (definition), 5.4 Typical index numbers in hydraulics (overview), 5.5 Dimensional analysis in physical modeling (outline), 5.6 Similarity and self-similarity (outline).Chapter 6. Pressurized currents

Lesson no 17: 6.2 Dragging action of a current, 6.3 Resistance index, 6.4 Analysis of laminar motion in cylindrical ducts with various sections (circular ducts and parallel flat plates only).

Lesson No 18: 6.5 Index of resistance in laminar motion (circular and general flow), 6.6 Overview of turbulence, 6.9 Medium turbulent motion in a circular section duct, 6.11 Turbulent viscosity and mixing length.

Lesson No 19: 6.13 Composite nature of the turbulent boundary layer, 6.14 Average velocity distributions in incompressible fluids on smooth surfaces (viscous substrate, fully turbulent region of the inner region, transition zone (buffer layer) of the inner region, external region), 6.15 Average velocity distributions in incompressible turbulent flows on rough surfaces with zero pressure gradient, The roughness, 6.16 Average velocity distributions in incompressible turbulent flows in smooth circular cylindrical ducts, 6.17 Average velocity distributions in incompressible turbulent flows in rough circular cylindrical ducts ( Absolutely turbulent motorcycles, turbulent motorcycles in transition).

Lesson No 20: 6.19 Laws of resistance in ducts in the presence of turbulent motion. Case of circular ducts, 6.20 Practical formulas, 6.24 Localized leakages.

Lesson No 21: 6.25 Problems of long pipelines, Verification of a laminar pipeline, Serial and parallel pipelines, 6.26 Pipeline with constant diameter with uniform delivery along the path.

Lesson No 22: 6.27 Duct with a lifting system, 6.29 Possible elevation traces of the pipelines, How to highlight the relative piezometric line and the absolute piezometric line

Relative hydrostatic loads line, in which a part of the pipeline is above the relative piezometric line, in which a portion of the pipeline is above the relative piezometric line and at the maximum point a free vent is installed, Vents and drains, a case where a section of the pipeline is above the relative piezometric line and the line of relative hydrostatic loads

A case where a section of the pipeline is above the relative piezometric line and the relative hydrostatic load line and a vent must be installed at the maximum point, in which case a section of the pipeline exceeds a value greater than the patm / the line joining the piezometric values of the upstream and downstream nodes, in which a section of the pipeline exceeds by a value greater than patm / the line joining the piezometric values of the upstream and downstream nodes and the line of hydrostatic loads relative, a case in which a section of the pipeline exceeds by a value greater than patm / the line joining the piezometric measurements of the upstream and downstream nodes and at the maximum of that same section of the pipeline there is a vent that exceeds the line of relative hydrostatic loads, in which case a part of the pipeline exceeds the line of absolute hydrostatic loads, 6.30 Closed networks.

Chapter 8. Free surface currents

Lesson No 23: 8.1 Classification of free-surface motions, 8.2 Classification of motions in the channels, Some early reflections on the varied motion in the channels, 8.3 Laws of resistance for the channels and case of uniform motion.

Lesson No 24: 8.5 Specific energy assessed with respect to the bottom of the canal section, 8.6 Weak and steep slopes. 8.7 Kinematic character of a current: surface wave velocity.

Lesson No 25: 8.8 Gradually changed motion, 8.9 Tracing of current profiles gradually changed, Rules for the qualitative tracking of current profiles gradually changed.

Lesson No 26: 8.10 Hydraulic survey, Concept and calculation of total thrust, Reduction of bottom slope of a riverbed from i> ic to i <ic, 8.11 Permanent motion profile tracking for integration

Numerical. 8.12 Application examples, Passage through a flat bulkhead, Change of roughness.

Lesson No 27: Passage of a current on a bottom threshold, Passage between the stacks of a bridge.

## Bibliography

Recommended texts

Mossa, Petrillo, Hydraulics, CEI, 2013

(available at the Library of Engineering and Architecture - 2 copies of which 1 admitted to the loan)

Citrini D., Noseda G. (1987). Hydraulics, CEA, Milan. (Available at the Library of Engineering and Architecture - 4 copies of which 3 are admitted to the loan)

In-depth texts

Marchi E., Rubatta A. (1981). Fluid mechanics, UTET, Turin. (Available at the Library of Engineering and Architecture - 2 copies of which 1 admitted to the loan)

White F.M. (1999). Fluid mechanics, McGraw-Hill, Singapore. (Available at the Library of Engineering and Architecture - 4 copies of which 2 are admitted to the loan)

Ghetti A. (1980), Hydraulics, Cortina International Library, Padua. (Available at the Library of Engineering and Architecture - 3 copies of which 2 are admitted to the loan)

Texts for exercises

Alfonsi G., Orsi E. (1984). Problems of Hydraulics and Fluid Mechanics, CEA, Milan. (Available at the Library of Engineering and Architecture - 2 copies of which 1 admitted to the loan)

Longo S., Tanda M.G. (2009). Exercises of Hydraulics and Fluid Mechanics, Springer, Milan. (Available at the Library of Engineering and Architecture - 2 copies of which 1 admitted to the loan)

Further teaching material

downloadable from the web page of the course on the Elly portal

## Teaching methods

The course is mainly divided into lectures with tablet video projection. During the exercises, problems of applicative interest are dealt with numerically. There are two visits to the Hydraulics laboratory.

The blended course is forecast, with videorecording of the lessons and with video files made available to the students.

## Assessment methods and criteria

The exam consists of a written test followed by an oral exam. Passing the written test is a necessary condition for access to the interview. The two tests must be held in the same exam session.

Alternatively: 3 written tests during the year, with the passing of at least 2 tests. The oral exam must be passed by the autumn session.

Evaluation criteria:

Written test 50% including:

- Resolution of 3 exercises (knowledge / competence)

Oral verification 50% including:

- Theoretical questions (knowledge)

- Applications of theory / exercises (competence / autonomy of judgment)

- Exposure properties (communication skills).

The vote is in thirtieths.

## Other information

The blended course is forecast, with videorecording of the lessons and with video files made available to the students.