# HYDRAULICS

## Learning outcomes of the course unit

Knowledge and understanding:

During the course the student will acquire the fundamentals of Fluids Mechanics and will develop the ability of understanding and analyzing critically the physical reason of various phenomena involving fluids in motion or at rest in natural or artificial systems. The investigation method is based on mathematical modeling.

Applying knowledge and understanding

The student will gain ability of applying the fundamentals of Hydraulics to basic problems typical of Civil and Environmental Engineering.

Making judgments:

The student will acquire the basic tools and will develop a critical capacity useful to deal in an independent way with simple problems of Hydraulics.

Communication skills:

At the end of the course, the student will be able to present the concepts learned with an adequate fluency and a good speaking ability.

Learning ability:

At the end of the course, the student will have strengthened basic knowledge and competences about the topic of Hydraulics that later will allow him to extend the theoretical and technical knowledge useful to design and verify simple hydraulic structures.

## Prerequisites

It is useful to have attended the courses of Mathematical analysis, Geometry, Physics, and Pure mechanics.

## Course contents summary

Fluid properties. The concept of fluid. The fluid as a continuum. Mass density, compressibility, vapour pressure, viscosity, surface tension. The stress state and the Cauchy theorem.

Fluid statics. Pressure distribution in a fluid at rest. Statics of incompressible and compressible fluids. Manometry. Hydrostatic forces on plane and curves surfaces. Buoyancy and stability. Rigid-body motion.

Fluid kinematics. Lagrangian and Eulerian description of a velocity field. The total derivative. Kinematic analysis of the fluid motion. Flow patterns: pathlines, streamlines and streaklines. The Reynolds transport theorem.

Fundamental of fluid dynamics. Integral and differential analysis. Basic physical laws: the mass conservation equation, the linear momentum equation, the angular momentum equation, the energy equation. Examples: reservoir emptying, computation of dynamic forces.

Frictionless flow. The ideal fluid model. The Euler equation. The Bernoulli theorem and energetic sense. Example: the Pitot-static tube. Flow through orifices; weirs. Power of a flow. Extension of the Bernoulli theorem to a flow. The Venturi meter.

Viscous flow. The viscous fluid model. The Navier-Stokes equations. Analytical solutions of the Navier-Stokes equations: the Couette flow between fixed and moving plates, the Hagen-Poiseuille flow.

Pipe flow. Laminar and turbulent regimes. Equations of motion. Continuous and minor losses. Resistance laws. Energy exchange between fluid and hydraulic machinery: pumps and turbines. Systems of ducts. Verification and project problems.

Open-channel flow. Uniform flow: the Chèzy formula. Specific energy. The critical state. Subcritical and supercritical flows. Steady gradually varied flow equations in prismatic channel. Hydraulic jump. Plotting longitudinal profiles: examples.

Numerical exercises strengthen the competence about the fundamentals of Fluid Mechanics and allow to acquire the ability of quantifying the physical characteristics of a phenomenon.

## Recommended readings

Recommended books

Mossa M., Petrillo A.F. (2013) Idraulica, CEA, Milano. Citrini D., Noseda G. (1987). Idraulica, CEA, Milano. (Available at the Library of Engineering and Architecture – 4 copies, 3 for loan)

Cengel Y.A., Cimbala J.M. (2007). Meccanica dei fluidi, McGraw-Hill, Milano. (Available at the Library of Engineering and Architecture – 2 copies, 1 for loan)

Additional books

Marchi E., Rubatta A. (1981). Meccanica dei fluidi, UTET, Torino. (Available at the Library of Engineering and Architecture – 2 copies, 1 for loan)

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

Ghetti A. (1980), Idraulica, Libreria internazionale Cortina, Padova. (Available at the Library of Engineering and Architecture – 3 copies, 2 for loan)

Books of exercises

Alfonsi G., Orsi E. (1984). Problemi di Idraulica e Meccanica dei fluidi, CEA, Milano. (Available at the Library of Engineering and Architecture – 2 copies, 1 for loan)

Longo S., Tanda M.G. (2009). Esercizi di Idraulica e di Meccanica dei fluidi, Springer, Milano. (Available at the Library of Engineering and Architecture – 2 copies, 1 for loan)

Lecture slides and additional educational material (downloadable from the webpage of the course on the University web site Elly)

## Teaching methods

The course is structured in frontal lessons on the blackboard (with projection of slides, if need) in order to explain theoretical aspects and complementary subjects. During the practice exercises, numerical problems are solved. Usually a technical visit to an engineering structure is organized in order to provide a direct awareness of the practical importance of the matter.

## Assessment methods and criteria

The exam consists of an written part followed by an oral part. To gain access to the oral exam, it is necessary to pass the written test. The two parts of the examination must be passed successfully in the same exam session.

Evaluation criteria:

Written examination 50% including:

- Resolution of no.3 exercises (knowledge/proficiency)

Oral examination 50% including:

- Theory questions (knowledge)

- Applications of theory and exercises (proficiency/making judgments)

- Speaking ability (communication skills)

## Other informations

Attending lectures is strongly suggested.