B028619 - HYDRAULICS

Italian

Introduction. Elements of calculus, differential operators. Fluid properties. Equations of state. Dimensional analysis. Fluid kinematics and dynamics. Hydrostatic. Ideal flows. Equations for currents. Fluid dynamical forces. Flows through orifices. Real flows. Navier-Stokes equations, analytical solutions. Introduction to turbulence. Steady flows in pipes. Uniform and steady free surface flows. Steady filtration problems.

Marchi E., Rubatta, A., Meccanica dei fluidi, UTET, 1981.
Citrini D., Noseda G., Idraulica, CEA, 1987.
Ghetti A., Idraulica, Libreria Cortina, 1980.
Chow V.T., Open-channel hydraulics, Blackburn Press, 1959-2009.
Henderson F.M., Open channel flow, Macmillan, 1966.
Batchelor G.K., An introduction to fluid dynamics, Cambridge University Press, 1967.
Cengel Y.A., Cimbala J.M., Meccanica dei fluidi, McGraw-Hill, 2007.
Cenedese A., Meccanica dei fluidi, McGraw-Hill, 2003.
Polubarinova-Kochina Y.A., Theory of ground water movement, Princeton University Press, 1962.
Camnasio E., Lazzarin A., Orsi E., Meccanica dei fluidi, esercizi, Società Editrice Esculapio, 2017.
Alfonsi G., Orsi E., Problemi di idraulica e meccanica dei fluidi, CEA, 1984.

The aim of the lectures is to introduce basic physical concepts of the fluid mechanic, writing the laws of conservation of mass, momentum, angular momentum, both in integral and differential forms. The mathematical formulation is then used in analysing simple problems of applied relevance.
The objectives of the course are listed below.
Knowledge and understanding of mathematical methods applied to the hydraulics. Understanding of the complete formulations and of the possible simplifications that can be used in solving practical problems (e.g. the concept of streams). Quantification of the physical variables and correct application of the dimensional analysis. Knowledge of the basic problem in hydraulics and of the methods of their solution.
Applying knowledge and understanding.
Application of the acquired knowledge to the solution (both in design and in control) of basic hydraulic problems, such as hydrostatic forces of plane and curved surfaces, dynamical forces, pipe flows, free surface flows, groundwater flows.
Making judgements.
Ability in choosing the best option of calculation between the different possible options.
Communication skills.
Use of a clear and synthetic communication, oral or written, of the logical processes the starting from the formulation lead to the solution of the problems.
Learning skills.
The objective is to give the necessary basis for the comprehension of the arguments and also to give supplementary information (such as textbooks, scientific papers etc..) in order to enlarge the cultural background of the students, also in the perspective of possible following studies.

Basic knowledges in mathematics, physics, calculus.

Classroom lectures.

Written examination (2 hs, solutions of simple problems, text are forbidden, only the use of a calculator is allowed). Oral examination after the fulfilment of the written one. It can be sustained in the same or in the following exam sessions.

Introduction. Scalar, vector and tensor fields. Differential operators: gradient, divergence, curl. Differential identities. Gauss’ theorems. Fluid properties: density, specific weight, viscosity. Newtonian, thixotropic, rheopectic fluids. Bingham’s fluids, pseudoplastic, dilating fluids. Surface tension. Equation of state. Perfect gas. Liquids. Barotropic states. Dimensional analysis. The PI theorem. Examples. Self-similarity, incomplete self-similarity. Dimensionless numbers (Reynolds, Froude, Mach, Strouhal, Weber). (approx. 9 hs, 1 ECTS).
Kinematics, Lagrangian and Eulerian description. The time derivative. Trajectories, streamlines, streaklines. Local analysis of the flow, the rotation tensor, the strain rate tensor. Fluid as a continuum. Integral definition of the physical quantities. The discharge. Reynolds’ transport theorem. Mass conservation (integral and differential formulations). Kinematic boundary conditions. (approx. 9 hs, 1 ECTS).
Dynamics. Integral equations for momentum and angular momentum. Cauchy’s equations. Differental equations of motion. Dynamic boundary conditions. (approx. 9 hs, 1 ECTS).
Hydrostatic. Pascal’s and Stevin’s laws. Absolute and relative pressure. The piezometric head. Pressure measurement. Forces on plane and curved surfaces. (approx. 9 hs, 1 ECTS).
Ideal flows. Euler’s equations. Bernoulli relationship and the total head. Definition of a rectilinear stream and extension of the Bernoulli approach. The power of a stream. The Coriolis’ coefficient. Integral momentum equation for a stream. The Boussinesq’s coefficient. Pitot’s tube, Venturi’s tube. Mouthpiece and diaphragms. Dynamic forces. Phoronomy. (approx. 9 hs, 1 ECTS).
Real fluids (viscous). Newtonian fluids. The Navier-Stokes equations. Analytical solutions (steady flows); Couette, Poiseuille. Viscometer. Integral momentum equation for streams. Piezometric and total head losses.
The Reynolds’ number. Examples. (approx. 9 hs, 1 ECTS).
Introduction to turbulence. The Reynolds averaged Navier-Stokes equations. Reynolds’ stress. The boundary-layer. Dimensional analysis. Velocity profiles (Prandtl, Von Karman, Nikuradse). Pipe flows. Hydraulic resistance coefficient. The influence of roughness. Prandtl-Von Karman, Prandtl-Nikuradse, Colebrook-White laws. The Moody’s chart. Localized head losses. Design and control problems. Pipes with negative pressure, syphon, pumps, NPSH. (approx. 9 hs, 1 ECTS).
Free surface flows. Energetic characteristic. The critical conditions, the Froude’s number. Uniform flow. Critical slope. Runoff scale. Slow and fast currents. The boundary conditions. Steady flow equations and profiles. The hydraulic jump. Examples. (approx. 9 hs, 1 ECTS).
Groundwater flows. Confined and unconfined aquifers. Porosity. Darcy’s law. Equations of motion for confined aquifers. Dupuit’s hypothesis. Equations of motions for unconfined aquifers. Wells. (approx. 9 hs, 1 ECTS).