Course detail

Advanced Fluid Mechanics

FSI-LMTAcad. year: 2025/2026

The course is intended to deepen and widen students' theoretical knowledge of fluid mechanics. The basic laws for 2D and 3D fluid flow will be explained in a broader context. Students will learn about different kinds of fluid flow such as non-vortex and vortex flow of ideal fluid and turbulent flow. They will be provided with basic information about a shear boundary layer, i.e. about how it develops and how to model it. Finally the students will be made familiar with some integral methods used for solving of fluid flow. These methods are Method of Singularities for Thin Profiles, Vortex Element Methods.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. Ing. Jaroslav Štigler, Ph.D.

Department

Energy Institute (EÚ)

Entry knowledge

Basic knowledge of hydromechanics, i.e. basic equations of hydromechanics (Benoulli equation, mass conservation, Euler equations, Navier-Stokes equation, etc.), knowledge of one dimensional fluid flow in pipes. Basic knowledge of the differential, integral and vector calculus.

Rules for evaluation and completion of the course

Course-unit credit is conditional on attendance at the exercises and completing given tasks. The exam has two parts. The first part is a test. The test consists of questions related to basic knowledge obtained in the lectures Second part is an oral exam.
Attendance at seminars is controlled. Absence has to be compensated for via extra work.

Aims

The aim of the course is to widen and deepen theoretical knowledge of fluid flow and present some possibilities how to solve fluid flow in hydraulic machines. To help students to be able analyse results of the CFD software. Another goal is to show some trends in research into theoretical hydraulics.
Students will extend their theoretical knowledge of fluid flow in 2D and 3D. They will have an overview of some basic methods intended for fluid flow modelling. They will be able to analyze results of the CFD software.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ALEKSEENKO, S. V., P. A. KUĬBIN a V. L. OKULOV. Theory of concentrated vortices: an introduction. New York: Springer, c2007. ISBN 978-3-540-73375-1. (EN)
BRDIČKA, Miroslav, Ladislav SAMEK a Bruno SOPKO. Mechanika kontinua. Vyd. 2., opr. Praha: Academia, 2000. ISBN 80-200-0772-5. (CS)
FLEISCHNER, Petr. Vybrané statě z mechaniky tekutin. Praha: Státní nakladatelství technické literatury, 1986. (CS)
LEWIS, R. I. Vortex element methods for fluid dynamic analysis of engineering systems. New York: Cambridge University Press, 1990. ISBN 05-213-6010-2. (EN)

Recommended reading

ALEKSEENKO, S. V., P. A. KUĬBIN a V. L. OKULOV. Theory of concentrated vortices: an introduction. New York: Springer, c2007. ISBN 978-3-540-73375-1. (EN)
BRDIČKA, Miroslav, Ladislav SAMEK a Bruno SOPKO. Mechanika kontinua. Vyd. 2., opr. Praha: Academia, 2000. ISBN 80-200-0772-5. (CS)

Classification of course in study plans

  • Programme N-ETI-P Master's

    specialization FLI , 1 year of study, summer semester, compulsory

  • Programme N-SUE-P Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Ing. Jaroslav Štigler, Ph.D.

Syllabus

1. Mathematical introduction, Einstein summation convection, tensor calculus.
2. Methods of continuum descriptions, basic terms of fluid mechanic, path line, stream line, vortex filament, vortex tube. Stokes formula.
3. The fluid flow types, basic equations describing fluid flow.
4. Bernoulli equation, Lagrange integral.
5. 2D fluid flow, flow function defining, non-vortex flow, complex potential function. Simple flow patterns in 2D flow
6.-7. Principle of superposition. Calculation of fluid flow round a fixed and rotating cylinder. Conformal projection.
8. Simple flow patterns in the space. Parallel flow, source/sink, vortex filament, Biot-Sawart law.
9.-10 Flow induced by vortex walls, flow induced by vorticity continuously distributed in the space.
11. Boundary shear layer, basic terms, definition, thickness BSL, solution of laminar shear layer, shear layer separation.
12. Method of singularities applied on the fluid flow round the thin profiles.
13. Fluid flow solution through line of profiles.

Exercise

13 hod., compulsory

Teacher / Lecturer

doc. Ing. Jaroslav Štigler, Ph.D.

Syllabus

1. Calculation with tensors. Practice of Einstein's convection.
2. Derivation of selected basic laws of fluid mechanics.
3. Conformal projection, Zukovsky's transformation.
4.-5. 2f Fluid flow around fixed and rotating cylinder analysis.
6. Models of the 2D vortex.
7.-9. Calculation of the induced velocity by the finite straight vortex filament.
10.-11. Derivation of velocity induced by plane and cylinder vortex walls.
12.-13. Laminar and turbulent mean velocity profile in straight tube derivation with using continuous vorticity distribution across tube.