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Toward Achieving Dimensional Homogeneity in Hydrologic Analysis
Author(s) -
Wong Shue Tuck
Publication year - 1978
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/j.1538-4632.1978.tb00655.x
Subject(s) - buckingham , dimensionless quantity , homogeneity (statistics) , homogeneous , mathematics , statistics , physics , thermodynamics , combinatorics , quantum mechanics
Dimensional analysis, through the application of Buckingham's π‐theorem, has been employed to formulate a functional relationship among a set of dimensionless products into an indeterminate homogeneous equation. In showing how dimensional homogeneity can be achieved for a given set of hydrologic variables involving the fundamental dimensions of mass, length, and time, the basic concepts and principles of dimensional theory are first presented; Buckingham's π‐theorem is next stated and then applied to the set of hydrologic variables. A great many ways of arranging dimensionless groups were revealed in the course of deciding the most meaningful combination of dimensionless terms for the final equation.