Mechanical Engineering

The course is divided into two parts. In the first part the fundamental laws for the motion of the fluids are derived in the context of the general framework provided by the continuum mechanics (about 30 hours of lesson). The second part of the course tackles ingenerasti problems relevances for the fluid dynamics starting from the general framework provide by the first part of the course (about 42 hours of lesson). Detailed Programm of the first part Introduction to tensor analysis. Kinematic of deformable bodies: Lagrangian and Eulerian description. Mass balance. Dynamics and thermodynamics of deformable bodies: momentum and energy balance. Constitutive relations for Newtonian fluids. Entropy balance. Complete set of equation for the solution of Fluid Dynamics fields. Non dimensional parameters. Detailed program of the second part Natural and forced convection. Balance equations for a control volume and applications. Asymptotic solution for low and high Reynolds numbers. Euler equations. Potential flows. Vorticity, circulation, irrotational flows, Kelvin circulation Theorem. Beltrami equation for the vorticty field, generalized Biot-Savart laws. Boundary layers. Bernulli and Crocco theorems. External solutions for compressible flows. Small perturbations solutions for subsonic and supersonic flows. Rankine Hugoniot relations for normal, oblique and curved shocks. Prandtl-Meyer flows. 1D isentropic flows in ducts. Applications to nozzles.

Calculus, geometry and Physics (bachelor courses)

Notes of the course freely available from the institutional website https://elearning.uniroma1.it/course/view.php?id=11843 Kundu P.K., Cohen I.R. Fluid mechanics (Accademic Press)

Blackboard lectures

8 hours frontal lessons per week (11/12 weeks) including theoretical subjects and practical applications.

Written test: pre-test and open answer questions on theoretical aspects and exercises discussed during the course Oral test: open answer questions on theoretical aspects relevant for technological applications

Batchelor - An introduction to Fluid Dynamics Landau and Lifshits - Fluid Mechanics

Blackboard lectures

The course is divided into two parts. In the first part the fundamental laws for the motion of the fluids are derived in the context of the general framework provided by the continuum mechanics (about 30 hours of lesson). The second part of the course tackles ingenerasti problems relevances for the fluid dynamics starting from the general framework provide by the first part of the course (about 42 hours of lesson). Detailed Programm of the first part Introduction to tensor analysis. Kinematic of deformable bodies: Lagrangian and Eulerian description. Mass balance. Dynamics and thermodynamics of deformable bodies: momentum and energy balance. Constitutive relations for Newtonian fluids. Entropy balance. Complete set of equation for the solution of Fluid Dynamics fields. Non dimensional parameters. Detailed program of the second part Natural and forced convection. Balance equations for a control volume and applications. Asymptotic solution for low and high Reynolds numbers. Euler equations. Potential flows. Vorticity, circulation, irrotational flows, Kelvin circulation Theorem. Beltrami equation for the vorticty field, generalized Biot-Savart laws. Boundary layers. Bernulli and Crocco theorems. External solutions for compressible flows. Small perturbations solutions for subsonic and supersonic flows. Rankine Hugoniot relations for normal, oblique and curved shocks. Prandtl-Meyer flows. 1D isentropic flows in ducts. Applications to nozzles.

The student is required to have knowledge in calculus, vector calculus (geometry) and physics The following exams are then mandatory: Analisi I, Fisica I and Geometria

Course notes freely available from the institutional website http://www.ingmecc.uniroma1.it/index.php?option=com_content&view=article&id=70%3Alaer-elenco-dei-corsi-aa-2010-2011&catid=37&Itemid=68&lang=it Kundu P.K., Cohen I.R. Fluid mechanics (Accademic Press)

The course is given through lessons to the class. The lessons want to show how from the classical mechanics principle the general equations for the motion of the fluid can be derived. During the second part of the course it is shown how any practical problem involving the fluid motion can be tackled by using the general system derived in the previous part of the course by introducing suitable approximation which are specific of the problem that is considered. The aim is to teach to the students how to develop a physical/mathematical model of a complex phenomena as represented by the motion of fluids in technological applications.

standard classroom lessons

The exam is composed by a two written tests (3h:30min) and and oral test. The first written test (30min) consists in a pre-test where simple but fundamental questions ara arisen to the students. The aim is to asses an elementary knowledge of fluid dynamics which are required by the next test. The pre-test serves also as self-evaluation for the students to check their knowledge of the mathematical tools required by the second test. The second test lasts 3 hours and covers the programme of the course via open questions where the students tackles theoretical and practical problems as discussed during the lessons. The aim is to asses and evaluate the ability of the students in the formulation of the different physical mathematical models that are used in technological applications. The oral discussion wants to evaluate the abilities of the students in solving complex problems starting from the knowledge acquired during the course.

.K. Batchelor "An introduction to Fluid Dynamics" (Cambridge University. Press) D.J. Tritton "Physical Fluid Dynamics" (Oxford Univ. Press) L D Landau, E.M. Lifshitz "Fluid Mechanics" (Pergamon Press)

The course is given through lessons to the class. The lessons want to show how from the classical mechanics principle the general equations for the motion of the fluid can be derived. During the second part of the course it is shown how any practical problem involving the fluid motion can be tackled by using the general system derived in the previous part of the course by introducing suitable approximation which are specific of the problem that is considered. The aim is to teach to the students how to develop a physical/mathematical model of a complex phenomena as represented by the motion of fluids in technological applications.