A Similarity Solution for Slow Viscous Flow Down an Inclined Plane,
Abstract
A similarity solution is found for the distribution of layer thickness in the slow flow of a three-dimensional, thin, viscous jet down an inclined plane. In the context of a formal asymptotic expansion in inverse powers of x, the distance downstream from the source, the solution is recognized as the zeroth-order asymptotic limit. Making use of physical arguments to exclude certain complementary functions, the solution of the first-order problem is found to be a polynomial of fourth degree. A simple experiment confirms the major features of the similarity solution. Deviations of the layer thickness measurements from the parabolic profile follow the trend predicted by the first-order corrections in the portion of flow near the edge, whereas systematically high values in the central region are explained qualitatively in terms of waves at the free surface. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1972
- Accession Number
- AD0737399
Entities
People
- Peter C. Smith
Organizations
- Massachusetts Institute of Technology