Abstract

MENDOZA-GONZALEZ, Ángel  and  AGUILAR-CHAVEZ, Ariosto. Method to estimate the constants of the logarithmic law. Tecnol. cienc. agua [online]. 2019, vol.10, n.5, pp.154-176.  Epub Feb 15, 2020. ISSN 2007-2422.  https://doi.org/10.24850/j-tyca-2019-05-06.

This paper presents a procedure to determine the empirical constants of von Kármán κ and additive A of the law of logarithmic velocity distribution, is based on a global estimation of the minimum values of error between the logarithmic law model and the data of a measurement. To verify the goodness of the proposed method, a comparison was made with other methods presented in the literature, using the data of a velocity profile obtained in a variable slope channel of rectangular section, with an Acoustic Doppler Velocimeter (ADV). The experimental test was in uniform flow with bed roughness 𝑘s = 0.000535 m and Reynolds number 𝑅𝑒 > 36 000. The proposed method allows to simultaneously estimate the empirical constants κ and A, locating an optimal value called 𝐸min in a two-dimensional plane of error estimation of the constants. The results of the proposed method compared to others reported in the literature indicate an improvement or at least a similar estimate. In addition, the adjustment of the logarithmic law with the values obtained from the experimental test in the established range 30 < 𝑦+ < 0.3𝛿+ was verified, using the calculated values of κ and A with the proposed method.

Keywords : Logarithmic law; von Kármán constant; additive constant; acoustic Doppler velocimetry.

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