Programme

Physical properties of fluids
• Density and Compressibility
• Vapor pressure
• Viscosity
• Surface tension

Statics of Fluids
• Stress in one point and dependence on position
• Fundamental equation of fluid statics
• Equilibrium of a finite mass of fluid at rest
• Effects of compressibility on the pressure distribution in a fluid at rest subjected to the force of gravity
• Hydrostatic thrust on a flat surface
• Hydrostatic thrust on a curved surface
• Rigid motion of a liquid. Relative balance

Fluid kinematics
• The material derivative
• Reynolds' theorem
• The velocity field around a point

Fluid dynamics
• Mass conservation equation
 Integral form
 Differential form
• Constitutive relationships
• Equation of conservation of momentum
 Integral form
 Differential form
• Euler's equation and its projection on the intrinsic triad
• Conservation of total energy in a non-ideal fluid
• Momentum conservation equation

Applications of Bernoulli's theorem and of the momentum conservation equation in integral form
• Behavior of the piezometric height in the stationary motion of a liquid in a curved axis pipe
• Applications of Bernoulli's theorem
 Outflow from a circular hole on the bottom of a tank
 Outflow from raised rectangular bulkhead on the bottom of a channel
 Outflow from rectangular opening on vertical wall
 Pitot tube
 Venturi tube
• Applications of the momentum conservation equation in integral form
 Thrust exerted by a free jet on a curved blade
 Drag force acting on a body immersed in a uniform current
 Propeller
 Torque acting on the shaft of a hydraulic machine

Uniform and stationary motion in pipes
• Equations of motion
• Time averaging in the turbulent regime
• The laminar regime
• Turbulent regime
• Experimental determination of the drag coefficient
• Concentrated pressure drops

Dimensionless form of the equations of motion

Motions at low Reynolds numbers
• Motion between flat parallel plates
• Hydrodynamic lubrication
• Stationary and uniform motion in a cylindrical tube
• Sphere hit by a uniform current of a viscous fluid
• Motion between concentric cylinders

Boundary layer
• Introduction
• The boundary layer equations
• Boundary layer on flat slab
• Pressure Gradient Effects – Boundary Layer Detachment
• Forces acting on bodies immersed in a uniform current
• Flow around a cylinder as the Reynolds number increases
• Integral equation of the boundary layer

Ideal fluids
• Equations of motion
• Irrotational motion
• 2D irrotational motion
• Uniform motion and source/sink potentials
• Free vortex potential
• Doublet potential
• Flow around a semibody
• Flow around a cylinder
• Force exerted on a body immersed in a uniform current

Compressible fluids
• Regimes of movement
• Stationary isentropic flow of an ideal gas
• Stagnation pressure
• Mass flow flowing in a convergent-divergent (Venturi tube)
• Flow in a convergent-divergent (Venturi tube)
• Stationary flow of an ideal gas in a long tube with constant section
• Normal shock wave

Core Documentation

Lecture notes and exercises distributed by the teacher.

Reference Bibliography

1. M Mossa, AF Petrillo, Idraulica, Casa Editrice Ambrosiana 2. D Citrini, G Noseda, Idraulica, Casa Editrice Ambrosiana 3. AC Yunus, JM Cimbala, Fluid mechanics: fundamentals and applications, International Edition, McGraw Hill Publication, 2006 4. BR Munson, AP Rothmayer, TH Okiishi, WW Huebsch, Fundamentals of Fluid Mechanics, Wiley & Sons, 7th edition, 2012 5. BE Larock, RW Jeppson, GZ Watters, Hydraulics of pipeline systems, CRC press, 2000 6. MH Chaudry, Applied Hydraulic Transients, Springer, 2014 7. EB Wylie, VL Streeter, Hydraulics Transients, Mc Graw Hill, 1967 8. GK Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, 1967 9. LD Landau, EM Lifshitz, Fluid Mechanics, Pergamon Press, 1987 10. SB Pope, Turbulent Flows, Cambridge University Press, 2000 11. E Marchi, A Rubatta, Meccanica dei Fluidi. Principi e applicazioni idrauliche, UTET

Type of delivery of the course

The lessons will take place in presence and simultaneously on the Teams platform.

Attendance

Attendance is optional, but strongly recommended.

Type of evaluation

The exam can take place in two distinct ways: Evaluation in progress through two written exemption tests, each consisting of the solution of two exercises and the discussion of a topic proposed by the teacher. If both ongoing tests are sufficient (evaluation greater than or equal to 18/30) the final result is the arithmetic mean of the two results. Evaluation in a single solution to be carried out during the exam sessions foreseen by the academic calendar, consisting of a written test which provides for the solution of three exercises and a subsequent oral test, which can be accessed if the written test is sufficient (higher evaluation or equal to 18/30) and in which a topic proposed by the teacher must be illustrated.