# TEP4156 - Viscous Flows and Boundary Layers

### Examination arrangement

Examination arrangement: School exam

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours C

### Course content

The viscous flow and boundary layer course should be considered mandatory for any student interested in the fundamental aerodynamics, renewable energy systems such as wind turbines and hydropower, as well as any applications of fluid flow in mechanical or aeronautical engineering in general. This course provides a more in-depth introduction to viscous flow beginning with exact solutions for flows where viscosity dominates (low Reynolds number) and laminar boundary layer theory. The latter part of the course introduces turbulent flow which occurs at higher Reynolds number. The course covers the following topics: Fluid properties and the equations of motion for basics of viscous flows, (Couette, Poiseuille, Combined Couette-poiseulle flows), the derivation of the stresses in a viscous fluid, Navier Stokes equation, laminar boundary layer theory, boundary layer equations, momentum integral equation, similarity solutions, effect of pressure gradients (flow separation), transition to turbulence and turbulent boundary layers.

### Learning outcome

The course provides the student with knowledge about boundary layer flows around bodies and internal flows which are the building blocks to a wide range of important mechanical and aeronautical engineering problems such as the origin of drag forces in aerodynamics and renewable energy applications such as wind turbines. Students will be able to:

• Formulate and solve problems in fluid mechanics where viscous effects are important.
• Apply and modify the boundary layer equations to account for pressure gradient effects and understand when such approaches are valid.
• Understand similarity solutions, the effect of pressure gradients on the flow, and the origin of drag.
• Apply approximate methods to solve for the boundary layer profile in flows with arbitrary pressure gradients typical of flows around aerofoils.
• Understand the basic concepts behind laminar to turbulent transition, the Reynolds decomposition and turbulent boundary layers.
• Compute critical parameters like the friction factor, shape factor, boundary layer thicknesses, as well as the mean velocity profile for laminar and turbulent boundary layers over simple geometries.

### Learning methods and activities

The lectures and exam will be in English.

### Further on evaluation

If there is a re-sit examination, the examination form may be changed from written to oral.

### Course materials

Written notes will be provided.

Recommended text book: F.M.White: Viscous Fluid Flow, McGraw Hill, 3rd ed.

More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Second degree level

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2023

Language of instruction: English

Location: Trondheim

Subject area(s)
• Energy and Process Engineering
• Marine Hydrodynamics
• Physics
• Mathematics
• Technological subjects
Contact information
Course coordinator:

Department of Energy and Process Engineering

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD School exam 100/100 2023-12-11 09:00
Summer UTS School exam 100/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

More on examinations at NTNU