Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Spring 2022
Content and learning outcomes
Course contents
Introduction, tensors, kinematics. Continuum mechanical conservation laws for mass, momentum and energy. Laminar viscous flow. Laminar boundary layers. Vorticity dynamics. Two-dimensional irrotational flow. Introduction to turbulent flow.
Intended learning outcomes
The student should be able to identify, apply and/or present derivations of mathematical models of fluid mechanical phenomena and make relevant approximations.
The student shall for simplified cases be able to apply the derived models (numerically or theoretically) and be able to interpret the result.
The student should show an ability to relate obtained data, observed phenomena and processes in a laboratory environment to the theoretical description of fluid mechanics.
The student should get a fundamental preparation in order to be able to work with fluid mechanical problems as an engineer.
Learning activities
Lectures (L1-14) and recitations (E1-E14)
The course contents will be presented in 14 lectures and 14 recitations divided into the following sections:
Introduction, tensors, kinematics (L1,L2, E1,E2)
Conservation laws (L3, E3)
Laminar viscous flow (L4,L5, E4-E6)
Conservation of energy (L6, E6, E9)
Laminar boundary layers (L7,L8, E7,E8)
Vorticity dynamics (L9,L10, E9, E10)
2D irrotational flows (L11, L12, E11, E12)
Introduction to turbulent flow (L13, L14, E13, E14)
Prepare for each lecture by reading Kundu & Cohen (4th edition) and/or Kundu, Cohen & Dowling (5th , 6th edition). Detailed reading instructions can be downloaded from Canvas.
Lab
A mandatory experimental lab (Self-similar boundary layer lab with a fauvourable pressure gradient) is scheduled in the Fluid Physics lab, Teknikringen 8. Detailed lab instructions can be downloaded from Canvas. You can sign up in Canvas (under “People” tab).
Detailed plan
Activity
Topic
Section
L1
Introduction and motivation of Navier-Stokes eq. Kinematics: Lagrange/Euler oord., material derivative.
1. Introduction, tensors, kinematics
E1
Tensors
L2
Kinematics: relative motion.
E2
Euler/Lagrange coordinates and relative motion
L3
Stress tensor, Reynolds transport theorem, Conservation of momentum and mass.
2. Conservation laws
E3
Stress tensor, application of conservation equations.
Tutorial homework 1.
L4
Navier-Stokes equations, examples
3. Laminar viscous flow
E4
Exact solutions to Navier Stokes equations
L5
Rotating cylinders and Stokes’ problem.
Due Homework 1
E5
Exact solutions to Navier Stokes equations
L6
Conservation of energy.
4. Conservation of energy.
E6
Exact solutions to the energy equation.
Tutorial homework 2.
L7
Boundary layer equations and Blausius flow.
5. Laminar boundary layers
E7
Boundary layers: Similarity and wake flow.
L8
Boundary layers with pressure gradient, separation of boundary layer.
E8
More boundary layers.
Tutorial Homework 2.
See lab group schedule.
L9
Vorticity dynamics, Kelvins circulation theorem
6. Vorticity dynamics
E9
Rankine vortex, Generation of vorticity in natural convection
L10
Flows at large Re, streamfunction, velocity potential, Bernoulli’s equation.
E10
Axisymmetric flows with vorticity, Hiemenz problem
7. Irrotational flow
Due Homework 2
L11
2D inviscid flow and the complex potential.
Tutorial homework 3.
E11
Bernoulli’s equation, pressure in solid body rotation/irrotational vortex, stream function.
L12
Flow past a circular cylinder with circulation, lift and drag
E12
Potential flow problems
L13
Averaged equations for turbulent flow, Reynolds stresses,
turbulent kinetic energy
8. Introduction to turbulent flow
E13
Turbulent flows.
L14
Turbulent channel flow. Summary
E14
Problems from old exams.
Due Homework 3 (lab report)
Exam
Written
Re-exam
Written
Preparations before course start
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.
Literature
The book by Kundu & Cohen & Dowling, Fluid Mechanics (6:th ed.), Elsevier AP. You can download E-book (5:th edition) from KTH library.
Support for students with disabilities
Students at KTH with a permanent disability can get support during studies from Funka:
INL1 - Assignments, 3.0 credits, Grading scale: P, F
TEN1 - Examination, 4.5 credits, Grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
INL1: Written assignments and participation and reporting of laboratory exercise
TEN1: Written exam.
Examiner decides, in consultation with KTH's coordinator for students with disability (Funka), about any adapted examination for students with documented, permanent disability. The examiner may allow another examination form when re-examining individual students.
The section below is not retrieved from the course syllabus:
INL1 - Assignments, 3.0 credits
Three sets of mandatory homework (HW) assignments can be download from Canvas (under “Assignments” tab). Upload your assignment on CANVAS from a PDF-file before deadlines (see Detailed plan for when HW are due).
Homework 1: Max 3p bonus on 1st exam Homework 2: Max 5.5p bonus on 1st exam Homework 3: Max 3.5p bonus on 1st exam
A mandatory experimental lab in the Fluid Physics lab, Teknikringen 8.
TEN1 - Examination, 4.5 credits
The grade scale is A-F according to (may be adjusted)
40 ≤ Points --> Grade A
35 ≤ Points < 40 --> Grade B
30 ≤ Points < 35 --> Grade C
25 ≤ Points < 30--> Grade D
20 ≤ Points < 25 --> Grade E
Points = 19 --> Grade Fx
Points <19 --> Grade F
Maximum number of points on the exam is 50+12, including bonus from homeworks. The points obtained from the homework problems can only be used to get a higher grade than E, they cannot be used to pass the exam. The grade Fx can be upgraded (through an oral exam) to E within six weeks after the exams have been corrected. There is a re-exam in December, but with no possibility to receive a Fx (i.e. Fx=F in re-exam).
By written presentations of solutions, possibly in cooperation with classmates, to at least one of the problems for each of the three homework assignments. At a written exam show the ability to clearly formulate a model and present a solution to basic fluid mechanical phenomena and/or to present coherent derivations of fluid mechanics theory.
D-A
By the requirements for E and showing larger width by solving more problems from the homework assignments and/or at the written exam deal satisfactory with more problems/derivations and/or show larger depth by solving and analysing homework assignments/exam problems with excellence and explain the results.
Learning outcome 3
E
By preparing for and execute the experimental lab in the course and submitting a lab
report.
Ethical approach
All members of a group are responsible for the group's work.
In any assessment, every student shall honestly disclose any help received and sources used.
In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.