On Transformations of the Velocity Hodograph in Certain Problems of Fluid Mechanics.

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. [ABSTRACT FROM AUTHOR]