Тo develop and rationalize the mathematics of viscous fluid flow using basic principles, such as mass, momentum аnd energy conservation, and constitutive equations and to exhibit the systematic application of these principles to flows occurring in fluid processing and other applications.

Student will develop and rationalize the mathematics of viscous fluid flow using basic principles, such as mass, momentum аnd energy conservation, and constitutive equations and to exhibit the systematic application of these principles to flows occurring in fluid processing and other applications.

Vector and tensor algebra. Tensors in fluid mechanics. Differential operators. Integral theorems. Continuum hypothesis - continuum mechanics. Conservation laws of mass, momentum and energy. Invariant forms of conservation equations. Reology and constitutive relations. Newtonian fluid. Analysis of Navier-Stokes equations. Laminar, steady and unsteady unidirectional flows. Dimensionless forms of conservation equation. Dimensionless numbers. Approximative methods - perturbation methods. Lubrication theory. Reynolds equation for lubrication. Laminar flow over a sphere.

Algebraic and differential operations with vectors and tensors. Principal values and directions of tensors. Tensor invariants. Invariant form of Navier-Stokes equations. Navier-Stokes equations in cartezian, polar and spherical coordinates. Steady and unsteady Coutte flow. Steady and unsteady Pouiselle flow. Steady laminar flow between rotating cylinders. Superposition of Coutte and Pousille flow. Flow near a plate suddenly set in motion. Flow due to an oscillating plate. Laminar flow in channel of rectangular and triangular cross-section. Laminar flow in a pipe of elliptical cross-section.

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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: 10
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 70
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 0

Viktor Saljnikov: Dynamics of viscous incompressible flow, Faculty of Mechanical Engineering Belgrade, 1985 (in Serbian); Cantrak S. Hydrodynamics, Faculty of Mechanical Engineering Belgrade, 2012 (in Serbian); Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou: VISCOUS FLUID FLOW, CRC Press LLC 2000