caa a22 4500 606189483 CHVBK 20210128100850.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10891-015-1303-6 doi (NATIONALLICENCE)springer-10.1007/s10891-015-1303-6 Bereslavskii É. State University of Civil Aviation, 38 Pilotov Str., 196210, St. Petersburg, Russia aut On Transformations of the Velocity Hodograph in Certain Problems of Fluid Mechanics [Elektronische Daten] [É. Bereslavskii] Consideration is given to the fl ow-velocity hodograph representing a circular hexagon in polar grids with two cuts, which is used in the theory of jets and cavitation, gliding theory, gas dynamics, the theory of groundwater motion, and filtration theory. It has been shown that in recording the parameter characterizing the ratio of the radii of circles, which are the opposite polygon sides with cuts, the configuration and relative position of the latter substantially change not so much with the properties of the functions on whose basis particular solutions of the corresponding Fuchsian-type equation are constructed, as with the ranges of conformal-mapping constants involved in the expressions for mapping functions. It has been established that to different ranges of variation in these constants there can correspond cuts varying in configuration and relative position. This is a manifestation of the transformation of liquid and gas filtration flows under the influence of different physical factors. Springer Science+Business Media New York, 2015 Fuchsian differential equations nationallicence conformal mapping nationallicence region of the velocity hodograph nationallicence circular and rectilinear cuts nationallicence elliptic Jacobian functions nationallicence theta functions nationallicence Journal of Engineering Physics and Thermophysics Springer US; http://www.springer-ny.com 88/5(2015-09-01), 1221-1227 1062-0125 88:5<1221 2015 88 10891 https://doi.org/10.1007/s10891-015-1303-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10891-015-1303-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bereslavskii É. State University of Civil Aviation, 38 Pilotov Str., 196210, St. Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Engineering Physics and Thermophysics Springer US; http://www.springer-ny.com 88/5(2015-09-01), 1221-1227 1062-0125 88:5<1221 2015 88 10891