# 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 basic knowledge of 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 basic knowledge of 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 units of measurement. Fluid properties. Stresses in a continuum.

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

Fluid kinematics. Lagrangian and Eulerian approach. Velocity and acceleration fields. Total derivative. Pathlines, streamlines, streaklines. The Reynolds transport theorem. Flow regimes.

Basic fluid dynamics. Differential and finite control volume analyses of a fluid flow. Basic laws of Fluid Mechanics. Conservation of mass. Continuity equation. The linear momentum equation. Dynamic load of a flow. The differential equation of linear momentum.

Frictionless flow. The ideal fluid model. Euler equation. The Bernoulli equation. Physical and geometrical interpretation. Examples of the use of the Bernoulli equation. Gradually varied flow. Extension of the use of the Bernoulli equation to streams.

Flow of viscous fluids. The viscous fluid model. The Navier-Stokes equations. Analytical solutions of the Navier-Stokes equations: Couette flow, Hagen-Poiseuille flow.

Flow in ducts. Laminar and turbulent regimes. Equations of motion. Reynolds number. Continuous and minor losses. Resistance laws. Moody chart. Pipe flow problems.

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 units of measurement. Fluid properties. Stresses in a continuum.

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

Fluid kinematics. Lagrangian and Eulerian approach. Velocity and acceleration fields. Total derivative. Pathlines, streamlines, streaklines. The Reynolds transport theorem. Flow regimes.

Basic fluid dynamics. Differential and finite control volume analyses of a fluid flow. Basic laws of Fluid Mechanics. Conservation of mass. Continuity equation. The linear momentum equation. Dynamic load of a flow. The differential equation of linear momentum.

Frictionless flow. The ideal fluid model. Euler equation. The Bernoulli equation. Physical and geometrical interpretation. Examples of the use of the Bernoulli equation. Gradually varied flow. Extension of the use of the Bernoulli equation to streams.

Flow of viscous fluids. The viscous fluid model. The Navier-Stokes equations. Analytical solutions of the Navier-Stokes equations: Couette flow, Hagen-Poiseuille flow.

Flow in ducts. Laminar and turbulent regimes. Equations of motion. Reynolds number. Continuous and minor losses. Resistance laws. Moody chart. Pipe flow problems.

## Recommended readings

Recommended books:

• Çengel Y.A., Cimbala J.M. (2015). Meccanica dei fluidi, III ed., McGraw-Hill, Milano, ISBN 978-88 386 6884-5 (also available in English).

• 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.

• Munson B.R., Okiishi T.H., Huebsch W.W., Rothmayer A.P. (2016). Meccanica dei fluidi, Città Studi Edizioni, Novara (also available in English).

Books of exercises:

• 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:

• White F.M. (1999). Fluid mechanics, McGraw-Hill, Singapore, ISBN 978-0-07-352934-9

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

• Mossa M., Petrillo A.F. (2013). Idraulica, Casa Ed. Ambrosiana, Milano.

Lecture slides and additional educational material (downloadable from the webpage of the course on the University web site elly.ingind.unipr.it).

Recommended books:

• Çengel Y.A., Cimbala J.M. (2015). Meccanica dei fluidi, III ed., McGraw-Hill, Milano, ISBN 978-88 386 6884-5 (also available in English).

• 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.

• Munson B.R., Okiishi T.H., Huebsch W.W., Rothmayer A.P. (2016). Meccanica dei fluidi, Città Studi Edizioni, Novara (also available in English).

Books of exercises:

• 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:

• White F.M. (1999). Fluid mechanics, McGraw-Hill, Singapore, ISBN 978-0-07-352934-9

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

• Mossa M., Petrillo A.F. (2013). Idraulica, Casa Ed. Ambrosiana, Milano.

Lecture slides and additional educational material (downloadable from the webpage of the course on the University web site elly.ingind.unipr.it).

## Teaching methods

The course is structured in frontal lessons on the blackboard (with the projection of slides and video educational) in order to present theoretical aspects and complementary subjects. Numerical problems will be solved during the practice exercises. A technical visit to an engineering structure is typically organized.

The course is structured in frontal lessons on the blackboard (with the projection of slides and video educational) in order to present theoretical aspects and complementary subjects. Numerical problems will be solved during the practice exercises. A technical visit to an engineering structure is typically organized.

## Assessment methods and criteria

The examination is based on a written exam consisting of numerical exercices and theory questions.

Evaluation criteria:

- Resolution of no. 3 exercises (knowledge/proficiency): 50%

- Theory questions (knowledge), applications of theory (proficiency/making judgments), presentation ability (communication skills): 50%

The examination is based on a written exam consisting of numerical exercices and theory questions.

Evaluation criteria:

- Resolution of no. 3 exercises (knowledge/proficiency): 50%

- Theory questions (knowledge), applications of theory (proficiency/making judgments), presentation ability (communication skills): 50%

## Other informations

Lectures attendance is highly recommended.

Lectures attendance is highly recommended.