222.586 Mixing and Transport Processes
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2022W, VO, 1.5h, 2.0EC


  • Semester hours: 1.5
  • Credits: 2.0
  • Type: VO Lecture
  • Format: Hybrid

Learning outcomes

After successful completion of the course, students are able to:

Part 1: Mixing processes

  • give examples of mixing and transport processes in the atmosphere, oceans, lakes, rivers in terms of specific physical quantities (solid/dissolved matter, heat/enthalpy, and momentum).
  • choose the mathematical framework with the appropriate level of complexity for modelling mixing and transport processes in a given configuration.
  • understand and explain the derivation of the mathematical formulations for mixing and transport processes.
  • explain and mathematically formulate the processes of advection, molecular and turbulent diffusion, and dispersion (longitudinal/transverse) of physical quantities.
  • define passive and (re)active physical quantities and consider them in computational models.
  • evaluate the relative importance of certain mixing and transport processes in a given configuration.
  • select adequate models/simplifications for specific problems in water bodies like lakes and rivers.
  • explain one-dimensional cross-section-averaged, two-dimensional depth-averaged and three-dimensional Reynolds-averaged models in terms of mixing and transport processes.
  • apply analytical solutions for problems using these models in simplified cases and to classify the application ranges and limits of these models (near/mid/far field).
  • quantify diffusion, dispersion as well as reaction coefficients.
  • determine/estimate the required/critical distance/duration for complete mixing across the cross-section of a stream with given geometric and hydraulic characteristics.
  • apply the Streeter-Phelps 1D model for water quality.
  • explain and apply the principle of discharge measurement by tracer/salt dilution method.
  • estimate the application limits of both analytical and numerical models as well as physical models and discuss their advantages and disadvantages.

Part 2: Sediment transport

  • discuss the field of application of the course material
  • discuss the semi-empirical nature of sediment transport theory
  • derive the control parameters of a problem based on dimensional analysis
  • estimate the settling velocity of sediment in water
  • explain the difference between bed load and suspended load sediment transport
  • quantify the threshold for the initiation of sediment transport as bed load and suspended load
  • design measures for the stabilization of a river bed
  • identify the main control parameters governing the transport of sediment
  • explain the modelling of the concentration of suspended sediment and the role of turbulence
  • quantify the rate of sediment transport as bed load, suspended load and/or total load
  • identify the most appropriate formula for quantifying the rate of sediment transport in a given configuration
  • discuss the uncertainty inherent in quantitative estimations of sediment transport
  • discuss the hypotheses underlying a sediment transport formula and its application range

Subject of course

1. Introduction : relevance, examples and summary of required pre-knowledge
2. Identification and mathematical description of mixing and transport processes
3. Simplified analytical solutions in laminar flow and 3D Reynolds-averaged models for mixing and transport processes in turbulent flow
4. 3D Reynolds-averaged models for mixing and transport processes in rivers
5. 1D Reynolds- and cross-sectional-averaged models for mixing and transport processes in rivers
6. Mixing and transport processes in the presence of chemical/biological processes
7. Engineering tools and project examples related to water-quality modelling
8. Sediment transport: modes of sediment transport, dimensional analysis
9. Sediment transport: initiation of motion and bedload transport
10. sediment transport : suspended load transport
11. Engineering tools and project examples

Teaching methods

A combination of plenary lecture and flipped classroom is used as follows:

  • Theory: Plenary lecture (for units with predominant theory) or flipped classroom (for units with predominant examples/exercises, first self-study followed by a plenary session)
  • Examples/exercises: flipped classroom (first self-study followed by a plenary session)

Note that it is important that the students understand the philosophy of the flipped-classroom concept. The fundamental assumption is that the lecturer-student interaction has more added value in the application of knowledge than in the acquisition of knowledge. Students acquire knowledge in an autonomous way through self-study. The forum and Sprechstunden are available for questions, discussion and feedback. The Plenary sessions focus on the application of the theory.

An important requisite for the successful implementation of the flipped-classroom concept is that students come well-prepared to the plenary session, i.e. they have thoroughly studied the theory and solved already some examples themselves.


Covid-19 format (if no present teaching should be possible):

Plenary lectures and plenary session are given online via Zoom. A complete transcription of the material is given in the notes of the corresponding ppt slides (TUWEL course - key: MTP22) .

Mode of examination


Additional information

All PowerPoint slides including the transcriptions are available on TUWEL (key MTP22). These Powerpoint slides are the only course material.

The exams are held in presence or online, depending on the currently valid requirements of the Ministry and the Rectorate. If the examinations have to be held online, the use of the same material as for the presence examination is permitted. If you are unable to attend a presence examination for good reason, as well as if you have any further questions, please contact the responsible assistant when registering for the examination (at least 7 days in advance).



Course dates

Thu14:00 - 16:0006.10.2022 - 26.01.2023EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Mixing and Transport Processes - Single appointments
Thu06.10.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu13.10.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu20.10.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu27.10.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu03.11.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu10.11.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu17.11.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu24.11.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu01.12.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu15.12.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu22.12.202214:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu12.01.202314:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu19.01.202314:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes
Thu26.01.202314:00 - 16:00EI 10 Fritz Paschke HS - UIW Mixing and Transport Processes

Examination modalities

The exam will be in English and concerns the materials included in the PowerPoint documents, which are the only lecture notes.

The exam consists of 2 parts, separated by a 15 min break.

  1. 30 minutes theoretical questions: short multiple choice and open questions aiming at testing your understanding of the theory; there is no need to memorize or be able to derive equations. You are not allowed to use any lecture or personal notes, formularies, calculators, electronic devices, etc..
  2. 90 minutes practical calculation exercises: Electronic devices are not allowed, except a non-programmable pocket calculator (for example TI-30-Models, Casio fx-82/991 WITHOUT Plus). The only extra documentation allowed is the formulary, which includes all relevant information required to solve the exercises.

The theoretical part counts for half of the reachable points and the exercises count for the other half. Only the total amount of gained points will determine whether or not you pass the exam. There is no oral exam.

ONLINE-exams (TUWEL and ZOOM, until at least March 2022)

The online exam will be organized exclusively through TUWEL and ZOOM. It concerns a combination of “written online exam as “Quiz” on TUWEL” („Schriftliche Online-Prüfung als „Test“ in TUWEL“) and “written online test on paper” („Schriftliche Online-Prüfung auf Papier“) as indicated in the TU Wien online exam guidelines.

The students are responsible to fulfil the technical and spatial requirements for an online exam. These include:

  • a PC/Notebook/Tablet with a camera, microphone and speakers (or a Headset)
  • a stable internet connection
  • an examination room in which the participant is alone
  • no disruptions during the duration of the exam
  • a PRINTOUT of the latest version of the formulary, printed in advance (to be found on TUWEL)
  • 6 pages of unlined, blank, white paper, writing utensils and other allowed tools (a transparent glass of water or a transparent drinking bottle without a label are, of course, allowed)
  • the means to digitalize/scan written on pages for the submission (a scanner or smartphone scanner app)

Examination supervision: For fair examination supervision, the students themselves, the desk and the screen must be visible in the ZOOM meeting! There are usually 2 possible variants for this:

  • if the webcam is integrated into the working device, the working device must be positioned so that the student AND the desk are visible. It must still be possible for the student to operate the working device (for multiple-choice input and communication) and it must also be possible to read the TUWEL page with exam questions and answers (e.g. external mouse/keyboard, adjust display size). At the same time, continuous screen sharing is required to be able to control its content.
  • if an external webcam is available and can be positioned in such a way that the student, the desk AND the screen are clearly visible, continuous screen sharing can be dropped.

The set-up should be tried and tested by the students in advance of the exam date. In case a student does not own a webcam (separate or built-in), a smartphone camera can also be used (possibly in combination with apps like DroidCam). The webcam should be turned on during the full duration of the exam.

On behalf of the supervision of the exam, it is necessary, that the complete Zoom web meeting will be RECORDED during the full duration of the exam in order of supervision. You will therefore be asked for your consent - upload through TUWEL at least 2 days before the exam.

If you do not want to consent to the recording or if you have other problems with the online exam requirements, please contact the responsible assistant at least 7 days in advance and a solution will be worked out (extended exam requirements with additional camera or taking the online exam at the institute).

At the starting time of the exam, the students that are registered for one of that day’s exam sessions, get access to all the relevant documentation and a Zoom web meeting link on the current TUWEL course page.

At least 10 minutes before the start of the exam, the student should enter the relevant Zoom web meeting, so there is enough time for the practical set-up. Upon entry into the Zoom web meeting, the student should introduce themselves using their first and last names.

At the start of the exam, the identity of each student will be checked by means of a video identification process (moving both head and ID in front of the camera). Then the student will be asked to turn the camera around and picture the whole room, in order to confirm that no unauthorized tools or other people are present in the room. After that the exam will be started.

During the exam every participants’ audio input (microphone) will be muted. Questions can only be asked to the supervisor through the chat function.

During the full duration of the exam the audio output (speakers/headphones) has to be activated, so that the supervisor’s announcements can be heard and directives can be adhered to. When there is an indication of exam fraud, the supervisor will give the student in question instructions (turning the camera around again or sharing the screen) which must be followed. In case the student does not comply or the suspected fraud is proven, the exam will be terminated for that student and will be counted as one of the total amount of allowed attempts.

In the case of technical malfunctions, the supervisor will decide (depending on duration and scope of the issue) whether the exam has to be terminated or can be carried on for the student in question. In case of an extensive technical problems/interruptions, contact the the responsible assistant/supervisor via mail.

30 minutes theoretical questions:

A TUWEL quiz will be made available, which has to be filled out and handed in within 45 minutes after starting the quiz. The quiz consists of multiple choice and open questions which can be answered until the deadline. During the online quiz, a continuous Zoom web meeting connection (eye contact) has to be running and no external tools (lectures notes, etc.) are allowed.

15 minutes break:

During the break, the student is allowed to leave the room (to use the restroom, get a drink or snack,…). During the theoretical and practical exam parts, the student is not allowed to leave their examination room!

90 minutes practical calculation exercises:

Before the start of the practical part, the examination room and the allowed tools (self-printed formulary, non-programmable calculator) will be checked again through the student’s camera. Afterwards the information and the submission page on TUWEL will be unlocked (can be printed or read on the screen) and the working time start running. As previously described, during the whole duration of the practical exam, the camera has to be positioned so that eye contact is possible and the table is within view.

The upper right corner of the first page (size of a student ID) should not be written on. Every exercise has to be answered on a separate page. The structure of your answers must follow and include the numbering of the questions.

To submit the practical part, all of the written pages have to be scanned (or photographed) completely and uploaded through TUWEL within 10 minutes after the end of the exam. The student ID has to be placed on the first page in the upper right corner (on the for this purpose reserved open space) and scanned with the rest of the page. It is not allowed to upload separate images. All scanned pages have to be combined into one PDF document (use apps like Adobe Scan, Office Lens, etc., test them and learn to operate them before the exam!). During the scanning (or photographing) and uploading, the Zoom web meeting has to keep running. This means that the scanning device already has to be placed within reach before the start of the exam. If a smartphone is used as a webcam, then it can NOT be used to scan (or photograph) the exam.

After a check of the exam submission, the Zoom web meeting will be ended BY THE SUPERVISOR. In the case a student wants to leave the exam before the time limit has been reached, they have to notify the supervisor through the Zoom chat. THE SUPERVISOR will then end the connection for that student. Should a student independently terminate the ZOOM web meeting connection during the exam, this will be considered an exam termination.

PRESENCE exams (expected from April 2022 on)

As before, the following applies to face-to-face examinations:

30 minutes theoretical questions:

A multiple-choice test is used for this, which is then evaluated automatically. A questionnaire and an answer sheet are issued. PLEASE NOTE: Only the correct ticks on the answer sheet will be evaluated! To prepare for the exam, it is essential to visit the tutorial in the TUWEL course. Extra tools, including lecture notes, formularies, pocket calculators, electronic devices, etc., are not permitted!

90 minutes practical calculation exercises:

PLEASE NOTE: Electronic devices are not permitted, with the exception of non-programmable pocket calculators. A formulary is issued during the examination (available for practice purposes on TUWEL).

Further information on the presence exam:

  • The available seats in the lecture hall are those where paper lies on the desk.
  • Do not forget to write your name and matriculation number on every page you use.
  • Put your Studentenausweis on the Table.
  • Beside your Studentenausweis, you are only allowed to have a pen and a Geodreieck on your desk for the theoretical part. For the exercises, you are allowed to have in addition a non-programmable pocket calculator and formulary (optional).
  • Questions can only be answered on official paper, i.e. the paper that you find on the desk. Additional paper can be obtained on request.
  • The theoretical questions must be crossed clearly on the answer sheet, not on the questionnaire (see tutorial in the TUWEL course).
  • Every exercise has to be answered on a separate page. The structure of your answers must follow and include the numbering of the questions.
  • All papers will be collected at the end, including drafts.


DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Mon10:00 - 13:0007.10.2024HS 7 Schütte-Lihotzky - ARCH written06.09.2024 12:00 - 03.10.2024 12:00TISSPrüfung
Mon08:00 - 11:0016.12.2024HS 14A Günther Feuerstein written15.11.2024 12:00 - 12.12.2024 12:00TISSPrüfung
Thu09:00 - 12:0016.01.2025HS 17 Friedrich Hartmann - ARCH written16.12.2024 12:00 - 14.01.2025 12:00TISSPrüfung
Tue12:00 - 15:0004.03.2025HS 17 Friedrich Hartmann - ARCH written04.02.2025 12:00 - 28.02.2025 12:00TISSPrüfung
Wed14:00 - 17:0014.05.2025HS 7 Schütte-Lihotzky - ARCH written14.04.2025 12:00 - 12.05.2025 12:00TISSPrüfung
Tue10:00 - 13:0017.06.2025HS 8 Heinz Parkus - CEE written16.05.2025 12:00 - 13.06.2025 12:00TISSPrüfung

Course registration

Begin End Deregistration end
28.09.2022 12:00 27.01.2023 12:00 27.01.2023 12:00


Study CodeObligationSemesterPrecon.Info
033 266 Environmental Engineering Mandatory3. SemesterSTEOP
Course requires the completion of the introductory and orientation phase


No lecture notes are available.

Previous knowledge

The course (VO) Hydraulics (222.564) is highly recommended !

Preceding courses