2) A.J. Chorin, J. E. Marsden: A mathematical introduction to fluid mechancs, Springer, 1980.
3) C. Trusdell, K.R. Rajagopal: An introduction to fluid mechanics, Birkhauser, 2000.
CA3: Applying knowledge and understanding related to the choice and application of appropriate analytical and modelling methods, based on mathematical and numerical analysis, in order to better simulate the behavior of components and plants in order to predict and improve their performance.
CA10: Applying advanced knowledge and understanding to operate effectively, individually and as members of a group, having a clear understanding of the context of engineering problems and of the interdisciplinary implications that characterize mechanical engineering.
CA12: Applying adequate knowledge and understanding to understand English texts.
CC2: In-depth knowledge and understanding of the theoretical-scientific aspects of mathematics and other basic sciences. To be able to use this knowledge to interpret and describe complex and/or interdisciplinary engineering problems.
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Office hours Prof. Farina, by prior appointmentDipartimento di Matematica e Informatica "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 2751435
E-Mail: angiolo.farina@ unifi.it
Type of Assessment
Final oral examination. A number of questions are posed. The oral examination is designed to evaluate the degree of understanding of the theory presented in the course. In the assessment, special attention is paid to communication skills, critical thinking and appropriate use of mathematical language.
• Ideal and incompressible fluids and their dynamics• Vorticity• Bernulli theorems, Lagrange-Thompson• Contour conditions• Stream function and potential function• External flow and aerodynamic action• D'Alambert's Paradox• Kutta-Joukowski's theorem• Conformal transformations• Plate, circle arch and generic Jukoswski profile.
• Thermodynamics of perfect fluids.• Sound speed, Mach number, fluid compressibility.• Sound waves.• Supersonic flows around thin profiles.• Characteristics lines.• Riemann Invariants• Prandtl-Meyer flows• Shock waves• Wave flat discontinuity finished. Rankine-Hugoniot Relations.• Uniqueness and condition of entropy.
• Dynamics of incompressible Newtonian fluids• Equations by Navier-Stokes• Vorticity in Newtonian Fluids• Reynolds Number, laminar and turbulent regime• Some laminar flows: Hagen-Poiseuille and Couette• Laminar boundary layer• Exact solutions for flat plate• Laminar separation