Bearing in mind that fluid mechanics is a basic theoretical science, it is the goal of the course to familiarize students with the basic laws of maintenance: matter, motion and energy and to master some methods of solving flow problems. That is why different mathematical methods are studied in the course based on: analytical approach (if possible, solution development in order, various transformations, similar solutions, etc., with which it is possible to arrive at flow solutions in some practical, relatively simple cases or geometries ).

As a result of studying fluid mechanics courses, PhD students are familiar with the methods of correct application of equations and calculation methods. Due to the complexity of the basic system of equations describing flow, it is necessary for researchers, when solving specific cases of flow, to identify ways of simplifying the initial system of equations and under what assumptions this applies; then to recognize the possible application of some of the existing analytical or approximation methods, and to acquire a general higher level of knowledge so that they can correctly interpret the results obtained from the calculation.

Introductory considerations: voltage state in fluid, rheological models. Basic equations: continuity, Navija-Stokes and energy in conservative and non-conservative form. Boundary and initial conditions. Some correct solutions of the NS equation: stationary flow around the sphere (Stokes and Ozen solution), non-stationary flow around the sphere, flow between parallel plates with variable fluid temperature. Stationary laminar flow through non-circular tubes and ducts. Methods for solving the basic system of differential equations. The concept of linearization of equations. Method of solution development in order.Метода уопштене сличности: примери нестационарног ламинарног струјања преко равне плоче и нестационарно струјање раванског вртлога. Теорија хидродинамичког подмазивања: уопштене Рејнолдсове једначине за слој подмазивања, примери ламинарног струјања у раваском и осносиметричном лежају. Теорија граничног слоја: Прантлове једначине, интегралне једначине граничног слоја, метода Карман-Полхаузена, гранични слој на равној плочи без (Блазијусово решење) и са градијентом притиска (Бокс-Келерова метода). Compressible laminar boundary layer, application of Stuartson transformations and Crock transformations. An axisymmetric laminar jet. Turbulent flow: averaging modes, Reynolds equations. Methods of modeling turbulent stresses: algebraic and differential: l-mixing path, k-l model, k-epsilon model, k-omega model, etc. Turbulence scales. Kolmogorov theory and turbulence energy spectrum. Spatio-temporal correlations. Turbulenni boundary layer. Flow in a turbulent plane and axisymmetric jet.

Introduction to relevant literature in fluid mechanics - books and scientific journals. Creation of seminar papers from various current fields of research.

It is imperative that undergraduate students have attended basic FLUID MECHANICS courses

In fluid mechanics, for the purpose of acquiring profound skills, there are many good foreign books available in the library of the Faculty of Mechanical Engineering, or available online, so that the course is completely littered with literature. To monitor contemporary achievements, it is necessary to use the leading journals in the library: Fluid Mechanics, Physics of Fluid, and others.

Total assigned hours: 65

New material: 50
Elaboration and examples (recapitulation): 0

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 0
Test: 10
Final exam: 5

Activity during lectures: 5
Test/test: 25
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 70
Requirement for taking the exam (required number of points): 0

Saljnikov V., (1969): Dynamics of a viscous incompressible fluid, Faculty of Mechanical Engineering, Belgrade. (in Serbian); Čantrak S., (2012): Hydrodynamics, Faculty of Mechanical Engineering, Belgrade (in Serbian); Crnojević C., (2014): Fluid Mechanics, Faculty of Mechanical Engineering, Belgrade (in Serbian); Čantrak S., Ćocić A. (2022): Fluid mechanics - physics of phenomena, Faculty of Mechanical Engineering, Belgrade