Skin-Friction and Forced Convection from Rough and Smooth Plates

The current models for skin-friction drag from a plate with a rough surface are derived by analogy to flow within pipes having rough interiors. But this analogy fails at low Reynolds number (Re) flow rates because the boundary-layer must compress into the center of the pipe, while the plate boundary-layer is unbounded. A significant discrepancy from the pipe analogy at low Re was found by the rough plate experiments of Pimenta, Moffat, and Kays (1975) and by experiments conducted by the present author (2019). An additional problem is that the roughness parameter in pipe analogy theories is tied to the drag measurements of flows inside Nikuradse's assortment of sand-roughened pipes (1933). Prandtl and Schlichting (1934) caution that their theory applies only to sand-roughness. More useful would be a theory based on direct measurements of roughness profiles. The present work derives the formula for a plate's skin-friction drag coefficient given its root-mean-squared height-of-roughness, and Re bounds from the roughness spatial frequency spectrum. The present theory is in close agreement with the Mills-Hang (1983) theory, the Pimenta et al measurements, and the experiments conducted by the author over their respective Re ranges. From boundary conditions of its rough plate analysis, the present work also derives an exact formula for skin-friction from a smooth plate; this formula is in very close agreement with measurements from Smith and Walker (1959) and Spalding and Chi (1964) over 4 decades of Re.Comment: Rewritten to include skin-friction from smooth plates. 20 pages; 17 figures; 16 reference

Matching Dependencies with Arbitrary Attribute Values: Semantics, Query Answering and Integrity Constraints

Matching dependencies (MDs) were introduced to specify the identification or matching of certain attribute values in pairs of database tuples when some similarity conditions are satisfied. Their enforcement can be seen as a natural generalization of entity resolution. In what we call the "pure case" of MDs, any value from the underlying data domain can be used for the value in common that does the matching. We investigate the semantics and properties of data cleaning through the enforcement of matching dependencies for the pure case. We characterize the intended clean instances and also the "clean answers" to queries as those that are invariant under the cleaning process. The complexity of computing clean instances and clean answers to queries is investigated. Tractable and intractable cases depending on the MDs and queries are identified. Finally, we establish connections with database "repairs" under integrity constraints.Comment: 13 pages, double column, 2 figure

Rhodes University: A Different Place

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