FLUID MECHANICS

By the end of the course, students will have acquired a basic knowledge of fluid mechanics and its associated theoretical framework. They will also be able to apply the principles of fluid mechanics to solve engineering problems relating to fluid statics and dynamics. These problems include:

- calculating the forces exerted by fluids in static and dynamic conditions;
- determining the characteristics of fluid flow and calculating resistances;
- using instruments to measure fluid dynamic quantities;
- calculating a pipeline;
- calculating a pumping system;
- determining the power of a turbine in a hydroelectric plant.

Studying fluid mechanics will stimulate the development of critical and analytical skills that can be applied to subsequent degree programmes and professional life.

The acquired skills can be applied to a wide range of fields, including industrial and civil engineering. These skills are particularly useful in the renewable energy sector, where wind and water power are used to help achieve goals 7, 11, 12 and 13 of the 2030 Agenda. These skills can also be applied in the water resources sector in line with goal 6.

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

If teaching is carried out remotely or in blended mode, any previous statements may need to be amended to align with the programme 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.

Denomination: Fluid Mechanics

Introduction to the course. Definition of fluid substance. The continuum hypothesis. Dimensions and measurement units. Mass forces and surface forces. The 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 and control volumes. Lagrangian and Eulerian approaches. Local and material derivatives. Velocity and acceleration.  The Reynolds transport theorem. Trajectories. Streamlines. Smoke lines. Flux tube. Steady flow. Unsteady flow. Uniform flow. Two-dimensional flow. The continuity equation in differential form. The continuity equation in global form. The continuity equation for currents. Rotation and deformation of fluid elements. Irrotational flows.

Fluid dynamics

The momentum equation in differential form.  The Euler equation.  Boundary conditions. The momentum equation in global form. The Euler equation in the intrinsic coordinate system of the trajectory. Pressure distribution in gradually varied currents. Bernoulli's theorem. Geometric representation of Bernoulli's theorem. The energy implications of Bernoulli's theorem. The mechanical energy equation. Outflow phenomena. Extension of the 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. Localised head losses. The constitutive relationship of viscous fluids. The Navier–Stokes equations. The momentum equation of viscous fluids in global form.
 

Confined flows

Reynolds' experiment: the laminar and turbulent regimes. The Reynolds number. Tangential stresses in uniform flow. Laminar flow in a pipe. The Poiseuille formula. Laminar flow between parallel plates. Turbulent flow. The mean flow equation. Viscous and turbulent shear stresses. Application of the Buckingham theorem to determine the resistance law formula. The Darcy–Weisbach formula. Friction factor. Flow in smooth pipes. Friction factor in smooth pipes. The mean velocity distribution of turbulent flow in smooth pipes. Flows in rough pipes. Nikuradse's experiments. Friction factor in rough pipes. Velocity distribution in turbulent flow in rough pipes. Commercial pipes. The Colebrook and White formula. Moody chart. Empirical formulas for calculating head losses. Localised head losses. Head loss due to abrupt enlargement and sharp-edged inlets and outlets 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 online via the Studium platform throughout the course.

The examinations consist of written and oral tests. The written test involves solving fluid mechanics problems numerically and answering a theoretical question. There are ten questions in total. Students who achieve a score of 15/30 or higher in the written test will be admitted to the oral test.

Three written tests will be held during the course. Students who have attended at least 70% of the lectures held by the date of the test are eligible to take these tests.

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.

The results of ongoing assessments only apply to 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.