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Breakdowns caused by water hammer
Kuřátko, Jiří ; Hudec, Martin (referee) ; Himr, Daniel (advisor)
The goal of this bachelors thesis is to explain how water hammer occurs, listing often used protective devices that help mitigate this event and research of accidents caused by water hammer. The thesis deals with theoretical introduction into the topic, describing preservation laws for fluids, most common causes of water hammer and characteristics connected to this phenomenon. Then it mentions often used protective devices for both overpressure and negative pressure. Finally there are accidents caused by water hammer, some with unusual causes, which however still need to be taken into consideration when designing a pipeline.
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Breakdowns caused by water hammer
Kuřátko, Jiří ; Hudec, Martin (referee) ; Himr, Daniel (advisor)
The goal of this bachelors thesis is to explain how water hammer occurs, listing often used protective devices that help mitigate this event and research of accidents caused by water hammer. The thesis deals with theoretical introduction into the topic, describing preservation laws for fluids, most common causes of water hammer and characteristics connected to this phenomenon. Then it mentions often used protective devices for both overpressure and negative pressure. Finally there are accidents caused by water hammer, some with unusual causes, which however still need to be taken into consideration when designing a pipeline.
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Conservation laws with respect to curved backgrounds associated with black holes and cosmological models
Pavičevič, Mak ; Bičák, Jiří (advisor) ; Schmidt, Josef (referee)
in English We review the problem of defining energy, momentum etc. and their con- servation in curved spacetimes and a possible resolution in the form of a background spacetime. Our focus is set on superpotentials, which, when in- tegrated on a spatial boundary, yield conserved charges, while a conserved vector current is a divergence of a superpotential. Within this thesis, we build a minimal mathematical formalism necessary to prove and interpret Noether's theorem which unites symmetries and conservation laws. We em- phasize the significance of Killing vector fields - generators of isometries. After a short historical overview, the KBL superpotential is presented in de- tail, which makes it possible to define conserved quantities with respect to a curved background spacetime. We then employ its generalization within the Horndeski scalar-tensor theory of gravity. We concentrate on a subclass con- taining non-minimal derivative coupling of the Einstein tensor and a scalar field. We find superpotentials for spherically symmetric, static spacetimes (e.g. exterior of black holes) and time-dependent cosmological spacetimes, in particular with respect to (Anti-)de Sitter backgrounds. 1
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Numerical Analysis of a polydisperse sedimentation problem
Dvořák, Daniel ; Felcman, Jiří (advisor) ; Feistauer, Miloslav (referee)
The problem of the polydisperse sedimentation as the system of the partial differential equations is formulated. The hyperbolicity of the problem and the determination of the eigenvalues of the Jacobi matrix of the flux function is studied. Based on the conservation laws of the mass and momentum completed by the constitutive relations the so called MLB model is derived. The one- dimensional problem is formulated. The Sherman-Morrison formula is used to find the inverse matrix of the sum of the diagonal matrix and the matrix being the product of two vectors. In order to find the eigenvalues of the Jacobi matrix of the flux function the rank two perturbation of the diagonal matrix is used. In such a way the problem of the determination of the eigenvalues is reformulated as the solution of the so called secular equation. The eigenvalues can be localized and the strong hyperbolicity of the problem under certain conditions is proved. 1
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