Course syllabus for Fluid mechanics

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

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.

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
- 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
- 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
- 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

- Potential flow

- Turbulence

- 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.