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Lecturer(s)
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Kulish Vladimír, doc. Ing. PhD., DSc.
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Course content
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1. Introduction & Fundamental Concepts - general classification of forces; normal & shear stresses; continuum hypothesis and physical properties of fluids (e.g., density, viscosity); Newton´s law of viscosity; Newtonian vs. non-Newtonian fluids; no-slip; ideal fluids 2. Flow governing equations - energy & mass conservation; causality & least action principles; general form of the conservation equation; mass (continuity equation) & momentum conservation (Cauchy equation) in a fluid flow; the Navier-Stokes equation 3. Dimensional analysis & modelling - dimensions & units; dimensional homogeneity; nondimensionalising of equations; dimensional analysis; similarity; dimensionless criteria (e.g., Reynolds number); flow governing equations in dimensionless form 4. Fluid statics (hydrostatics) - fundamental equation of fluid statics as approximation of the Navier-Stokes equation; solving the fundamental equation of fluid statics in the case when gravity is the only acting force; Pascal´s principle and some of its applications; buoyancy & Archimedes´ principle; some applications of Archimedes´ principle (e.g., density measurements; floating stability); surface tension 5. Fluid kinematics - scalar & vector fields and flow field; Lagrangian & Eulerian descriptions of fluid flow; material derivative; Reynolds transport theorem; fundamentals of flow visualization (e.g., pathlines & streamlines; other kinematic descriptions); vorticity; variation of flow parameters in time & space) 6. Elementary fluid dynamics - mass flow rate & volume flow rate; the simplest application of mass conservation; flows with no external forces; the Euler equation as an approximation of the Navier-Stokes equation; fluids in rigid-body motion; integrating the Euler equation along a streamline (the Bernoulli equation); some applications of the Bernoulli equation 7. Some exact solutions of the Navier-Stokes equation - Couette flows with & without applied pressure gradient; flow over a vertical wall; Poiseuille flow; Stokes´ flow; summary of other known exact solutions of the Navier-Stokes equation 8-10. Some approximate solutions of the Navier-Stokes equation - creeping flow; potential flow; boundary layer flow 11. The phenomenon of turbulence - introduction to turbulence; turbulent shear stress; the mixing length hypothesis; turbulent velocity profile; viscous stream buckling & transition to turbulence 12. Course overview & summary - brief overview of the course content and its logical structure; overview of problem-solving techniques; overview of some typical exam questions Outcomes: Upon completion of the course, the student will understand the fundamental principles of fluid mechanics, including the behaviour of Newtonian and non-Newtonian fluids, the Navier-Stokes equations, and dimensional analysis. They will be able to apply the laws of conservation of mass and momentum, analyse fluid statics and dynamics, including turbulence, and use this knowledge to solve practical problems in fluid flow.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The course aims to provide PhD students with a rigorous understanding of the fundamental principles governing fluid flows. Special emphasis is placed on the derivation and application of the governing equations of fluid mechanics, exact and approximate analytical solutions, dimensional analysis, and turbulence. The course equips students with advanced analytical tools required for modelling and solving practical problems in thermal-fluid sciences and related interdisciplinary fields.
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Prerequisites
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Prior knowledge of undergraduate-level calculus, ordinary and partial differential equations, vector calculus, classical mechanics, and introductory fluid mechanics is assumed. Familiarity with tensor notation and basic numerical methods is advantageous but not essential.
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Assessment methods and criteria
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unspecified
Independent study of assigned literature; preparation and presentation of a course project on a selected topic; passing the written examination.
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Recommended literature
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Vladimir Kulish, OVERVIEW OF THERMAL-FLUID SCIENCES at https://www.amazon.com/OVERVIEW-THERMAL-FLUID-SCIENCES-THERMODYNAMICS-DEFINITIONS-ebook/dp/B01GYLGENK.
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Yunus A. Çengel & John M. Cimbala, FLUID MECHANICS: FUNDAMENTALS AND APPLICATIONS, 2014, McGraw Hill, 3rd Ed. (ISBN 978-0-07-338032-2)..
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