Fluid mechanics 1

The objective of the course is to introduce students to the basic principles and laws in the field of fluid flow science. A fundamental understanding of the core equations of fluid mechanics enables students to successfully apply them in practice to solve specific engineering problems, as well as to support their further academic and professional development.

Students are trained to: -Apply the fundamental equations of fluid mechanics—namely the continuity, momentum, and energy equations—to describe one-dimensional compressible fluid flows, two-dimensional incompressible potential flows, and fluid flows within the boundary layer. -Calculate one-dimensional subsonic and supersonic compressible fluid flows, including: isentropic flows, adiabatic and isothermal flows with friction, inviscid gas flows with heat transfer, changes in properties across a normal shock wave, as well as gas flows through convergent and Laval nozzles. -Determine velocity and pressure fields within incompressible potential flows, enabling them to calculate the aerodynamic/hydrodynamic force exerted by the fluid on a contour in an inviscid fluid flow. Additionally, based on the acquired knowledge and by applying the complex potential function, they can formulate complex flows to obtain the desired shape of the streamlined contour. -Solve boundary layer equations for the case of flow over a flat plate to calculate the shear stress on the plate, and consequently, the drag force. -Model turbulent flows based on the theory of turbulent flows and fundamental models for turbulent stresses.

Physical and Mathematical Foundations of Fluid Mechanics. Forces, general state of stress, and stress models of fluids. Governing equations of fluid mechanics. Conservation laws: conservation of mass, momentum, and energy. Dynamics of Inviscid Fluids: Planar and axisymmetric flows, stream function, and the Cauchy-Riemann equations. Application of complex variables, complex potential, and complex velocity. Rankine half-body (source in a uniform flow), doublet, cyclic and acyclic flow past a circular cylinder. Forces on a body in an inviscid fluid flow, conformal mapping, flow past airfoil shapes, Kutta-Joukowski condition. Dynamics of Viscous Fluids. Navier-Stokes equations. Exact solutions of the N-S equations, flow in circular pipes, flow past a sphere. Fundamentals of the theory of hydrodynamic lubrication. Turbulent Flows of Incompressible Fluids. Reynolds equations (RANS). Modeling of turbulent stresses. Fully developed turbulent velocity profile. Turbulent flow in hydraulically smooth and hydraulically rough pipes. Free turbulent jet. Boundary Layer Theory. Prandtl equations, boundary layer on a flat plate, application of integral methods for boundary layer calculation, Pohlhausen method. One-Dimensional Fluid Flows. Fundamental equations of one-dimensional fluid flow. One-dimensional flow of a viscous incompressible fluid. Cavitation. Water hammer: speed of sound in elastic pipes, mitigation measures for water hammer effects. Application of the Momentum Theorem. Turbojet engines, Euler's turbomachine equation, Pelton turbine. One-Dimensional Flow of Compressible Fluids. Speed of sound, Mach number, differences between subsonic and supersonic gas flows, the energy equation, stagnation (total) and critical values of physical properties, inviscid gas flow with heat transfer. Shock wave theory, Prandtl's relation, measurements in gas flows. Adiabatic and isothermal gas flow in pipes. Gas flows through convergent and Laval nozzles, and supersonic diffusers.

One-Dimensional Flows of Viscous Fluids in Pipelines. Calculation and analysis of complex pipeline systems. Water hammer. One-Dimensional Flows of Compressible Fluids in Pipes and Nozzles. Isothermal and adiabatic flows with friction. Flow in nozzles. Normal shock waves. Dimensional Analysis. Determination of drag and lift forces on a streamlined body. Planar Flows of Inviscid Fluids. Stream function, potential, complex velocity. Conformal mapping. Exact Solutions of the Navier-Stokes Equations. Turbulent Flows in Pipes, Channels, and Jets. Application of Integral Methods for Boundary Layer Calculation.

Passed exam in Fluid Mechanics B

Books authored by the Department's faculty, problem collections published by the Department's faculty, laboratory equipment and rigs, written lecture notes.

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

Црнојевић Ц., Механика флуида, 2014, Машински факултет Универзитета у Београду, ИСБН: 978-86-7083-846-8; М., Павловић М., Марјановић П., Црнојевић Ц., Механика флуида, теорија и пракса, 2005, Машински факултет Универзитета у Београду, ИСБН: 86-7083-531-2 ; Чантрак С., Хидродинамика, 2012, Машински факултетУниверзитета у Београду, ИСБН: 978-86-7083-770-6;