At the end of the course, students will be able to -Apply the concepts of vector fields (velocity, force acceleration), scalar fields (pressure, density, temperature) and differential and integral calculus to engineering analysis of fluids systems. -Properly apply systems and control volume methods based on mass, momentum, and energy conservation, as appropriate, to the analysis and design of engineering fluids systems. -Correctly interpret and apply the various differential forms of the conservation laws. -Properly apply mass, momentum, and energy conservation to steady internal (pipe) flows and estimate head loss and power requirements (pumps) in piping systems. -Develop mathematical models through justifiable approximations. Correctly interpret and apply the "inviscid" approximation and the "Bernoulli" relationships to analysis of fluid systems, and estimate levels of approximation in engineering models. -Apply energy, mass and momentum balance principles to qualitatively and quantitatively assess the behaviour of open channel flows

Differential, integral and vector calculus: integrals, derivatives, operations with vectors, basic knowledge of tensors and invariants, operations with matrices. Physics: basic concepts of classical mechanics: Newton's laws of mechanics, forces and moments, moments of inertia

Fluids and their characteristics. Definition of fluid; continuum approximation; properties of fluids; strain rates, strain-stress relation and newtonian fluids; equation of state; stress state and Cauchy theorem; definition of pressure and incompressibility hypothesis. Fluid statics. Local and global force balances; Stevin's law; pressure measurement devices; resultant on plane surfaces and curved surfaces; buoyancy. Kinematics. Eulerian and Lagrangian approaches. Material derivative and Eulerian acceleration; streamilines, streaklines, trajectories; streamtubes. Reynolds Transport theorem; mass conservation; energy conservation: Bernoulli's theorem and its applications and extensions. Power of a stream. Integral equation for momentum conservation; Dimensional analysis and Pi-Theorem; pipe flows: laminar, transitional and turbulent flows, Reynolds number and relative roughness. Wall shear stress, Hagen-poiseuille theory; darcyweisbach friction factor in laminar and turbulent flows; compuation of major losses; minor losses; brief consideration on pipe networks; pumps and pipe systems; biref introduction to water hammer issues and computation of rapid vs slow closures. Differential flow analysis: introduction to CFD and engineering applications. mass conservation in differential form; vorticity, strain rate tensor; Cauchy equation and Navier Stokes equation; boundary conditions. Open channel flows. Basic concepts; de Saint Venant equations; uniform motion (including compound channels); critical motion; Specific energy and Froude number; critical slope. Steady flows; water surface profiles; hydraulic jump; important examples of applications; flow measurements with weirs. Flows in porous media and filtration; Darcy equation; hydraulic conductivity tensor; analytical solutions.

The course is divided in lectures and tutorials. Tutorials are targeted to deepen the understanding of the concepts that are addressed in the lectures. Visits to the laboratory of Hydraulics and Fluid Mechanics as well as in the field will also be scheduled.

The slides of the curse will be made available on the Polito Teaching Portal https://didattica.polito.it Suggested reading: Fluid Mechanics: Fundamentals and Applications. Second Edition in SI Units. Y.A. Çengel and J. M. Cimbala, McGraw-Hill, New York, 2010.

Exam: Written test;

The exam is WRITTEN ONLY and includes numerical problems as well as theoretical questions that the students have to address in 2 HOURS. The students are allowed to bring only a pen and a calculator (lengthy empirical formulae will be always provided in the exam script). The exam is passed provided that a minimum score of 18/30 is achieved.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.