Civil and environmental engineering
Study-unit Code
In all curricula
Bruno Brunone
  • Bruno Brunone
  • 80 ore - Bruno Brunone
Course Regulation
Coorte 2022
Learning activities
Ingegneria ambientale e del territorio
Academic discipline
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Basic differential equations for fluids
Fluid Statics
Inviscid fluids
Finite control volume analysis
Viscous liquids
Short pipes: analysis of functioning conditions
Long pipes in uniform flow
Unsteady flow in pressurised pipes
Open channel flow in steady-state conditions
Flow through porous media (basics)
Reference texts
All texts are in Italian; however the staff is available to teach in English within ad hoc meetings.
For the theory, the following classical textbook is suggested:
Citrini, G. Noseda: IDRAULICA, casa editrice Ambrosiana, Milano.
Students can practice by using the texts:
Brunone, B., Ferrante, M., Berni, A. Esercizi di Idraulica – parte I. Morlacchi Editore, Perugia.
Brunone, B., Ferrante, M., Meniconi, S., e Almandori, C.. Esercizi di Idraulica – parte II. Morlacchi Editore, Perugia.
where all execises are solide. During te lessons, the pdf file of the following paper is provided:
C. Montuori: "Le equazioni globali della meccanica dei fluidi e l'interpretazione energetica del carico idraulico".
Moreover, to improve the dialogue between the students and the teaching staff, the following Facebook page is active:
Educational objectives
The course of IDRAULICA is the first one concerning water resources. Its main aim is to provide students with the basic analytical tools to analyze quantitatively flow processes. In such a context, both the local (by means of differential equations) and global approach will be followed. Particularly, the continuity equation and the momentum equations will be derived from the fundamental eqautions of Physics, as relaible tools for engineers. Moreover, attention will be paid to empirical relationships that are used for solving practical problems of the hydraulic engineering. For each empirical relationship, the range of validity will be pointed out. Great attention will be devoted to 1-D models which are the hearh of IDRAULICA with respect to Fluid Mechanics.
The main competence will be:
- to use the proper approach (local, global, 1-D modeling);
- to analyze the given problem selecting data and unknowns properly;
- to solve implicit equations (e.g. the friction formulas) reliably;
- to use EPANET code and make practice with AQUALIBRIUM.
In order to be able to understand and apply most of the topics explained during the course, you must have successfully passed the Analisi Matematica 1 exam as well as know topics of the Geometria Analitica and Fisica I exams; moreover you should attend the Meccanica Razionale and Analisi II courses. Particularly you should be familiar with continuous functions, limits, derivatives, and simple and double integrals.
Teaching methods
The course is organized as follows:
- lectures on all the topics of the course;
- exercises about all the practical topics discussed during the course;
- laboratory tets at the Water Engineering Laboratory of the Dipartimento di Ingegneria Civile ed Ambientale (http://www.ing1.unipg.it/laboratori/sede-principale/laboratorio-di-ingegneria-delle-acque) about open channel flow and transients in pipe systems;
- EPANET short course (http://epanet.de/) and AQUALIBRIUM competition (http://www.aqualibriumcompetition.net/joomla/) coupled.
For all topics, the strong links between theory and practical engineering problems are pointed out.
Other information
As additional teaching activity, students will execute tests at the Water Engineering Laboratory (WEL). Specifically, steady- and unsteady state tests will be carrie out in pressurized pipes to analyze energy dissipation and pressure wave mechanisms. Moreover open channel flow tests will be considered in the laboratory channel. A set of lessons will concern the analysis of pipe network behavior by means of both EPANET code and the EQUILIBRIUM setup at WEL.
Learning verification modality
With regard to the modality of the exam, you have the following two options:
two-steps exam: within such a modality, the exams consists in two phases. The first phase happens immediately before the beginning of the second semester: it is a written exam concerning the topics explained during the first semester but with no exercise (usually three questions; available time: 1.5 hours). The second phase consists in an oral test, with a duration of about 30 minutes, which includes two questions about the topics explained during the second semester and an exercise about one of the practical topics discussed during the whole course.
unique-step exam: within such a modality, the exams consists in an oral test, with a duration of about 1 hour, which includes four questions about all the topics explained during the course and an exercise about one of the practical topics discussed during the whole course.
Within both the modalities, your communication skill and autonomy in the organization and exposure of the topics will be tested.
A problem concerning hydrostatics, steady-state flow in pressurised pipes, and steady-state flow in open channels has to be solved numerically to be admitted to the oral exam.
Extended program
Basic differential equations for fluids
Some characteristics and properties of fluids and liquids. Stresses. Cauchy's theorem. Newton's law and Newtonian fluids. State equation. Kinematics of fluids. Lagrangian and Eulerian approach. Flow field description. Continuity equation. Newton's second law and fluid dynamics equation.

Fluid Statics
Basic equation for pressure field. Stevin's law. Hydrostatic pressure behavior. Hydrostatic force on a plane and curve surface. Mariotte's formula. Problems.

Inviscid fluids
Euler's equation. Bernoulli theorem. Gradually varied flows. Venturi principle. Orifice equation and Torricelli free fall velocity. Bernoulli theorem for a gradually varied flow.

Finite control volume analysis
Continuity equation. Continuity equation for a flow. Momentum equation. The energy equation and the Bernoulli equation. Problems.

Viscous liquids
Bernoulli equation for viscous liquid flows. Reynolds pipe flow experiments: laminar and turbulent flows. Darcy - Weisbach equation and friction losses (Moody chart, Poiseuille equation, Blasius equation, Colebrook-White equation. Swamee-Jain equation).

Short pipes: analysis of functioning conditions
Sudden expansion of a pressurised flow: the Borda equation. Minor losses (inlets, valves, bends, outlets,...). Hydraulic grade line. Short and long pipes. Problems.

Long pipes in uniform flow
Design and analysis of functioning conditions (branched and looped systems). Pumping stations. EPANET. Problems.

Unsteady flow in pressurised pipes.
Pressure wave speed. 1-D differential equation (water hammer equation). Initial and boundary conditions. Rigid column model. Transients in elevatory mains. Air vessel design by means of Evangelisti charts. Problems.

Open channel flow
Characteristics of open channel flow with respect to pressurised flow. Uniform depth channel flow. Gradually varied flow. Hydraulic jump. Problems.

Flow through porous media
The Darcy law. Well in artesian and phreatic aquifer. Pumping tests.

Measurement of hydraulic quantities (pressure, local velocity, pipe discharge, open channel flow depth).
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