(Created 2008-07-17.)

ADVANCED HYDRAULICS | VVRN01 |

**Aim**

The objective of the course is to provide a fundamental understanding of the phenomena and processes that govern water flow with the special purpose of providing the students with knowledge to analyze flow conditions both in technical systems and in nature. Emphasis is put on the ability to describe advanced flow problems in mathematical terms in order to compute primary variables such as pressure and velocity and how they vary in time and space. The course discusses both fundamental and applied aspects of water flow.

*Knowledge and understanding*

For a passing grade the student must

- In detail understand de basic processes that govern water flow.
- Be able to interpret and formulate advanced mathematical models to describe water flow based on the conservation equations for mass, momentum, and energy.
- Understand and describe in a comprehensive manner the common flow situations in technical systems and in nature.

*Skills and abilities*

For a passing grade the student must

- Be able to analyze common flow situations in technical systems and in nature with respect to the governing processes.
- Be able to formulate mathematical models to describe common flow situations.
- Be able to simplify the governing equations for water flow based on an understanding of the flow situation and the dominant processes.
- Be able to apply mathematical models to solve specific flow problems.

*Judgement and approach*

For a passing grade the student must

- Be able to present the basis for analyses and calculations, including simplifications and assumptions made, when formulating mathematical models.
- In quantitative terms be able to communicate the results of analyses performed to a qualified group of stakeholders.

**Contents**

Basic concepts concerning flow kinematics and dynamics together with the control volume approach. Fundamental equations for conservation of mass, momentum, and energy. Euler's equations. Navier-Stokes equations. Solutions to the fundamental equations for special flow problems (e.g., flow between two plates, creeping flow). Laminar and turbulent boundary layers. Turbulence theory and models (e.g., mixing length models, k-epsilon models). Density effects and stratified flow. Application to specific flow situations in:

- Meteorology and oceanography (e.g., geostrophic wind, athmospheric boundary layers, Ekman spirals)
- Free-surface flows (e.g., non-uniform flow, dynamic and kinematic waves, flow in water courses and on the surface)
- Circulation in lakes (e.g., wind-induced circulation, seiching)
- Jets and plumes (e.g., evolution of and mixing in jets and plumes, interaction with the ambient, density effects)
- Transport of substances in water including heat (e.g., mixing, transport processes, diffusion, advection)

**Literature**

Ligget, J.A. Fluid mechanics, McGraw-Hill, 1994.

Various papers and handouts on specific topics.