Course syllabus for Fluid mechanics

Basic courses on calculus, diffrential equations, complex analysis, and linear algebra.

After completion of this course, the student should be able to:

- understand and explain basic concepts such as fluid, the continuum hypothesis, Eulerian and Lagrangian reference frames, density, viscosity and molecular stresses

- analyze problems related to the pressure distribution in motionless fluids

- apply the control volume technique to solve relevant engineering problems involving moving fluids

- derive and use relevant balance equations for a control volume from the fundamental mechanical laws by the use of the Reynolds transport theorem

- derive and analyze differential relations in fluid mechanics from the corresponding control volume expressions

- determine simple fluid flow patterns by the introduction of reasonable simplifications to the Navier-Stokes equations

- use dimensional analysis to rewrite equations on dimensionless form and to derive relevant dimensionless groups

- determine what is needed for dynamic similarity and to explain what dynamic similarity means

- design industrial piping systems

- explain what characterizes turbulence, what the energy cascade in turbulent flow is, what a turbulent energy spectrum looks like in the limit of infinite Reynolds number

- derive the Reynolds-averaged Navier-Stokes equations and discuss how the turbulent stresses can be modelled

- use the stream function and the velocity potential to study analytically applicable fluid flow situations

- explain when and where assumptions of frictionless flow are acceptable

- analyze fluid flow in turbulent and laminar boundary layers by using the control volume technique and by introducing simplifications into the differential expressions

- understand and explain the concept of separation

Fluid mechanics occupies a central position in applied science and is fundamental to a wide array of scientific and engineering disciplines. The aim of this course is to learn the basic concepts in describing the behaviour of a fluid. These concepts are used to grasp the fundamentals of fluid mechanics.

The course starts by discussing the nature of fluids and mathematical tools to describe this nature. The continuum assumption, a fundamental prerequisite within a large area of classical physics, is discussed. Building on the continuum assumption, a number of basic concepts describing a fluid are discussed. From these concepts, the basic equations of fluid dynamics are derived, including the Euler equations, the Navier-Stokes equations, and the Bernoulli equation. Along the way, many implications and applications are discussed.

The following topics within fluid mechanics are treated in the course:

- Introduction and fundamental concepts

- Pressure distribution in a stationary fluid

- Control volume analysis

- Differential relations

- Flow patterns

- Dimensional analysis

- Pipe flow

- Turbulence

- Potential flow

- Boundary layer theory

The course consists of lectures and problem solving sessions, plus one (optional) computer exercise. 

"Fluid Mechanics (Eighth Edition in SI Units)" by Frank M. White, Edition: 8 Rev ed, 2016, ISBN: 978-9-814-72017-5.

"An Introduction to Turbulence Models" by Lars Davidson, Chalmers Publication 97/2.

There is a written examination at the end of the course. In addition, there are three optional hand-in exercises and one optional computer lab report that may be awarded bonus points.