Water is a key element in the field of agriculture. It is necessary for the growth of plants, and can be used to carry fertilizers and phytopharmaceutical products. Nonetheless, water can carry and contribute to the spread of pathogens harmful for human health or the crop itself, as well as of phytopharmaceutical products back to the environment. It is clear that technologies for more sustainable crop productions cannot disregard/forget the role of water (and, more in general, of fluids) in agriculture. In this picture, the aim of the course is to provide a basic knowledge of fluid mechanics. The focus will be on phenomena and related applications more relevant to the field of agriculture. The course will first provide a basic theoretical knowledge of fluid static and fluid dynamics. From this basic knowledge, more applied topics will be derived and discussed: hydrostatic, perfect fluids, turbulence and its effect on dispersion, distribution of water by pressure pipe systems, open channel flow, filtration, boundary layer and bluff bodies, droplet dynamics and water-driven spread of pathogens.

Upon completion of this course, students should be able to: • Interpret the properties that distinguish fluids from other forms of matter, and the broad range of engineering applications which involve fluid mechanics. • Apply the concepts of vector fields (velocity, force acceleration), scalar fields (pressure, density, temperature), and vector differential and integral calculus to engineering analysis of fluids systems, and to the interpretation of flow physics through the conservation laws. • Apply Newton's second law to analysis and design involving fluids at rest using integral and differential calculus, including pressure variation, forces and moments on plane surfaces, and buoyancy. • Interpret and apply the various differential forms of the conservation laws, particularly Newton's law and its various approximate forms, to engineering analysis and design. • Interpret and apply the "inviscid" approximation and the "Bernoulli" relationships to analysis of fluid systems. • Interpret and apply the "Navier-Stokes" equations to analysis of fluid systems. • Apply the “Dimensional analysis” to analysis of fluid systems. • Interpret and apply laminar and turbulent flow models. • Calculate head loss and power requirements in piping systems. • Assess the hydraulic behavior of piping systems (evaluation of flow rate, evaluation of the conditions for the safe operation of the system) • Design a pumping system, taking into account hydraulic and energy issues. • Calculate normal flow conditions in open channels. • Interpret and apply the concepts of “sub-critical” and “super-critical” flow conditions. • Assess the hydraulic behavior of open channel flow systems (qualitative evaluation of backwater profiles). • Apply “Darcy’s law” to analysis of flow in porous media. • Apply empirical and theoretical models to the analysis of boundary layer flows, and to drag and lift on bluff bodies. • Apply empirical and models to the analysis of droplet dynamics (especially impact of droplets on surfaces) and relate this dynamics to the water-driven spread of pathogens.

Basic knowledge of calculus, in particular: • Concepts of ordinary and partial differential equations • Derivation rules • Analytical solution of simple ordinary differential equations • Integrals (indefinite integrals; definite integrals; line, surface, and volume integrals). Green, Stokes, and Gauss’s theorems. Basic knowledge of linear algebra, in particular: • Concepts of vector and tensor • Vector operations Basic knowledge of physics and mechanics, in particular: • Particles kinematics • Newton’s second law • Concepts of vector and scalar fields • Concepts of gradient of a scalar and vector field; divergence and curl of a vector field. A self-assessment test covering these prerequisites will be provided before the beginning of the course. Online tutorial and additional exercises will also be provided.

This course is an introduction to fluid mechanics, and emphasizes fundamental concepts and problem-solving techniques. Due to the nature of the program, special emphasis will be put on applications to agricultural problems. Topics to be covered include: • fluid properties, • continuity and momentum equations of an infinitesimal control volume of fluid, • hydrostatic and floating, • fluid kinematics, • perfect fluids (special emphasis on agricultural tools such as sprinklers and differential pressure injectors), • real fluids and Navier Stokes equations, • Reynolds experiment and Dimensional analysis, • laminar flow regime, • turbulence (special emphasis on dispersion of pollutants, pathogens, phytopharmaceutical products and accuracy of weather forecast), • pressure pipe systems (fundamentals such as head loss evaluation, evaluation of flow rate, evaluation of the conditions for the safe operation of the system). Special emphasis will be given on economics and examples of hydraulics of irrigation systems, • pumping systems (sizing of pumps and evaluation of the conditions for the safe operation of the system to avoid pump cavitation). Special emphasis will be given on economical aspects and variable speed pump technology, • fundamentals of open channel flow (fundamentals such as normal flow conditions, “sub-critical” and “super-critical” flow condition, qualitative evaluation of backwater profiles). Special emphasis will be given on examples of irrigation systems, • flow in porous media and the “Darcy’s law”, • fundamentals of boundary layer flows, and to drag and lift of bluff bodies, • fundamentals of droplet dynamics (especially impact of droplets on surfaces). Special emphasis will be given on the effect of droplets impact on the spread of pathogens in crops.

The course is divided in lectures and tutorials. Tutorials are targeted to deepen the understanding of the concepts that are addressed in the lectures. Additional activities will also be planned (e.g., lab @ home on selected topics, visit to the laboratory of hydraulics).

Fluid Mechanics: Fundamentals and Applications. Second Edition in SI Units. Y.A. Çengel and J. M. Cimbala, McGraw-Hill, New York, 2010.

Slides; Esercizi; Strumenti di simulazione; Strumenti di auto-valutazione;

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... The exam (duration 2 hours) is WRITTEN ONLY and includes numerical problems as well as theoretical questions. Theoretical questions may consist in the derivation of formulas. Students are allowed to bring only a pen and a calculator. Lengthy empirical formulas will be provided in the exam script, and the list of provided formulas will be made available to students. The exam is passed provided that a minimum score of 18/30 is achieved. Additional activities can provide additional points (to be determined based on the type of activity and on the quality of the delivered reports). Points from additional activities will be awarded only if the minimum score of 18/30 is achieved at the written exam.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.