


Politecnico di Torino  
Academic Year 2017/18  
08BEKMC, 08BEKMO Hydraulics 

1st degree and Bachelorlevel of the Bologna process in Civil Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Environmental And Land Engineering  Torino 





Subject fundamentals
The course provides the basic knowledge of fluid mechanics, concerning the static and dynamic behavior of ideal and realNewtonian fluids. Particular attention is paid to practical applications and engineering aspects.

Expected learning outcomes
Basic knowledge of (i) fluid statics, (ii) realNewtonian fluid dynamics, (iii) flow in pressurized pipes and in open channels, and (iv) flow in porous media.
Students will be able to (i) evaluate static and dynamic forces exerted by fluids on rigid walls, (ii) design and test pressurized pipes and flow in open channels (rivers), and (iii) deal with simple problems concerning flow in porous media. 
Prerequisites / Assumed knowledge
The basic concepts provided by the courses of Mathematics and Physics in the first two years of the degree in Engineering are required. In particular, knowledge of differential equations, integrals and vector calculus is necessary.

Contents
Fluids and their characteristics. Definition of fluid; fluids as continuous media; variables and units of measure of fluid mechanics; flow regimes; deformations, deformation velocities and stresses in a fluid medium; equation of state.
Statics of fluids. Local and controlvolume equations; statics of uncompressible heavy fluids; pressure measurement; forces on flat surfaces; forces on curved surfaces; forces on immersed bodies; stability of floats; relative equilibrium. Kinematics of fluids. Eulerian and Lagrangian approaches: velocity and acceleration; flow regimes; continuity equations. Dynamics of ideal fluids. Euler’s equation; global equations; Bernoulli's theorem; applications; extensions and applications of the Bernoulli’s theorem. Dynamics of real fluids. NavierStokes equations; global equations for Newtonian fluids; Reynolds number. Laminar flow. Definition; global equations; analytical solutions for simple geometries. Turbulent flow. Reynolds’ experiment; general properties; temporal and ensemble average; equations of the average motion; Reynolds stresses; vortex cascade model; vortex stretching; piGreco theorem; wall turbulence and velocity profile of the flow. Pipe flow. Empirical approach; Moody's chart; head losses; practical laws; energy grade line and hydraulic grade line. Long pipelines. Definition; design and test problems; emblematic cases. Open channel flow. Basics; De Saint Venant equations; steady uniform motion; critical flow conditions; Froude number; channel critical slope. Steady open channel flow. Profile equations; general integrals; hydraulic jump; typical cases; flow over weirs; curved open channel flow. Potential flow. Definition; velocity potential; ChauchyRiemann relations; differential equation for potential flow; velocity complex function and its properties; examples (flow near a corner; sourcesink system; vortexes; flow around a cylinder and around a body); Blasius theorem. Flow in porous media. General characteristics and approaches; Darcy’s law; hydraulic conductivity tensor; analytical solutions for simple geometries in unconfined and confined aquifers. 
Delivery modes
Laboratory activities and exercises on the theoretical principles presented in class will be performed.

Texts, readings, handouts and other learning resources
The topics covered in the course are found in various texts of Hydraulics (e.g., Citrini e Noseda, Idraulica, CLUT; Munson et al., Fundamentals of Fluid Mechanics).
For further details:  Marchi, Rubatta, Meccanica dei Fluidi, UTET  Tritton, Physical Fluid Mechanics  Kundu, Fluid Mechanics. 
Assessment and grading criteria
The exam consists of a written test and an oral exam.
The written test is carried out at LAIB and consists of 20 multiple choice questions (1 point for each correct answer, with a maximum of 20 points). The questions will cover both theoretical issues and numerical exercises in order to assess the understanding of basic concepts and the ability to perform simple quantitative evaluations. The duration of the written test is 2 hours. The written test is passed with a grade of at least 12 points. This condition is necessary to access the oral exam. The result of the written test is only valid for the corresponding oral exam. The oral exam (up to 10 points) covers all topics discussed in the course in order to assess the understanding of the theoretical and practical aspects presented during the course. 
