# THEORETICAL CALCULATION OF THE VALUE OF THE VON KARMAN CONSTANT

Section
Methods, models and technologies
• Alexey Yu. Vinogradov Scientific and Industrial Research Association Gidrotehproekt, Valday, Russia Saint Petersburg State Forest Technical University, St. Petersburg, Russia
• Mariya M. Kadatskaya Scientific and Industrial Research Association Gidrotehproekt, Valday, Russia
Keywords: the von Karman constant, coefficient of turbulent exchange (viscosity), Reynolds number, cient of hydraulic friction, velocity distribution diagram, turbulent mode
(+) Abstract

The article considers various approaches to assessing the physical essence of the von Karman constant characterizing the vertical distribution of the flow velocity. On the one hand, the von Karman constant is a proportionality coefficient between the length of the mixing length and the depth; on the other hand, it characterizes the tilt angle of the vertical velocity profile. It is considered that this parameter is universal, that means it is constant as long as the averaged velocity distribution is constant. However, depending on estimation way of this constant, its values under the same conditions may differ to 2 orders.

Two methods for estimating the von Karman constant are considered. In the first case, determination of the von Karman constant is on the grounds of direct measurements of the maximum and average flow velocities, depth and slope of the water surface in a particular area. Propagation of the obtained value to other objects will lead to errors.

In the second case, the parameter is defined as a function of the coefficient of hydraulic friction. The authors showed that the von Karman constant is a function of the coefficient of turbulent exchange (viscosity) and indirectly is a function of the depth. As a result of the calculations, it was shown that the maximum values of the von Karman constant observed on the bottom.

Additionally, the authors propose a new version of the calculation of the von Karman constant through the tension shift for a turbulent flow.

It is concluded that since for velocities <1 meter per second the changes in the von Karman constant values from 0.27 to 0.38 the maximum velocity with variation do not exceed 3%, which fits into the accuracy of the velocity measurements, it is practically impossible to estimate the value of von Karman constant by first method for flat rivers even with multiple measurements with standard hydrometric equipment.

Keywords: the von Karman constant; coefficient of turbulent exchange (viscosity); Reynolds number; coefficient of hydraulic friction; velocity distribution diagram; turbulent mode

Scientific and Industrial Research Association Gidrotehproekt, Valday, Russia Saint Petersburg State Forest Technical University, St. Petersburg, Russia

E-mail: gd@npogtp.ru
eLibrary SPIN-код: 3692-8409
Scopus ID: 56909443300
ORCID iD:0000-0001-6834-2507

Scientific and Industrial Research Association Gidrotehproekt, Valday, Russia

E-mail: mk@npogtp.ru
eLibrary (РИНЦ) SPIN-код: 6624-6450
Scopus ID:
ORCID iD: 0000-0002-5979-0970

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