# FLUID MECHANICS

## Learning outcomes of the course unit

Knowledge and understanding:

At the end of this course the student should know the main theoretical and applicative aspects of Fluid Mechanics. Moreover, he should gain understanding of the techniques of analysis of the problems in Fluid Mechanics, paying attention to the differences between models and real behavior of the physical processes.

Applying knowledge and understanding:

The student should be able to describe the physical process by using applied mathematics; to select the parameters and the variables involved in the process; to solve the most common applicative cases checking the results with engineering approach.

Making judgments:

By the end of the course, the student should be able to evaluate the reliability of the simplified models or the need to adopt advanced models.

Communication skills:

The student should be able to clearly present the results of the analysis, in oral or written form, also by means of tables and charts.

Knowledge and understanding:

At the end of this course the student should know the main theoretical and applicative aspects of Fluid Mechanics. Moreover, he should gain understanding of the techniques of analysis of the problems in Fluid Mechanics, paying attention to the differences between models and real behavior of the physical processes.

Applying knowledge and understanding:

The student should be able to describe the physical process by using applied mathematics; to select the parameters and the variables involved in the process; to solve the most common applicative cases checking the results with engineering approach.

Making judgments:

By the end of the course, the student should be able to evaluate the reliability of the simplified models or the need to adopt advanced models.

Communication skills:

The student should be able to clearly present the results of the analysis, in oral or written form, also by means of tables and charts.

## Prerequisites

Differential analysis, Geometry, Rational Mechanics, Physics.

Differential analysis, Geometry, Rational Mechanics, Physics.

## Course contents summary

The course provides the students with the necessary knowledge related with fluid mechanics in the context of classical mechanics. The students shall be able to solve the main technical problems related with the interaction between fluids and structures and with pressurized flow. Numerical exercises about the topics listed in the program will be developed.

The course provides the students with the necessary knowledge related with fluid mechanics in the context of classical mechanics. The students shall be able to solve the main technical problems related with the interaction between fluids and structures and with pressurized flow. Numerical exercises about the topics listed in the program will be developed.

## Course contents

Introduction to vector fields and to differential operators, to tensors. Dimensional analysis. Fluids and fluid behaviour. Definition of fluid as a continuum. Fluid mechanics variables and measurements units. Stresses in a continuum. Density and specific weight. Compressibility. Surface tension. Viscosity. Gas sorption. Vapor pressure of a fluid.

Fluid statics. Internal stresses in fluids at rest. Differential analysis of fluid statics. Finite control volume analysis of fluid statics. Pressure variation of incompressible fluids. Hydrostatic force on plane and curved surfaces. Buoyancy.

Fluid kinematics. Velocity and acceleration fields. Pathlines, streamlines, streaklines. Continuity equation. Flow regimes.

Basic fluid dynamics. Differential and finite control volume analyses of a fluid flow. Euler equation. Gradually varied flow. The Bernoulli equation. Physical and geometrical interpretation. Examples of the use of the Bernoulli equation. Viscous fluids. Extension of the use of the Bernoulli equation to streams. Energy exchanges between fluid and hydraulic machinery. Pumping stations.

Flow of viscous fluids. Moody chart. Navier-Stokes equations. Finite control volume analysis.

Introduction to vector fields and to differential operators, to tensors. Dimensional analysis. Fluids and fluid behaviour. Definition of fluid as a continuum. Fluid mechanics variables and measurements units. Stresses in a continuum. Density and specific weight. Compressibility. Surface tension. Viscosity. Gas sorption. Vapor pressure of a fluid.

Fluid statics. Internal stresses in fluids at rest. Differential analysis of fluid statics. Finite control volume analysis of fluid statics. Pressure variation of incompressible fluids. Hydrostatic force on plane and curved surfaces. Buoyancy.

Fluid kinematics. Velocity and acceleration fields. Pathlines, streamlines, streaklines. Continuity equation. Flow regimes.

Basic fluid dynamics. Differential and finite control volume analyses of a fluid flow. Euler equation. Gradually varied flow. The Bernoulli equation. Physical and geometrical interpretation. Examples of the use of the Bernoulli equation. Viscous fluids. Extension of the use of the Bernoulli equation to streams. Energy exchanges between fluid and hydraulic machinery. Pumping stations.

Flow of viscous fluids. Moody chart. Navier-Stokes equations. Finite control volume analysis.

## Recommended readings

Recommended book:

• Marchi, E., Rubatta, A., 1981. Meccanica dei fluidi, UTET, Torino, pp xvi+800, ISBN 88 02 03659 4

• Citrini, D., Noseda, G., 1982. Idraulica. Casa Ed. Ambrosiana, Milano, pp x +468.

• Longo, S., Tanda, M.G., 2009. Esercizi di Idraulica e di Meccanica dei Fluidi. Springer & Verlag Italia, Collana UNITEXT Ingegneria, ISBN 978-88-470-1347-6, V+386 pp.

• Alfonsi, G., Orsi, E., 1984. Problemi di Idraulica e Meccanica dei fluidi. Casa Ed. Ambrosiana, Milano, pp 507, ISBN 88 408 0735 7

Reference books:

• Longo, S., 2011, Analisi Dimensionale e Modellistica Fisica – Principi e Applicazioni alle Scienze Ingegneristiche. Springer & Verlag Italia, Collana UNITEXT Ingegneria, ISBN 978-88-470-1871-6, X+370 pp.

• Çengel, Y. A., Cimbala, J. M., 2007. Meccanica dei fluidi. McGraw-Hill, ISBN: 9788838663840 (also available in english)

• Ghetti, A., 1996. Idraulica. Edizioni Libreria Cortina, Padova, pp xi+566, ISBN 88 7784 052 8

Recommended book:

• Marchi, E., Rubatta, A., 1981. Meccanica dei fluidi, UTET, Torino, pp xvi+800, ISBN 88 02 03659 4

• Citrini, D., Noseda, G., 1982. Idraulica. Casa Ed. Ambrosiana, Milano, pp x +468.

• Longo, S., Tanda, M.G., 2009. Esercizi di Idraulica e di Meccanica dei Fluidi. Springer & Verlag Italia, Collana UNITEXT Ingegneria, ISBN 978-88-470-1347-6, V+386 pp.

• Alfonsi, G., Orsi, E., 1984. Problemi di Idraulica e Meccanica dei fluidi. Casa Ed. Ambrosiana, Milano, pp 507, ISBN 88 408 0735 7

Reference books:

• Longo, S., 2011, Analisi Dimensionale e Modellistica Fisica – Principi e Applicazioni alle Scienze Ingegneristiche. Springer & Verlag Italia, Collana UNITEXT Ingegneria, ISBN 978-88-470-1871-6, X+370 pp.

• Çengel, Y. A., Cimbala, J. M., 2007. Meccanica dei fluidi. McGraw-Hill, ISBN: 9788838663840 (also available in english)

• Ghetti, A., 1996. Idraulica. Edizioni Libreria Cortina, Padova, pp xi+566, ISBN 88 7784 052 8

## Teaching methods

Lessons with the use of a PC tablet connected to a projector, used as multimedia board. Projection of video educational. Solving numerical exercises.

Lessons with the use of a PC tablet connected to a projector, used as multimedia board. Projection of video educational. Solving numerical exercises.

## Assessment methods and criteria

The examination is based on a written exam and an oral exam. Admission to the oral exam is subject to passing the written exam. The score is weighted as follows: 50% written test; 50% oral exam.

The examination is based on a written exam and an oral exam. Admission to the oral exam is subject to passing the written exam. The score is weighted as follows: 50% written test; 50% oral exam.

## Other informations

Lectures attendance is highly recommended.

Lectures attendance is highly recommended.