ENCN441-22S1 (C) Semester One 2022

Fluid Mechanics of Environmental Systems

15 points

Start Date: Monday, 21 February 2022
End Date: Sunday, 26 June 2022
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 6 March 2022
  • Without academic penalty (including no fee refund): Sunday, 15 May 2022


Navier-Stokes equations. Scale and dimensional analysis. Description and modelling of turbulence. Dispersion in rivers. Dynamics of jets and plumes and applications to building ventilation.

Environmental systems have a wide range of interesting fluid mechanics phenomena associated with them. The importance of this branch of fluid mechanics is shown by it being given its own name – environmental fluid mechanics. Environmental fluid mechanics focuses on the interaction of humans with naturally occurring fluid bodies such as the atmosphere, the oceans, rivers, and lakes. Turbulence and buoyancy forces are often important things to consider when trying to understand or model these systems.

Human civilisation is impacted by these fluid bodies in a number of critical ways

 They provide critical resources such as water to drink, air to breathe, and energy for power generation.
 We modify them through engineering interventions such as drawing water for irrigation and the construction of buildings and cities into the atmosphere.
 We use them for disposal of our wastes such as municipal waste discharged into the ocean and smokestacks and chimneys discharging into the atmosphere.

Environmental fluid dynamics is a very broad topic and this course can only provide an introduction to it. However by the completion of the course you should appreciate some of the fundamental characteristics of these natural flows – in particular turbulence, wave motion, and convection– and you should be able to undertake basic modelling of certain aspects of our interactions with them – in particular the modelling of turbulent mixing in the ocean, rivers, atmosphere, and within buildings.

Learning Outcomes

  • This course is broken down into three sections, the Navier-Stokes equations, turbulence and far field mixing, and jets and plumes. Each section comprises a set of modules with associated learning outcomes.

    Navier-Stokes Equations: (6 lectures + 2 tutorials) – Craig McConnochie

    Module 1: The governing equations (4 lectures)
    Module 2: Solutions to the governing equations (2 lectures)

    At the conclusion of the Navier-Stokes equations section you should be able to:

  •    Provide a description of the various terms within the Navier-Stokes equations.
  •    Simplify the full set of equations and find a solutions to a simple problem.

    Turbulence and Far Field Mixing:   (15 lectures + 5 tutorials) – Craig McConnochie

    Module 1: "Introduction to Turbulence" "(5 lectures)"
    Module 2: "Turbulent Dispersion" "(5 lectures)"
    Module 3: "Turbulence Modelling" "(5 lectures)"

    At the conclusion of the turbulence section you should be able to:

  •    Provide a qualitative description of turbulent flow that includes the ideas of a spectrum of eddies of varying sizes, the energy cascade and turbulent kinetic energy dissipation.
  •    Describe the basis of Reynolds averaging, why it is often required to make headway in solving turbulent flow problems, and the closure problem that results.
  •    Explain the concept of an eddy viscosity and describe two turbulence models, Mixing Length Theory and the k- model, that are based upon it.
  •    Understand how far field mixing can be modelled using the turbulent advection diffusion equation and be able to model such mixing using an appropriate model.
  •    Understand the difference between different turbulence models and their key strengths and weaknesses.

    "Jets and Plumes:   (15 lectures + 5 tutorials) – Craig McConnochie"
    "Module 1:" "Introduction" "(1 lecture)"
    "Module 2:" "Jets" "(3 lectures)"
    "Module 3:" "Plumes" "(4 lectures)"
    "Module 4:" "Ocean outfall design" "(3 lectures)"
    "Module 4:" "Building Ventilation" "(4 lectures)"
    At the conclusion of the jets and plumes section you should be able to:

  •    Explain the important differences between jets, axisymmetric plumes, buoyant jets, line plumes and wall plumes.
  •    Use models of the above flows to calculate the velocity and dilution experienced at various locations.
  •    Provide a description of turbulent entrainment and how it manifests in each of the above flows.
  •    Model the environment within a room and understand simple methods of natural ventilation."




Course Coordinator / Lecturer

Craig McConnochie

Although I do not hold scheduled office hours I encourage you to contact me, either in
tutorials or in my office, if you have questions. This is particularly true as you work through each of the three projects. My door is generally open for you to drop in but during some periods I will be spending significant time in the fluids lab and it might be easier to arrange a
meeting time by email.


Assessment Due Date Percentage  Description
Disperson project 15%
Jets and Plume project 15%
Final exam 60% Final exam
Navier Stokes Assignment 10%

The assessment for this course will comprise two components – three assignments and the
final exam. The projects aim to provide you with the opportunity to work through substantial practical problems, putting into practice the analysis and design skills you have learnt. The final exam will focus more on the theoretical aspects of the course where the solution of complex practical problems is not possible due to the limited time available. The breakdown of all of the assessment items is listed below. Please read the notes following the table carefully.


1.         You cannot pass this course unless you achieve a mark of at least 40% in the final exam. A student who narrowly fails to achieve 40% in the exam, may still may be eligible for a pass in the course if they have performed very well in the internal assessment items.

2.         All projects must be submitted by the due date. Late submissions will not be accepted. If a student is unable to complete and submit an assignment by the deadline due to personal circumstances beyond their control they should discuss this with the lecturer involved as soon as possible.

3.         Students in this course can apply for special consideration provided they have sat the final exam.

4.         All projects must be done individually.

Indicative Fees

Domestic fee $1,002.00

International fee $5,625.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Civil and Natural Resources Engineering .

All ENCN441 Occurrences

  • ENCN441-22S1 (C) Semester One 2022