Programme

Physical Properties of Fluids
 Density and Compressibility
 Vapor Pressure
 Viscosity
 Surface Tension
 Fluid Statics
 Stress at a Point and Dependence on Direction
 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 Gravity
 Buoyancy on a Flat Surface
 Buoyancy on a Curved Surface
 Rigid Motion of a Liquid. Relative Equilibrium

Fluid Kinematics
 The Material Derivative
 Reynolds' Theorem
 The Velocity Field Around a Point

Fluid Dynamics
 Conservation of Mass Equation
 Integral Form
 Differential Form
 Constitutive Relations
 Conservation of Momentum Equation
 Integral Form
 Differential Form
 The Euler Equation and Its Projection onto the Intrinsic Triple
 Conservation of Total Energy in a Nonideal Fluid
 Conservation of Momentum Equation

Applications of Bernoulli's theorem and the integral motion equations
 Behavior of the piezometric head in the steady flow of a liquid in a curved-axis tube
 Applications of Bernoulli's theorem
 Outflow from a circular hole at the bottom of a tank
 Outflow from a raised rectangular bulkhead at the bottom of a channel
 Outflow from a rectangular opening on a vertical wall
 The Pitot tube
 The Venturi tube
 Applications of the integral momentum conservation equation
 Thrust exerted by a free jet on a curved blade
 Drag force acting on a body immersed in a uniform flow
 Propeller
 Torque acting on the shaft of a hydraulic machine

Dimensionless Form of the Equations of Motion
Flows at Low Reynolds Numbers
 Steady Flow between Parallel Flat Plates
 Hydrodynamic Lubrication
 Sphere Impinged by a Uniform Flow of a Viscous Fluid
 Steady Flow of an Incompressible Viscous Fluid
inside a Pipe
 Steady Flow between Coaxial Circular Cylinders
Rotating

Boundary Layer
 Introduction
 Boundary Layer Equations
 Boundary Layer on a Flat Plate
 Effects of Pressure Gradients – Boundary Layer Detachment
 Forces Acting on Bodies Immersed in a Uniform Flow
 Flow Around a Cylinder as the Reynolds Number Increases
 Boundary Layer Equations in Integral Form

Ideal Fluids
 Equations of Motion
 Irrotational Flow
 2D Irrotational Flow
 Uniform Flow and Source/Sink Potentials
 Free Vortex Potential
 Doublet Potential
 Flow Around a Half-Body
 Flow Around a Cylinder
 D'Alembert's Paradox in Three-Dimensional Space

Uniform and steady flow in pipes
 Equations of motion, flow regimes
 Time averages in the turbulent regime
 The laminar regime
 Turbulent regime
 Experimental determination of the drag coefficient
 Concentrated pressure drops

Compressible Fluids
 Flow Regimes
 Steady Isentropic Flow of an Ideal Gas
 Stagnation Pressure
 Mass Flow Rate in a Convergent-Divergent Venturi Tube
 Flow in a Convergent-Divergent Venturi Tube
 Steady Flow of an Ideal Gas in a Long Tube with Constant Cross-Section
 Normal Shock Wave

Core Documentation

Lecture notes and exercises distributed by the teacher.

Reference Bibliography

1. 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

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 three written exemption tests, each consisting of the solution of two exercises and the discussion of a topic proposed by the teacher. If all the 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.