Abstract
This chapter covers the modelling of two applied problems in fluid dynamics in brief case studies. The problems, on air bearing sliders and rivulet flows in wedges, build on a common core model called lubrication theory, which is derived in the beginning of the chapter. The case studies differ in many physical aspects (compressible versus incompressible flows, and free-surface versus squeeze film flows) and mathematical techniques employed (similarity solutions versus boundary layers and linear stability analysis). They serve to illustrate the power of the modelling methods to handle a diverse range of types of problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The derivation for the full three-dimensional system follows analogously.
- 2.
Referring to the number of lateral dimensions.
- 3.
This analysis is based on the paper [16] to which we refer the interested reader for more details.
- 4.
The sides of a Plateau border are actually circular arcs and there is no free-surface, but the model equations that we derive here are still applicable. This is an example of how modelling and investigating one problem can also provide useful information for other related problems.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Witelski, T., Bowen, M. (2015). Modelling in Applied Fluid Dynamics. In: Methods of Mathematical Modelling. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23042-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-23042-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23041-2
Online ISBN: 978-3-319-23042-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)