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Birkhoff G.D.'s A Theorem on Series of Orthogonal Functions with an PDF

By Birkhoff G.D.

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Additional resources for A Theorem on Series of Orthogonal Functions with an Application to Strum-Liouville Series (1917)(en)

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The relationship between the change in filter porosity and the extent of deposition can be considered in the following manner. If one assumes that the particle deposition on the outside of the filter granules forms a relatively smooth surface on the granules, then a filter grain’s effective diameter increases as the extent of deposition increases. 4). , 1979), but it can be used to develop, from experimental data, empirical expressions for G. 3 is presented a list of expressions for G proposed by various investigators.

Ornatski, N. , E. V. Sergeev, and Y. M. Shekhtman, “Investigations of the Process of Clogging of Sands,” University of Moscow (1955). Payatakes, A. , R. M. Turian, and C. Tien, “Integration of Filtration Equations and Parameter Optimization Techniques,” Proc. 2nd World Congress of Water Resources, Vol. 241 (1975). m. Page:58 Trimsize:156×234 MM CHAPTER 2 MACROSCOPIC DESCRIPTION OF GRANULAR FILTRATION Shekhtman, Y. R. Academy of Science (1961). Stein, P. , “A Study of the Theory of Rapid Filtration of Water Through Sand,” DSc.

M. 72b) where n0 is the total number of open pores in a clean filter. 73b) For a clean filter, all the pores are open. 74b) yields the distribution of the pore-blockage probabilities. 73b) is unnecessary. m. 18)]. Since the consequence of particle deposition is to block some of the pores, the effective cross-sectional area of the filter flow decreases as the number of blocked pores increases. Therefore, under the constant flow condition, the effective superficial velocity is inversely proportional to the number of pores remaining unblocked.

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A Theorem on Series of Orthogonal Functions with an Application to Strum-Liouville Series (1917)(en) by Birkhoff G.D.


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