Learning objectives
Knowledge and Ability to Understand:
During the course, the student will learn the fundamentals of Fluid Mechanics and develop the ability to understand and critically analyze the physical reason for phenomena involving fluids at rest or in motion in natural or artificial systems. The method of investigation is mathematical modeling.
Competencies:
The student will develop the ability to apply the basics 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 ability useful for analyzing and dealing independently with elementary problems in Hydraulics.
Communication Skills:
Upon completion of the course, the student will be able to expound on the knowledge acquired with adequate command and good language skills.
Learning skills:
At the end of the course the student will have consolidated basic knowledge and skills in the field of hydraulics that will allow him to subsequently deepen the theoretical and technical knowledge useful for the design and verification of simple hydraulic engineering works.
Prerequisites
It is essential to have previously completed courses in Mathematical Analysis, Geometry, General Physics, and Rational Mechanics.
Course unit content
Fluid properties. The concept of fluid. The fluid as a continuum. 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.
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: 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: Current passing over a threshold, Current passing between bridge piers.
Bibliography
Recommended books
Mossa, Petrillo, Idraulica, CEI, 2013 (Available at the Library of Engineering and Architecture – 2 copies, of which 1 can be got on loan)
Citrini D., Noseda G. (1987). Idraulica, CEA, Milano. (Available at the Library of Engineering and Architecture – 4 copies, of which 3 can be got on loan)
Additional books
Marchi E., Rubatta A. (1981). Meccanica dei fluidi, UTET, Torino. (Available at the Library of Engineering and Architecture – 2 copies, of which 1 can be got on loan)
White F.M. (1999). Fluid mechanics, McGraw-Hill, Singapore. (Available at the Library of Engineering and Architecture – 4 copies, of which 2 can be got on loan)
Ghetti A. (1980), Idraulica, Libreria internazionale Cortina, Padova. (Available at the Library of Engineering and Architecture – 3 copies, of which 2 can be got on loan)
Books of exercises
Longo, S., Tanda, M. G., Chiapponi, L., 2021, Problems in Hydraulics and Fluid Mechanics. Springer, https://doi.org/10.1007/978-3-030-51387-0 Print ISBN 978-3-030-51386-3, Online ISBN 978-3-030-51387-0, XVII+391 pp. (Available for loan at the Library of Engineering and Architecture)
Alfonsi G., Orsi E. (1984). Problemi di Idraulica e Meccanica dei fluidi, CEA, Milano. (Available at the Library of Engineering and Architecture – 2 copies, of which 1 can be got on 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, of which 1 can be got on loan)
Lecture slides and additional educational material (downloadable from the webpage of the course on the University web site "Web LEArning in Ateneo")
Teaching methods
The course is mainly articulated in frontal lessons videoprojected for the presentation of the theoretical aspects and of the topics of deepening. During the exercises are addressed numerically problems of application interest. Two laboratory visits are planned.
Assessment methods and criteria
The examination consists of a written test followed by an oral test. Passing the written test is a prerequisite for admission to the interview. The two tests must be taken at the same exams session.
Evaluation criteria
Written test 50% including:
- Solving 3 exercises (knowledge/competence)
Oral examination 50% including:
- Theoretical questions (knowledge)
- Applications of theory/exercises (competence/autonomy of judgement)
- Ownership of exposition (communication skills)
Other information
The way the lessons are delivered will depend on the indications dictated by the Covid-19 pandemic.
