Topic outline

  • Objectives of the course

    The aim of the course is to deepen your understanding of the physical background of fluid flow phenomena (particularly the influence of viscosity) and the mathematical description and solution of different fluid flow problems. It is assumed that you already have a basic understanding of fluid flow (e.g. conservation principles, kinematics, material derivative, pressure, shear stress, Bernoulli equation). We will shortly revise the derivation of the fundamental flow equations to give you an idea of the fundamental physical processes in fluid flow. We will discuss the possibilities for the solution of Navier-Stokes equations in their full form and the simplifications and solution of the equations in specific cases with particular emphasis on boundary layer and boundary layer like flows. You will learn what turbulence is, how it affects the mean flow and how it is typically handled in the mathematical model. You will also get an introduction to the numerical solution of the flow equations.


    You should register on the course in the Sisu service at Note that you have to have the course in your primary study plan in order to successfully register on the course.

    Completing the course and grading

    The assessment of the course is based on mandatory exercises and an exam. The weight of the exercises and the exam in the final grading is 40% and 60%, respectively.

    There are five rounds of exercises corresponding to each weekly topic. Each round will be graded with 0-5 points. In order to pass the exercises you need at least 8 points, which will correspond to a grade of 0.5. Full points for the exercises correspond to a grade of 5.7. More info on the exercises can be found under the Exercises section.

    In order to pass the exam you need at least one third of the full points, which will correspond to a grade of 0.5. Full points in exam correspond to a grade of 5.7. The exam will be organised at the end of period I. In case you miss this or wish to retake it, another opportunity to take the exam is offered at the end of period II.

    Peer-support on the course is encouraged. In addition to the tutoring sessions, you can ask questions and discuss topics you consider difficult in the Questions and answers forum.

    Course material

    The main material for the course is Kundu, P. and Cohen, I. (2008), Fluid Mechanics, 4th edition. The book is available as an electronic version for Aalto students on Knovel. You can also use Panton, R. (2013), Incompressible flow, 4th edition as an additional reading to complement Kundu and Cohen. This is also available as an electronic version for Aalto students via the ProQuest ebrary service. Further details on these including instructions, how to access these, are provided in the Materials section.

    For some parts there will be additional supplementary material.


    The course is based loosely on a Description, Analysis, Synthesis (DAS) cycle. We will have five two hour sessions each week. Two of the session are more lecture like (Description and Analysis), one is a hybrid session (Synthesis) and two are reserved for tutoring and guidance for the exercises. All of the sessions are organised on campus. D, A and S sessions are recorded and recordings provided to support self-study. The weekly schedule is as follows

    Description of flow phenomena, the associated physics and their mathematical treatment Tuesdays at 10:15-12:00

    Analysis of the phenomena using relevant mathematical derivations and solutions Wednesdays at 8:15-10:00

    In-class problem solving and support for homework assignments
    Wednesdays at 10:15-12:00
    Thursdays at 8:15-10:00

    Exercise deadline
    Mondays at 14:15

    Synthesis of the weekly topics and of the cumulative understanding
    Mondays at 14:15-16:00

    Note that the first session on the 4th of September will be an introductory session presenting the course aims, objectives, content and arrangements. The final session will be on Wednesday the 11th of October.

    Course programme

    The topics of each week are presented below

    Week 1
    Typical phenomena, notations and governing equations
    Chapter 4 (Chapter 2 has support on notations)
    Week 2
    Solution of the Navier-Stokes equations
    Chapter 9
    Week 3
    Boundary layers and shear flows
    Chapter 10
    Week 4
    Turbulence Chapters 12 and 13
    Week 5
    Numerical solution of the flow equations
    Chapter 11
    Week 6