Course content

Derivation and discussion of the basic equations for viscous fluid flow, including heat conduction and compressibility. Molecular background for viscosity. Exact solutions like; Couette flow, Stokes 1. - and 2. problem, Hiemenz stagnation point flow, Von Karman flow near a rotating disk. The boundary layer approximation, Blasius and Falkner-Skan solutions, effects of pressure gradient; Pohlhausen's method, criteria for separation. Non-steady boundary layers. Stability of laminar flow, Kelvin-Helmholtz instability, Orr-Sommerfeld equation and transition to turbulence.
Examples from internal flows, and from flows around bodies.

Learning outcome

Knowledge:
The course provides the student with knowledge about:
- Formulating and solving problems in fluid mechanics where viscosity and heat conductivity are of importance, in particular at high Reynolds numbers where the boundary layer approximation applies.
- Primary focus is on the laminar flow regime. Briefly about stability and transition to turbulence.
- Quantitative methods for classical cases, such as Stokes problems, stagnation point flow, Blasius and Falkner-Skan problems, and integral methods for other boundary layers with pressure gradient and possible separation. Qualitative and quantitative aspects of the stability theory for parallel flows in simple geometries.
- Applications for internal flows in pipes and channels and for simple process components, as well as for external flow around wing profiles.
- The course gives the student insight about:
- Application of basic theory for viscous and thermal boundary layers to estimate spatial distribution of flow properties, as well as to determine friction forces and heat transfer between fluid and solid boundaries in an engineering context.

Skills:
The course should enable the student to:
- Compute critical parameters like friction factor and heat flux at wall, in addition to local details in the flow field, for systems of simple geometries.
- To some extent design process components for specific purposes from performance requirements, such as pressure recovery and thermal development in the flow field.

General competence:
The course should give the student insight on:
- Systematic applications of the general theoretical background for thermo-viscous flows in a technological context, in particular for high Reynolds numbers.
- Coupling to potential theory in elementary fluid mechanics, and construction of composite solutions for complete flow domains.
- Use of standard mathematical tools for analyzing and solving real-flow problems, in particular in the area of mechanical engineering.

Learning methods and activities

Lectures, written exercises and one compulsory laboratory exercise. The lectures and exercises are in English when students who do not speak Norwegian take the course. If the teaching is given in English the Examination papers will be given in English only. Students are free to choose Norwegian or English for written assessments.

Compulsory assignments

• Exercises

Recommended previous knowledge

Basic fluid mechanics.

Course materials

F.M.White: Viscous Fluid Flow, McGraw Hill, 3rd ed.
T.Ytrehus: The governing equations in fluid mechanics (16 pages).

Credit reductions