# FLUID MECHANICS

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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- VALERIO CALEFFI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- ICAR/01

#### Training objectives

- The module is the basic teaching of fluid mechanics and treats the main concepts concerning the physical properties of fluids, the forces exerted by fluids in statics, the fluids' motion and their interaction with solid boundaries and technical devices. The module treats also some typical technical problems, even with a basic approach, such as the design and operating principles of pressure pipes in uniform and steady flow.

The module's primary purpose consists of giving students the bases to face the study of the systems of forces acting on hydraulics devices and infrastructures and to acquire the proper skills concerning the energy and momentum balances governing the motion of the fluid in practical hydraulic engineering.

The main knowledge that must be acquired can be summarized as follows:

- Mechanical properties of fluids, with a specific reference to incompressible fluids;

- Fundamental equations of fluid statics, kinematics and dynamics of incompressible of weakly compressible fluids;

- Differential and integral analysis in fluid mechanics problems;

- Fundamental equations governing uniform and steady flow in pressure pipes.

The main skills that must be acquired can be summarized as follows:

- To evaluate hydrostatic forces acting over the plane and curved surfaces;

- To apply mechanical balances of mass, energy, momentum to simple systems of technical interest, to evaluate the dynamic forces of several devices and the mechanical energy exchanges between fluid flows and fixed or mobile surfaces;

- To evaluate the flow resistances in external and internal flows, both laminar and turbulent;

- To design and verify simple pressure pipes in steady flow conditions. #### Prerequisites

- It is necessary to have understood and assimilated the contents of Mathematical Analysis I and General Physics, and it is strongly suggested to have understood and assimilated the contents of the courses of Mathematical Analysis II and Analytical Mechanics. More specifically, a proper skill in managing the following topics is required:

- Differential and integral calculus;

- Vector fields analysis (Gauss theorem, gradient, divergence, curl (Stokes) theorem);

- Mechanical balances of forces and moments, momentum and angular momentum, potential, kinetic and total mechanical energy;

- Conservative and non-conservative force fields, work and energy;

- Mechanics of the rigid body;

- Mass and area geometry. #### Course programme

- INTRODUCTION and PHYSICAL PROPERTIES OF FLUIDS [4 h]. Definition of a fluid. Equation of state. Perfect gases, barotropic fluids, incompressible fluids. Continuum model. Density and specific weight. Fluid compressibility. Surface tension. Dynamic and kinematic viscosity. Vapour pressure. STRESS ANALYSIS [1 h]. Cauchy Theorem. Stress tensor and its mathematical properties. FLUID STATICS [15 h]. Isotropic pressure. Integral and differential equations. Piezometric head. Static forces against plane and curved surfaces, submerged and floating bodies. FLUID KINEMATICS [3h]. Path lines, streamlines, streak lines. Material derivatives. Acceleration. Velocity gradients tensor. CONTINUUM MECHANICS [3 h]. Reynolds theorem. Integral and differential equation of continuity. First and second integral and differential equation of motion. INVISCID FLUID MECHANICS [10 h]. Euler Equations. Boundary conditions. Total head. Bernoulli’s theorem. INTEGRAL EQUATIONS IN FLUID DYNAMICS [3 h]. Continuity equation. Discharge. Linear momentum balance and angular momentum balance. One-dimensional flow. Flow over orifices and weirs. External flows. Free jets. Dynamical forces. Hydraulic machinery. VISCOUS FLUID MECHANICS [5 h]. Stokes/Newton assumptions. Navier-Stokes equations. Boundary conditions. Viscous laminar flows in circular closed conduits. Friction slope and resistance coefficient. TURBULENT FLOWS [3 h]. Reynolds equations. Uniform flows. Mixing length theory. UNIFORM FLOW IN CLOSED CONDUITS [2 h]. Velocity and stress distributions. Distributed head losses and resistance laws (Coolebrook/Moody). TRAINING AND EXAMINATION STANDARD [11 h].
#### Didactic methods

- The lectures are organized as follows:

- Frontal lectures concerning the described topics;

- Practical examples, that are devoted to explaining engineering applications of theoretical concepts;

- Support to carry out practical exercises (including numerical computations), that are extracted from written tests of previous academic years. #### Learning assessment procedures

- The main purpose of the final examination consists of verifying the proper achievement of the previously defined training objectives.

The exam is divided into two parts, a written test and the oral examination, in different dates.

The written test (2 hours) consists of 2 exercises; each of them is evaluated as 1/2 of the total mark (30): 1) Static force on a curved surface; 2) Bernoulli’s theorem applications and dynamic forces computation using momentum balances or computation of friction in pipes. A mark of 16/30 (at least) is required to sit the oral examination. The validity of the written text (if the mark is 18/30 at least) is twelve months. The validity of the written test, if the mark is less than 18/30, expires at the date of the following written text.

The oral test will focus primarily on course topics not covered directly in the written test. The final mark is not the simple mean between the written part and oral part (anyway is never less than this mean), but is a synthetic mark, expressed as a fraction of 30. If the candidate retreats during the oral examination, he must repeat the written test just if his mark on such test is less than 18/30. #### Reference texts

- MARCHI E., RUBATTA A., Meccanica dei fluidi. Principi ed applicazioni idrauliche. UTET, 1981.

CENGEL Y.A., CIMBALA J. M., Meccanica dei fluidi, IV edizione, McGraw-Hill Education, Milano, 2020 (edizione italiana a cura di G. Cozzo e C. Santoro).

MUNSON B.R., OKIISHI T.H., HUESBSBSCH W.W., ROTHMAYER A.P., Meccanica dei Fluidi, I edizione, CittàStudi Edizioni, 2016 (edizione italiana a cura di E. Larcan e P. Escobar Rojo).

KUNDU P.K., CHOEN I.M., DOWLING D.R, Fluid Mechanics, Academic Press, 2015

MOSSA M., PETRILLO A. F., Idraulica, CEA, Milano, 2013.

LONGO S., TANDA M.G. Esercizi di Idraulica e Meccanica dei Fluidi. Springer, 2009.