Fundamentals of fluid mechanics

The goal of the course is to teach the student the basics and applications in science of fluid flow. The essence in that sense is good understanding of fundamental equations of fluid mechanics. That good understanding of the equations makes the process of finding the solution in particular engineering problems which are dealing with fluid flow much easier. Also another important goal of the subject is the teach the student the basics of experimental methods in fluid mechanics. This will be accomplished by the work in the laboratory.

Learning the topics from the course student will get the knowledge about basic principles in fluid mechanics and capabilities of analytical thinking, then how to apply the knowledge in practical work, and also to make the connection between various subjects from mechanical engineering.

Fluids. Compressibility, viscosity, Newtonian and non-Newtonian fluids. The equation of state. Analysis of forces that acts on the fluid. State of stress, stress tensor. Fluid statics: Euler equation of statics and it's application. Pressure distribution in incompressible fluid. Hydrostatic forces on plane and curved surfaces. Pressure distribution in compressible fluid. Standard atmosphere. Fluid kinematics: Euler and Lagrange approach of description of fluid flow, streamlines, stream tubes, flow rate, mean values of physical quantities. Material derivative. Physical explanation of divergence of velocity. Continuity equation: differential and integral form. Motion of fluid particle: translation, rotation and deformation. Potential and rotational flow. Circulation and free vortex. Dynamics of inviscid flow: state of stress in inviscid flow, Euler equation. Bernoulli integral of Euler equation for steady and unsteady flow. Velocity measurements with Pitot and Prantdl probes. Basics of gas dynamics: energy equation, isentropic and isothermal flow, total and critical values of physical quantities, aerodynamic heating of the body, flow through convergent nozzle. Dynamics of viscous flow: state of stress in viscous flow, Navier-Stokes equation. Similarity theory, characteristic dimensionless similarity numbers. Dimensional analysis - wall shear stress in pipe flow and drag and lift force. Some exact solutions of Navier-Stokes equation: laminar flow between parallel plates and laminar flow in circular pipe. Basics of turbulent flow. Reynolds equations, basics of turbulence modeling. Prantdl mixing length theory. Turbulent flow in smooth pipes. Basics of boundary layer theory and Prandtl equations. Boundary layer separation. Dynamics of one-dimensional flow: Bernoulli equation for viscous fluid, continuity equation, momentum equation. Mean values and corrections coefficients. Friction effects in incompressible flow. Moody chart. Calculations of fluid flow in pipelines.

Physical properties of fluid. Calculations of stress state in fluid. Fluid statics. Absolute and relative pressure. Hydrostatic forces which acts on plane and curved surfaces. Pressure distribution in rigid-body motion of the fluid: constant acceleration and rotation in a cylindrical container. Pressure distribution in Earth's atmosphere. Kinematics of the flow: determination of streamlines, volume and mass flow rates. Bernoulli equation. Some elementary problems from compressible fluid flows. Application of momentum and momentum of momentum equation. One dimensional flow in the pipes. Calculation of simple of complex pipeline systems. Basic examples in dimensional analysis. Laboratory work: measuring of velocity profile in pipe flow, determination of friction coefficient and pressure drop on local resistances.

Listener must be a student of the third year of undergraduate studies.

Some chapters from books written by professors from the Chair, Handouts, and laboratory equipment.

Total assigned hours: 65

New material: 15
Elaboration and examples (recapitulation): 10

Auditory exercises: 20
Laboratory exercises: 3
Calculation tasks: 12
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: 2
Test: 0
Final exam: 3

Activity during lectures: 5
Test/test: 35
Laboratory practice: 5
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 55
Requirement for taking the exam (required number of points): 10

Crnojević C., (2018): Fluid Mechanics. Faculty of Mechanical Engineering, Belgrade (in Serbian); Čantrak S., Lečić M., Ćocić A. (2008) Fluid Mechanics B (handout) (in Serbian); Đorđević V., (2000): Dynamics of one-dimensional fluid flows, Faculty of Mechanical Engineering, Belgrade (in Serbian); Crnojević C (2013) Classic and oil hydraulics. Faculty of Mechanical Engineering, Belgrade (in Serbian); Čantrak S., Benišek M., Pavlović M., Marjanović P., Crnojević C (2005): Fluid mechanics, theory and practice, Faculty of Mechanical Engineering, Belgrade (in Serbian)