Course detail

# Theory of Hydraulic Machines

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 methods used for solving of fluid flow. These methods are: - Method of Singularities for Thin Profiles, - Vortex Element Methods, - Finite Difference Method, - Finite Volume Method.

Learning outcomes of the course unit

Students will extend their theoretical knowledge of fluid flow in 2D and 3D. They will an overview of some basic methods intended for fluid flow modelling.

Prerequisites

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

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Brdička Miroslav, Samek Ladislav, Sopko Bruno: Mechanika Kontinua
Brdička Miroslav, Samek Ladislav, Sopko Bruno: Mechanika Kontinua
LEWIS, R.I: Vortex element methods for fluid dynamic analysis of engineering systems, , 0
FLEISCHNER, P.: Vybrané statě z mechaniky tekutin, , 0
Hydraulické stroje: Hydraulické stroje, , 0
ŠOB, F.: Hydromechanika, , 0
NECHLEBA, M.: Vodní turbíny, , 0
NECHLEBA, M.: Vodní turbíny I., , 0

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

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 ten questions related to basic knowledge. The second part is an oral exam.

Language of instruction

Czech

Work placements

Not applicable.

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. Another goal show some trends in research into theoretical hydraulics.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is controlled. Absence has to be compensated for via extra work.

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

1. Mathematical introduction, Einstein?s summing symbolic, tensor and calculation with it.
2. Methods of continuum descriptions, basic terms of fluid mechanic, path line, stream line, vortex filament, vortex tube.
3. The fluid flow types, basic equations describing fluid flow.
4. Bernouli equation, Lagrange integral. 2D fluid flow, flow function defining, non-vortex flow, conformal projection, function of complex potential.
5. Finite difference method and its application on the 2D channel and axially symmetrical channel.
6. Non vortex fluid flow, simple flow pattern, principle of superposition. Calculation of fluid flow round a rotary cylinder.
7.-8. Method of singlularities applied to the fluid flow round the thin profiles and profile net.
9.-10. Vortex flow of ideal fluid, vortex element method, Biot-Savart law.
11. Turbulent flow, models of turbulence, basic principal of finite volume method.
12.- 13. Shear boundary layer, basic terms, solution of laminar shear boundary layer.

Exercise

13 hours, compulsory

Teacher / Lecturer

Syllabus

1. Calculation with tensors. Practice of Einstein's convection. 2. Derivation of selected basic laws of fluid mechanics. 3. Conformal projection, Zhukovsky's transformation. 4-5 Finite difference method and its application on the 2D channel and axially symmetrical channel. 6. Models of the 2D vortex. 7.-9. Fluid flow solution of round a non-rotary and rotary cylinder. Calculation of the lift force. 10. Calculation of the induced velocity by the finite straight vortex filament. 11.-12. Solution of the laminar shear boundary layer.

eLearning

eLearning: opened course