FLUID MECHANICS

On completion of the course, the student will have acquired the fundamental knowledge of Fluid Mechanics together with the necessary theoretical framework. In addition, he/she will be able to apply the principles of Fluid Mechanics to the solution of static and dynamic fluid problems of engineering relevance, such as:
calculation of the forces exerted by fluids under static and dynamic conditions, determination of the characteristics of a fluid flow and calculation of resistances, use of instruments for measuring fluid dynamic quantities, calculation of a pipeline, calculation of a lifting plant, determination of the power of a turbine in a hydroelectric plant.

In approaching the study of Fluid Mechanics, the student is encouraged to develop critical and analytical skills that may be useful in subsequent subjects of the degree programme and in professional life.

The teaching will be carried out through lectures and classroom exercises.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Prior knowledge of Physics, Rational Mechanics, Mathematical Analysis and Algebra are important.

Attendance of at least 70% of the lessons is required.

Introduction to the course

Definition of fluid substance. The continuum hypothesis. Dimensions 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. Stevin's law. Pressure measurements. Hydrostatic thrusts on plane surfaces. Hydrostatic thrusts on curved surfaces. Hydrostatic thrusts on immersed body. Fluids of low specific weight.

Fluid kinematics

Generalities on fluid kinematics. Material volume and control volume. Lagrangian and Eulerian approaches. Local derivative and material derivative. Velocity and acceleration.  The Reynolds transport theorem. Trajectories. Streamlines. Smoke lines. Flux tube. Steady flow. Unsteady flow. Uniform flow. Two-dimensional flow. Continuity equation in differential form. Continuity equation in global form. Continuity equation for currents. Rotation and deformation of fluid elements. Irrotational flows.

Fluid dynamics

Momentum equation in differential form. Euler equation. Boundary conditions. Momentum equation in global form. Example of application.
Euler equation in the intrinsic coordinate system. Pressure distribution in gradually varied currents. Bernoulli's theorem. Geometric representation of Bernoulli’s theorem. Energy implications of Bernoulli's theorem. Mechanical energy equation. Outflow phenomena. Extension of Bernoulli theorem to a current. Exchange of energy between a current and a machine. Venturimeter. Pitot tube. Extension of Bernoulli's theorem to real fluids. Continuous head losses. Localized head losses.
Constitutive relationship of viscous fluids. The Navier-Stokes equations. Momentum equation of viscous fluids in global form.
 

Confined flows
Reynolds experiment. Flow regimes. Laminar regime. Turbulent regime. The Reynolds number. Tangential stresses in uniform flow. Laminar flow in a pipe. Poiseuille formula. Laminar flow between parallel plates. Turbulent flow. The mean flow equation. Viscous and turbulent shear stresses. Application of the Buckingham theorem to the determination of the resistance law formula. Darcy-Weisbach formula. Friction factor. Flow in smooth pipes. Friction factor in smooth pipes. Mean velocity distribution of a turbulent flow in a smooth pipe. Flows in rough pipes. Nikuradse's experiments. Friction factor in rough pipes. Velocity distribution in turbulent flow in a rough pipe. Commercial pipes. Colebrook and White formula. Moody chart. Empirical formulas for the calculation of the head losses. Localized head losses. Head loss due to abrupt enlargement, sharp-edged inlet and outlet in a reservoir. Flows subject to negative pressure.

1) Y. A. Cengel, J.M. Cimbala "Meccanica dei Fluidi " Quarta Edizione, McGraw-Hill.

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.

The examinations consist of a written and an oral test. The written test consists of the numerical solution of fluid mechanics problems and the answer to a theoretical question. There are 10 questions in total. The student will be admitted to the next oral test if he/she scores 15/30 or higher in the written test.

There are three written tests during the course. Students who, on the day of the test, have attended at least 70% of the lessons of the course already held will be admitted to the test.

In each test the student shall report a mark expressed out of thirty. If the mark given in each test is greater than or equal to 12/30 and the average of the marks given in the three tests is greater than or equal to 15/30, the student will be admitted to the next oral test.

Test results taken during the course are only valid for the examination session immediately following the end of the course.

In one of the examination sessions immediately following the end of the course, the student has the option of repeating one of the three written tests taken during the course. The mark obtained in this test will be added to the marks obtained in the other two tests and, if the average is greater than or equal to 15/30, and in none of the tests does the student obtain a mark lower than 12/30, he/she will be admitted to the next oral test.

Verification of learning can also be carried out electronically, should the conditions require it.

As a guarantee of equal opportunities and in compliance with the laws in force, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures, based on their educational objectives and specific needs.

They can also contact the CInAP (Centre for Active and Participatory Integration - Services for Disabilities and/or SLDs) reference teacher in their Department.

Differential equation of statics. Plotting of the pressure diagram in hydrostatic conditions. Hydrostatic thrusts. Equation of momentum. Bernoulli's theorem. Resistances in confined currents. Viscous and turbulent tangential stresses. Calculation of a pumping plant. Turbine power in a hydroelectric plant.