SG2214 Fluid Mechanics 7.5 credits


All fluid flows are governed by a single set of partial differential equations, the Navier-Stokes equations. This includes for instance, the aerodynamics of bumble bees and aerospace planes, the turbulence around vehicles and in the atmosphere and the convection in the sun and around a human body. The course is an in-depth introduction to fluid mechanics, with an emphasis of understanding fluid phenomena using on the Navier-Stokes equations. The equations are derived in detail and numerous examples of solutions are presented. Fluid Mechanics also has many important applications in engineering, geo- and astro-physics and bio-physics, for example, which makes this course ideal as a starting point for students with a varied interest in applications.

  • Education cycle

    Second cycle
  • Main field of study

    Mechanical Engineering
  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 18 Doktorand for single courses students

  • Periods

    Autumn 18 P1 (7.5 credits)

  • Application code


  • Start date


  • End date


  • Language of instruction


  • Campus

    KTH Campus

  • Tutoring time


  • Form of study


  • Number of places *

    Max. 1

    *) If there are more applicants than number of places selection will be made.

  • Course responsible

    Anders Dahlkild <>

  • Teacher

    Anders Dahlkild <>

  • Target group

    For doctoral students at KTH.

Intended learning outcomes

  • The student shuold be able to formulate mathematical models of fluid mechanical phenomena, and make relevant approximations.
  • The student should be able to apply the these models (numerically or theoretically) and interprete the result.
  • The student should get a basic preparation for the future ability as a master of engineering to work with computational fluid mechanics in technical applications.

Course main content

The student should be able to

  • derive the Navier-Stokes equations and explain the meaning of its terms, including the stress and deformation rate tensors
  • describe the method of transferring from compressible to incompressible equations
  • compute the flow field for a number of so called exact solutions
  • derive the vorticity equation and give a physical explanation of its terms
  • use the concepts of stream function, velocity potential and apply the Bernoulli equation
  • discuss the principles of and derive the boundary layer approximation of the Navier-Stokes equations, and to give self similar solutions of these equations including simple thermal boundary layers
  • describe the phenomena of separation of streamlines.
  • describe simple phenomena in turbulence, as e.g. turbulent stresses.
  • derive the Reynolds averaged equations
  • suggest methods to measure the velocity in a flowing medium


Lectures: 28h

Recitations: 28h

Tutorials: 4h

Laboration: 3h


Compulsory courses of the main programmes at F or T. Alternatively, compulsory courses at B or M and in addition SG1217 or SG1220.

Recommended prerequisites

The student should have good knowledge in linear algebra and calculus in more than one variable, vector analysis, Gauss and Stokes theorems and solution of elementary partial differential equations, basic knowledge of fluid mechanics phenomena, computer programming in e.g. Matlab.


Kundu & Cohen, Fluid Mechanics, Academic Press.

Additional course material may be available via course home page.


  • INL1 - Assignments, 3.0, grading scale: P, F
  • TEN1 - Examination, 4.5, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

Homework assignment (INL1; 3 cr)
Exam (TEN1; 4,5 cr.)

Offered by



Anders Dahlkild


Anders Dahlkild <>

Supplementary information

The course is compulsory for students in Fluid Mechanics track in Masters program in Engineering Mechanics.

Add-on studies

SG2218 Turbulence

SG2215 Compressible flow

SG2221 Wave motions and hydrodynamic stability

SG2212 Computational Fluid Mechanics


Course syllabus valid from: Autumn 2012.
Examination information valid from: Autumn 2007.