Scientific Sector
ICAR/01 Hydraulics
Number of University Credits
6
Educational Goals
The course deals with fundamental issues of the Degree Class of Civil Engineering, of which is an essential and distinctive educational activity. The teaching of hydraulics provides students with the necessary information and details on pipe networks, openchannel flows and basics of physical hydraulic modeling. The program is divided into three parts. In the first part the course aims to address the topics of current in ducts, through the solution of the typical problems of steady or unsteady flows. In the second part the openchannel topics are presented and typical problems are solved, with the analysis of the gradually varied flow profiles and the unsteady flow. In the third part the course aims to provide the fundamentals of physical hydraulic modeling, with the principles of the dimensional analysis, the geometric, kinematic and dynamic similarity. In addition, students are given the skills necessary for understanding the fluid dynamics through laboratory training.
Summary of the program
· Viscous Flow in Ducts (2.5 credits)
o Steady flows in ducts.
o Pipe network: typical design and check problems.
o Unsteady flows in ducts.
· OpenChannel Flows (2.5 credits)
o Uniform flows. Steady flows.
o Unsteady flows.
· Physical Hydraulic Modeling (1 credit)
o Basics. Dimensional analysis and Pi theorem.
o Geometric, kinematic and dynamic similarity.
o Principles of the physical model construction.
Preparatory exams
Physics, Theoretical Mechanics and Hydraulics.
Lab training requirements
The activities of lab training are required, since they are fundamental also the theoretical part of the course.
Structure in different typological educational activities
Educational activities

Credits

Didactics (hours)

Studying (hours)

Theoretical classes

4

32

68

Excecises

1

16

9

Laboratory training

0.5

12

0.5

Seminar

0.5

12

0.5

Total

6

72

78

Final examination
The final exam of Hydraulics II is composed of:
1) Two written test (a classwork and a homework).
2) Oral test on the theoretical part of the course.
During the classes one written test (exemption from the classwork written test) will be proposed to the students who attend the lessons. The students that pass this test will be successively examined only with the homework written test and orally on the theoretical part of the course. In case of fail of the exemption test (also for absence), the students will be examined also with the written test. Generally the homework will verify the capability of the students to solve a problem of gradually varied flows in steep and mild sloped channels.
Detailed program of the course
Hydraulic grade lines of pipe: different cases. Exercises on the pipe network check. Transitional and fully developed turbulent flow in conduits. Friction Reynolds number. Exercises on the pipe network design.
Over head pump and under head pump. Exercises on the pump positioning.
Closed pipe networks: characteristics and typology . Exercises on the check of networks. Proof of the Cross method. Exercises on the Cross method. Design of a closed pipe network and its check using the Cross method. Exercises of the pump design in order to increase the discharge in a pipe.
Celerity of the water hammer in the case of elastic ducts (with proof). Slow and abrupt pipe closure: formula of Michaud (with proof). Exercises on the check of pipe network with new and old roughness, localized head losses due to a valve, exercises on design of pipes with a pump. Motion field in U tubes. Mass oscillations (with proof).
Openchannel flows; specific energy, the energy diagram as a function of the water height; diagram of the water height in a channel section as a function of discharge per unit width; hydraulic radius: the case of a large rectangular section; steep and mild sloped channels; gradually varied flow profiles (with proof) in steep and mild sloped channels.
Hydraulic jump. Proof of the equation of the conjugate depths of a hydraulic jump. Energy loss in a hydraulic jump. Gradually varied flow profiles downstream of a gate. Gradually varied flow through bridge piers or over a bump.
Proof of the celerity of small perturbations in the channels. Absolute and relative celerity in steep and mild sloped channels. Exercises on the gradually varied flow profiles. Finite difference method applied to the gradually varied flow profiles.
The dimensional analysis and the principle of the dimensional homogeneity. The Pi theorem. Nondimensionalization of the basic equations. Dimensional analysis applied to the shear wall of a pipe with circular cross. Dimensional analysis of the Darcy friction factor. Comparison of the results of the dimensional analysis with the known results from theory.
Modeling and its pitfalls. Geometric, kinematic and dynamic similarity. Dimensional analysis applied to physical modeling. Interpretation of the numbers of Reynolds and Froude. Example of a physical model that requires both the analogy of Reynolds and Froude. Scale effects.
Recommended book
M. Mossa, A.F. Petrillo, Idraulica, ISBN 9788808180728, Casa Editrice Ambrosiana, Milano, 2013 (in Italian).
Other books
F.M. White, Fluid Mechanics, McGrawHill, 4th edition, 1999.
Y.A. Çengel, J.M. Cimbala, Mechanics of fluids, McGrawHill, 2011 (2nd edition).
D. Citrini, G. Noseda, Idraulica, Ed. CEA, Milano (in Italian).
A. Ghetti, Idraulica, Edizioni Libreria Cortina, Padova, 1981, 2nd edition (in Italian).
E. Marchi, A. Rubatta, Meccanica dei Fluidi: principi ed applicazioni idrauliche, UTET, Torino, 1981 (in Italian).
G. Alfonsi, E. Orsi, Problemi di idraulica e meccanica dei fluidi, Ed. CEA, Milano (in Italian).