## Learning objectives

Knowledge and understanding:

At the end of this course the student should know the main theoretical and applicative aspects of Fluid Mechanics for planning industrial hydraulic plants, river structures and maritime structures.

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.

## Course unit content

The course provides the students with the necessary knowledge related with hydraulics and fluid mechanics. The students shall be able to solve some technical problems of environmental hydraulics, river and maritime hydraulics.Numerical exercises about the topics listed in the program will be developed.

## Full programme

First part (6cfu)

•Lesson 1: Flow through orifices, weirs, orifices with internal/external pipe. Flow under a gate.

•Lesson 2: Thin weirs. Bazin, Thomson, Hegly, Cipolletti, triangular thin weirs. Unsteady flows.

•Lesson 3: Reaction. Practical problems for long pipes. Pipe with constant diameter and distributed discharge.

•Lesson 4: Networks of pipes. Cross method balancing the discharges or the hydraulic heads.

•Numerical practice No 1: siphon, pipe with varying diameter and constant discharge, with constant diameter and distributed discharge.

•Lesson 5: Economical planning of pipes. Pumping stations, penstocks, vertical geometry of pipes.

•Lesson 6: The equations of unsteady flow. Oscillations 'en bloc'.

•Lesson 7: Oscillating chamber with and without optimal constriction. Oscillation in a U tube. Application to the pumping stations. Pressurized air chamber.

•Numerical practice No 2: chained equations of Allievi and the method of characteristics for the water hammer.

•Lesson 8: The celerity of elastic waves. The simplified equations for the water hammer.

•Lesson 9: The boundary conditions for the hydropower plants and for the pumping stations. The chained equations of Allievi.

•Lesson 10: The complete equations for the water hammer.

•Lesson 11: The method of characteristics for the water hammer analysis. Graphical methods.

•Numerical practiceNo 3: the chained equations of Allievi and the method of characteristics (cont'd).

•Lesson 12: Elements of ffree surface flows. Backflows.

•Numerical practice No 4: pressurized air chambers for pumping stations.

•Lesson 13: Free surface profiles in natural streams.

•Lesson 14: lateral weir. Channel with increasing discharge in the flow direction. Sediment transport: general concepts.

•Lesson 15: Bed load and suspended load. Bedforms.

•Lesson 16: Flow resistance in streams with bedforms. Erosion near a pier of a bridge.

•Numerical practice No 5: computing the current profiles in a natural stream. Sediment transport.

Second part (3cfu): Physical models and Hydraulic measurements

•Lesson 17: Dimensional analysis: the fundamental variables, the monomial expression for the dimensional equations.

•Lesson 18: The theory of similarity. The direct analysis. Geometric, kinematic, and dynamic similarity.

•Lesson 19: Similarity of Euler, Reynolds, Froude, mach. Similarity in cavitation. Similarity of oscillating chambers. The hydroelastic models.

•Lesson 20: The geometrically distorted physical models. Similarity in sediment transport. Similarity in water-hammer. Similarity in gravity waves.

•Lesson 21: Applications of physical models: weirs and bottom discharge systems. The main pipe. The dissipation basin. The local bed erosions.

•Lesson 22: River management physical models. Models for wave propagation. Coastal hydrodynamics in physical models. The analogic models. The aerodynamics models. The hybrid models.

•Lesson 23: Elements of a meter instrument. Active and passive transducers. Analogic and digital processes. Balancing effect instruments. Generalised configuration I/O of an instrument. Filters. Static and dynamic performances of an instrument.

•Lesson 24: Pressure transduce. Dead weight manometers, Bourdon manometer. Diaphragms and membranes manometers.

•Lesson 25: Velocity measurements in a fluid flow: hot film anemometer, laser doppler, PIV. Pitot tube. Ultrasound velocimeter.

•Lesson 26: Discharge meters: Venturi and orifices. Floating bodies free surface velocity measurements. Turbine meters. Volumetric measurement tools. Magnetic flowmeters. Liquid level measurements: floating body, bubbles, inductive meters.

• Visit to the Hydraulic Lab. Fluid velocity measurements with PIV and with Ultrasound velocity profiler.

## Bibliography

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

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

• Mossa M. e Petrillo A. F., 2013. Idraulica. Casa Ed. Ambrosiana, Milano, pp xix +612

• Longo, S., Appunti sul colpo d’ariete.

• 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.

• Longo, S. Petti, M., 2006. Misure e Controlli Idraulici. McGraw-Hill Italia, Collana di Istruzione Scientifica, serie di Ambiente e Territorio, ISBN 88-386-6137-5, XI+415 pp.

• Adami, A. 1994. I modelli fisici nell’Idraulica, CLEUP Ed., ISBN 88-7178-361-1

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

• Longo, S. e 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. e Orsi, E., 1984. Problemi di Idraulica e Meccanica dei fluidi. Casa Ed. Ambrosiana, Milano, pp 507,

ISBN 88 408 0735 7

## 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.

## 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.

## Other information

Lectures attendance is highly recommended.