FLUID MECHANICS

The main objective of the course is to provide the basic knowledge of fluid mechanics. After a preliminary part where the physical characteristics of the fluids are described with particular emphasis to those that distinguish them from the solids, the course introduces the fundamental topics of fluid mechanics, accompanied by the necessary theoretical framework. The course also includes lessons to be dedicated to carrying out exercises in the classroom, relating to the application of the principles of fluid mechanics to the solution of engineering problems.

Introduction to the course

Definition of fluid substance. The continuum hypothesis. Quantities and measurement units. Mass forces and surface forces. Stress tensor and its properties. Fluid properties: compressibility, thermal elasticity, surface tension, viscosity. Non-Newtonian fluids. Gas absorption.
Fluid statics
Stress in fluids at rest. Equations of fluid statics in differential form. Equation of fluid statics in global form. Statics of incompressible fluids under the action of gravity force. Pressure measurements. Forces applied on plane surfaces. Forces applied on curved surfaces. Statics of fluids in a non-inertial reference frame.

Kinematics.

Generalities on the fluid kinematic. Eulerian and Lagrangian approaches. Velocity and acceleration. Visualization of the flow field. Trajectories. Streamlines. Smoke lines. Flux tubes. Types of fluid motions. Permanent flows. Unsteady flows. Uniform flows. Two-dimensional flows. Flow regimes. Laminar flows. Turbulent flows. Continuity equation in differential form. Continuity equation for a fixed control volume. Continuity equation for a current. Rotation and deformation rate of fluid elements.
Fluid dynamics: the momentum equation
Momentum equation in differential form. Euler equation. Boundary conditions. Momentum equation in global form.
Bernoulli's theorem
Bernoulli's theorem. Pressure distribution. Geometric representation of Bernoulli’s theorem. Energy implications of Bernoulli's theorem. Outflow phenomena. Venturi tube. Pitot tube. Extension of Bernoulli's theorem to real fluids. Head losses. Extension of Bernoulli's theorem to a current. Energy exchange between a current and a machine.

The equations of motion of viscous fluids
Constitutive equations of viscous fluids. The Navier-Stokes equations. Momentum equation of viscous fluids in global form.
Pressurized flows
Drag force exerted by a current on a pipe. Tangential stress. Laminar flow in a pipe of circular section. Poiseuille formula. Flow between flat parallel plates. Turbulent flow. The mean flow equation. Viscous and turbulent shear stresses. Application of the Buckingham theorem for the determination of the form of the resistance law. Darcy-Weisbach formula. Resistance index. Flow in smooth pipes. Resistance index in smooth pipes. Mean velocity distribution of a turbulent flow in a smooth tube. Flows in rough pipes. Resistance index in rough pipes. Notes on the velocity distribution in a turbulent flow in a rough tube. Moody chart. Practical formulas for the calculation of the flow resistances. Localized head losses. Dissipations of energy because of abrupt enlargement, sharp-edged inlet and outlet in a reservoir. Flows subject to negative pressure.

1) D. Citrini, D. Noseda "Idraulica", CEA Milano, 1987

2) G. Alfonsi, E. Orsi "Problemi di Idraulica e Meccanica dei Fluidi" CEA Milano, 1984.

3) G. Pezzinga "Esercizi di Meccanica dei Fluidi" Aracne editrice, 2008.

4) Notes provided by the teacher available during the course on the Studium platform.