Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body, thermodynamics, and fluid dynamics (properties of a fluid, substantial derivative, Reynolds transport theorem, conservation equation of mass, momentum, and energy).

The course aims at providing future aerospace engineers with basic knowledge of aerodynamics. The syllabus can be organized into two main parts.
The first part discusses the basic theory of one-dimensional and two-dimensional gas dynamics. Both steady and unsteady gas dynamics theory will be discussed while analyzing fundamental flows like de Laval nozzle, Fanno's flow, and Rayleigh's flow. The interactions of supersonic flows with airfoils will also be described using the shock-expansion theory and the thin airfoil theory.
The second part of the course deals with the description of irrotational flows. The potential flow theory will be presented and applied to canonical flows using the conformal mapping technique. The theory for linearized flows will be derived with particular attention to linearized compressible flows.

At the end of this course, students in aerospace engineers should have a good knowledge of: 
- one-dimensional unsteady as well as two-dimensional steady gas dynamics;
- basic principles of two-dimensional potential flow theory;
- principles of linearized flow theory in subsonic as well as supersonic regimes.

54 hours of lecture

An oral exam consisting of three questions.

• Recap of basic knowledge: conservation equation for a fluid, fluid properties (5 hours)
• Steady quasi-one-dimensional flow: general properties of quasi flows, total and critical quantities, area-velocity relation, mass flux, shock waves and Rankine–Hugoniot relations, convergent nozzles, convergent-divergent nozzles (7 hours)
• Steady non-isentropic one-dimensional flows: adiabatic flow with friction, flow with friction and heat exchange, Rayleigh's flow (4 hours)
• Two-dimensional gas dynamics: oblique shocks, Prandtl-Meyer expansions, shock polars, interactions between different waves, bow shocks, isentropic compressions and expansions, flow past a convergent-divergent nozzle, shock-expansion theory, thin-airfoil theory (9 hours)
• Potential flow theory: Kelvin and Helmholtz theorems, irrotational acyclic and cyclic flows, analytic functions of complex variables, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, conformal mapping, potential flow past a Joukowski airfoil (6 hours). 
• Linearized flow theory: Linearized potential flow equations, linearized pressure coefficient, linear two-dimensional subsonic flow, compressibility corrections, critical Mach number, linear supersonic two-dimensional flow (10 hours)
• Flow over airfoils: airfoil nomenclature and characteristics, Thin airfoil theory (symmetric and cambered airfoil case), Vortex Panel Numerical Method (8 hours)
• Flow over finite wings: downwash and induced drag, Vortex filament, Prandtl’s Lifting-Line Theory, Numerical non-linear lifting line method (5 hours)

Anderson, John David. Fundamentals of Aerodynamics. Fifth edition. McGraw-Hill, 2010.

Anderson, John David. Modern compressible flow: with historical perspective. Fourth edition. McGraw-Hill, 2020.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics.

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written and an oral test.
During the written test, students have two hours to solve two or three problems about the topics analyzed during the course.
Students will be admitted to the oral test upon successful completion of the written test. Knowledge about the main theoretical aspects of the course will be assessed during this second part of the exam.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence, and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension, and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a fluid without shear stress, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Fluid kinematics: Lagrangian and Eulerian frames of reference, definitions of pathlines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Fluid dynamics: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum, and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: the second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation (9 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations, and approximate solutions (7 hours).

Turbulence: description of the phenomenon, a short overview of the Reynolds equations (6 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, particular flow classes (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics.

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written and an oral test.
During the written test, students have two hours to solve two or three problems about the topics analyzed during the course.
Students will be admitted to the oral test upon successful completion of the written test. Knowledge about the main theoretical aspects of the course will be assessed during this second part of the exam.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence, and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension, and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of pathlines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum, and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: the second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation (9 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations, and approximate solutions (7 hours).

Turbulence: description of the phenomenon, a short overview of the Reynolds equations (6 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, particular flow classes (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body, thermodynamics, and fluid dynamics (properties of a fluid, substantial derivative, Reynolds transport theorem, conservation equation of mass, momentum, and energy).

The course aims at providing future aerospace engineers with basic knowledge of aerodynamics. The syllabus can be organized into two main parts.
The first part discusses the basic theory of one-dimensional and two-dimensional gas dynamics. Both steady and unsteady gas dynamics theory will be discussed while analyzing fundamental flows like de Laval nozzle, Fanno's flow, and Rayleigh's flow. The interactions of supersonic flows with airfoils will also be described using the shock-expansion theory and the thin airfoil theory.
The second part of the course deals with the description of irrotational flows. The potential flow theory will be presented and applied to canonical flows using the conformal mapping technique. The theory for linearized flows will be derived with particular attention to linearized compressible flows.

At the end of this course, students in aerospace engineers should have a good knowledge of: 
- one-dimensional unsteady as well as two-dimensional steady gas dynamics;
- basic principles of two-dimensional potential flow theory;
- principles of linearized flow theory in subsonic as well as supersonic regimes.

54 hours of lecture

An oral exam consisting of three questions.

• Recap of basic knowledge: conservation equation for a fluid, fluid properties (5 hours)
• Steady quasi-one-dimensional flow: general properties of quasi flows, total and critical quantities, area-velocity relation, mass flux, shock waves and Rankine–Hugoniot relations, convergent nozzles, convergent-divergent nozzles (7 hours)
• Steady non-isentropic one-dimensional flows: adiabatic flow with friction, flow with friction and heat exchange, Rayleigh's flow (4 hours)
• Two-dimensional gas dynamics: oblique shocks, Prandtl-Meyer expansions, shock polars, interactions between different waves, bow shocks, isentropic compressions and expansions, flow past a convergent-divergent nozzle, shock-expansion theory, thin-airfoil theory (9 hours)
• Potential flow theory: Kelvin and Helmholtz theorems, irrotational acyclic and cyclic flows, analytic functions of complex variables, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, conformal mapping, potential flow past a Joukowski airfoil (6 hours). 
• Linearized flow theory: Linearized potential flow equations, linearized pressure coefficient, linear two-dimensional subsonic flow, compressibility corrections, critical Mach number, linear supersonic two-dimensional flow (10 hours)
• Flow over airfoils: airfoil nomenclature and characteristics, Thin airfoil theory (symmetric and cambered airfoil case), Vortex Panel Numerical Method (8 hours)
• Flow over finite wings: downwash and induced drag, Vortex filament, Prandtl’s Lifting-Line Theory, Numerical non-linear lifting line method (5 hours)

Anderson, John David. Fundamentals of Aerodynamics. Fifth edition. McGraw-Hill, 2010.

Anderson, John David. Modern compressible flow: with historical perspective. Fourth edition. McGraw-Hill, 2020.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics.

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written and an oral test.
During the written test, students have two hours to solve two or three problems about the topics analyzed during the course.
Students will be admitted to the oral test upon successful completion of the written test. Knowledge about the main theoretical aspects of the course will be assessed during this second part of the exam.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence, and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension, and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of pathlines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum, and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: the second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation (9 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations, and approximate solutions (7 hours).

Turbulence: description of the phenomenon, a short overview of the Reynolds equations (6 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, particular flow classes (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics,

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written and an oral test.
During the written test, students have two hours to solve two or three problems about the topics analyzed during the course.
Students will be admitted to the oral test upon successful completion of the written test. Knowledge about the main theoretical aspects of the course will be assessed during this second part of the exam.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence, and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension, and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of pathlines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum, and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: the second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation (9 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations, and approximate solutions (7 hours).

Turbulence: description of the phenomenon, a short overview of the Reynolds equations (6 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, particular flow classes (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics,

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written test and an oral exam.

During the written test, the student has two hours to solve two or three problems about the topics analyzed during the course.

If the score in the first part of the exam is sufficient to pass, the student will be admitted to the oral exam where his knowledge about the main theoretical aspects of the course will be tested.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of path lines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, irrotational  acyclic and cyclic motions, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation, analytic functions of complex variables, conformal mapping, potential flow past a Joukowski airfoil (12 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations and approximate solutions (7 hours).

Turbulence: description of the phenomenon, short overview on the Reynolds equations (3 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, study of particular classes of flows (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics,

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written test and an oral exam.

During the written test, the student has two hours to solve two or three problems about the topics analyzed during the course.

If the score in the first part of the exam is sufficient to pass, the student will be admitted to the oral exam where his knowledge about the main theoretical aspects of the course will be tested.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of path lines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, irrotational  acyclic and cyclic motions, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation, analytic functions of complex variables, conformal mapping, potential flow past a Joukowski airfoil (12 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations and approximate solutions (7 hours).

Turbulence: description of the phenomenon, short overview on the Reynolds equations (3 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, study of particular classes of flows (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics,

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written test and an oral exam.

During the written test, the student has two hours to solve two or three problems about the topics analyzed during the course.

If the score in the first part of the exam is sufficient to pass, the student will be admitted to the oral exam where his knowledge about the main theoretical aspects of the course will be tested.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of path lines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, irrotational  acyclic and cyclic motions, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation, analytic functions of complex variables, conformal mapping, potential flow past a Joukowski airfoil (12 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations and approximate solutions (7 hours).

Turbulence: description of the phenomenon, short overview on the Reynolds equations (3 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, study of particular classes of flows (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.

Knowledge of calculus (derivatives and integrals), algebra (basic vector and tensor operations), dynamics of a rigid body and thermodynamics,

The course provides the basic tools to understand the motion of a fluid. The conservation equations that describe the dynamics of a fluid are analyzed in the case of inviscid and viscous flows. During this process, a description of the main fluid properties is provided as well as the continuum assumption and the definition of Eulerian and Lagrangian frames of reference. The derived equations are used in order to describe the motion of fluid in canonical configurations such as the Poisseuille flow (flow between flat plates), the Couette flow (flow between flat plates in relative motion), and the Hagen-Poisseuille flow (flow inside a pipe). The forces exchanged between the fluid and an immersed body are analyzed by means of the potential flow theory and boundary layer theory. During this course, the Buckingam PI theorem will be applied to canonical flows in order to derive a dimensionless description of the dynamics of the fluid. An outline about the main phenomena involving turbulence will also be provided.

After the course, a student should know:

• the main properties of a fluid;
• the basic equations that describe the static, kinematics and dynamics of a fluid;
• the principal physical phenomena involved in the motion of a fluid;
• the main interactions between a fluid and an immersed body.

54 hours of lecture

The exam consists of a written test and an oral exam.

During the written test, the student has two hours to solve two or three problems about the topics analyzed during the course.

If the score in the first part of the exam is sufficient to pass, the student will be admitted to the oral exam where his knowledge about the main theoretical aspects of the course will be tested.

Recap of basic knowledge: definitions of a scalar, vector, tensor, divergence operator, gradient operator, curl operator, divergence and Stokes theorems (1.5 hours).

Properties of a fluid: definition of a fluid, continuum hypothesis, density and thermal expansion, compressibility, viscosity, vapor tension, surface tension and capillary action (1.5 hours).

Statics of a fluid: pressure distribution in a steady fluid, standard atmosphere, pressure forces on a flat and curved surface, buoyancy, stability of a buoyant body, pressure gauges (6 hours).

Kinematic of a fluid: Lagrangian and Eulerian frames of reference, definitions of path lines, streamlines and streaklines, material derivative, e. Local flow analysis: simplified two-dimensional case, general three-dimensional case (3 hours).
Dynamic of a fluid: Reynolds transport theorem; integral and differential form of the conservation equations for mass, momentum and total energy; stress tensor; constitutive relations; Navier–Stokes equations; several expressions of the energy conservation equation (12 hours).
Bernoulli Equation: second law of the dynamics for an ideal fluid, the Bernoulli equation, the Crocco theorem, the Pitot tube, the Venturi tube (3 hours).

Potential flow theory: Kelvin and Helmholtz theorems, irrotational  acyclic and cyclic motions, two-dimensional potential flows (uniform flow; source/sink; vortex, doublet), superposition of simple flows, flow past a circular cylinder without and with circulation, analytic functions of complex variables, conformal mapping, potential flow past a Joukowski airfoil (12 hours).

Exact solutions of the Navier-Stokes equations: flow between two parallel flat plates, the Couette flow, the Hagen–Poiseuille flow (3 hours).

Boundary layer theory: Boundary-layer equations, integral equations and approximate solutions (7 hours).

Turbulence: description of the phenomenon, short overview on the Reynolds equations (3 hours).

Dimensional analysis and similitude: Buckingham PI theorem, dimensional analysis, dynamic similarity, study of particular classes of flows (immersed bodies; with a free surface) (2 ore).

[1] Irving H. Shames, Mechanics of Fluids, McGraw-Hill International editions
[2] Barnes W. McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley.