• Mechanics, Semester 2, position 2

Aims of the course is to introduce students to basic principles and laws in fluid mechanics. Deeper understanding of basic equations of fluid mechanics allows the student to successfully apply them in process of finding the solution to specific engineering problems, and also improves his scientific and practical development.

Students are trained to: - apply the basic equations of fluid mechanics ie. equations of continuity, momentum and energy to describe the one-dimensional compressible fluid flow, two-dimensional potential incompressible fluid flow and fluid flow in the boundary layer; - calculate one-dimensional subsonic and supersonic compressible fluid flow, such as: isentropic flow, adiabatic and isothermal flow with friction, inviscid gas flow with heat transfer, shock wave as well as the gas flow through the convergent and Laval nozzle; - determine the velocity and pressure field for potential incompressible fluid flow which enables them to calculate forces which act on the contour in inviscid fluid stream. Also, based on acquired knowledge, by applying complex potentials, they can form complex flows which enable obtaining the desired contour shape and force which act on it; - solve the boundary layer equations for flow over a flat plate and calculate friction shear stress at the plate surface, and therefore the drag force. - modeling the turbulent flow by using the theory of turbulent flow and turbulent stresses models.

Physical and mathematical models, principles and phenomena of fluid mechanics. Physical and mathematical foundations of fluid mechanics. Forces, the general state of stress and stress models in fluids. General equations in fluid mechanics. Laws of conservation. Conservation of mass, momentum and energy. Dynamics of inviscid fluid. Two-dimensional potential flow of inviscid fluid. Application of hydrodynamic singularities and theory of analytical functions of complex variable. Basic and complex potential flows. Combined straight line flow and sink, doublet. Flow past a cylinder. Kutta-Joukowski`s low. Dynamics of viscous flow. Navier-Stokes equation. Steady, laminar flow of Newtonian incompressible fluid. Exact analytical solutions of the Navier-Stokes equation. Hydrodynamic lubrication theory. Turbulent flows of incompressible fluid. Reynolds equation. Turbulent stress models. Turbulent flow in a hydraulically smooth and hydraulically rough pipe. Application of momentum equation: turbo-reactive jet engine, Euler`s equation for turbo-machines, Pelton turbines. Boundary layer theory. Prandtl theory. Boundary layer over a flat plate. Application of integral methods to boundary layer calculation. One-dimensional model of fluid flow. Basic equations of one-dimensional flow. One-dimensional flow of incompressible fluid. One-dimensional flow of compressible fluid. Mach number. Adiabatic and isothermal compressible flow with friction. Shock waves. Inviscid gas flow with heat exchange. Gas flow in the convergent, divergent and Laval nozzle.

One-dimensional viscous incompressible flow. Methods of calculation of complex pipe networks. Hydraulic jump. Cavitations in turbo-machines and pipes. One-dimensional invisced and viscous compressible flow through pipes and jets. Adiabatic and isothermal compressible flow with friction. Shock waves. Dimensional analysis and similarity theory. Drag and lift forces. Two-dimensional ideal flow. Stream function, velocity potential. Applications of Cauchy-Riemman equations. Basic and complex potential flows. Joukovsky function. Exact solutions of Navier-Stokes equations. Basic theory of hydrodynamic lubrication. Turbulent flows modelling. Fully developed turbulent flow in hydraulically smooth and rough pipes. Prandtl equations of boundary layer. Integral methods application to boundary layer calculation.

Passed exams in following subjects: Fluid Mechanics B.

Books of professors from the department, laboratory equipment; printed and hand-written materials (handouts).

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 28
Laboratory exercises: 2
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: 2
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 5
Test: 3
Final exam: 5

Activity during lectures: 0
Test/test: 45
Laboratory practice: 5
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 20

Crnojevic C., Fluid Mechanics (in Serbian), 2014, Faculty of Mechanical Engineering, University of Belgrade, ISBN: 978-86-7083-846-8; Cantrak S., Hydrodynamics (in Serbian), 2012, Faculty of Mechanical Engineering, University of Belgrade, ISBN: 978-86-7083-770-6; Djordjevic V., Dynamics of One-Dimensional Fluid Flows (in Serbian), 2005, Faculty of Mechanical Engineering, University of Belgrade, ISBN: 86-7083-526-6; Crnojevic C., Classical and Oil Hydraulics (in Serbian), 2006, Faculty of Mechanical Engineering, University of Belgrade, ISBN: 86-7083-555-X; Cantrak S., Benisek M., Pavlovic M., Marjanovic P., Crnojevic C., Fluid Mechanics, Theory and Practice, 2005, Faculty of Mechanical Engineering (in Serbian), University of Belgrade, ISBN 86-7083-531-2