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Germplasm Evaluation of Cowpea
(Vigna unguiculata (L.) Walp.) in Dang District
Bereslavskii Eduard Naumovich* and Dudina Liliya Mihailovna
Saint Petersburg State University of Civil Aviation, USA
Submission: October 23, 2019; Published: November 06, 2019
*Corresponding author: Bereslavskii Eduard Naumovich, Saint Petersburg State University of Civil Aviation, USA
How to cite this article: Bereslavskii Eduard Naumovich, Dudina Liliya Mihailovna. On Accounting for Evaporation or Infiltration Free Surface in Some
Problems of Filtration Theory. JOJ Wildl Biodivers. 2019: 1(5): 555573. DOI: 10.19080/JOJWB.2019.01.555573
Within the theory of the flat established filtering of an incompressible fluid under Darci’s law in homogeneous and isotropic soil some tasks connected with currents in the presence of evaporation or infiltration on a free surface of subsoil waters are considered.
The task about flow of a groove was for the first time studied by NE Zhukovsky  where Kirchhoff’s method altered by it in the theory of streams was used for a solution of tasks with a free surface and special analytic function which is widely used in the theory of filtering is entered. Since function, and a task and a groove bear a name of Zhukovsky [2–6]. Work  opened a possibility of mathematical modeling of the movement of subsoil waters under Zhukovsky’s groove and laid the foundation for researches of the specified class of filtration currents (see, for example, reviews [2-6]).It should be noted that in tasks about flow of a groove of Zhukovsky application of function of Zhukovsky only then results in effective results when in addition to a free surface the border of area of a current contains only horizontal lines of equal potential and vertical lines of current (V.V. Vedernikov, FB Nelson Furriers SN Numerov, VI Aravin, etc). However in actual practice hydrotechnical construction, [2–5], the irrigated agriculture [2,4,7], etc. directly under integumentary deposits along with horizontal pres
sure head water-bearing layers more high-permeability  also horizontal waterproof inclusions often meet that radically affects the nature of filtration currents [8–12]. At the same time so far there are no works devoted to a special research of impact of evaporation or infiltration on filtration processes. Accounting of these important physical factors for the present did not become broad property of exact analytical solutions. In the presented work on the example of two limit filtration schemes which arise at flow of a groove of Zhukovsky, the impact of evaporation or infiltration on a current picture is studied [13-16].
The first limit scheme corresponds to a case when the layer of earth on all the extent is spread by the impenetrable horizontal basis and from a free surface there is a uniform evaporation of intensity ε (0 <ε <1). The current is provided with water inflow from the left part of a band of flooding with a liquid layer, invariable on time. As the right edge of a band of flooding serves the impenetrable vertical screen in the form of a groove of Zhukovsky which basis is located in layer, at the same time the static height of a capillary raising of a subsoil water can be considered (Figure 1a). In the second limit scheme the layer of earth is spread by well permeable pressure head aquifer in which pressure has constant H0 value, and on a free surface there is a uniform infiltration of intensity ε. Far from a groove (at x →∞) the curve of a depression is horizontal and located at H0 height over an aquifer (Figure 1b).
The exact solution of a task on a fluid influx to the imperfect
well with the flooded filter (i.e. an axisymmetric task) or the tubular
well representing an impenetrable pipe with the filter in
some (usually lower) its part is connected with great mathematical
difficulties and so far is not found. Therefore, in due time
as first approximation to a solution of similar tasks by PYa Polubarinova-
Kochina, VG Pryazhinska, VA Postnov and VN Emikh
[2,6,7,17,18] considered some corresponding flat task analogs
about filtering in a rectangular jumper with partially impenetrable
vertical wall and to imperfect gallery. It should be noted that
areas of values of complex speed in the specified cases allow to
apply by means of inversion at a solution Christoffel-Schwartz’s
In work the exact analytical solution of a task on a current of
subsoil waters in a rectangular jumper with slopes of A0A1 and
D0B, width of L located on the impenetrable horizontal basis of
length of L is given. Water height is equal in an upper byef to H,
lower reach with water level of H2, having partially impenetrable
vertical wall CD (screen), adjoins a basis sole. The upper bound of
area of the movement is free pover khnost AD which is coming out
with which there is a uniform evaporation to intensity ε (Figure
2). In the considered area of complex speed, unlike [2,6,7,17,18],
there are not rectilinear, but circular polygons that does not give
the chance to use classical integral of Christoffel-Schwartz. the
task solution on a current to the imperfect well formally turns out
from a task solution on filtering in a rectangular jumper with partially
impenetrable vertical wall in case of its infinite width, i.e. at
L = ∞ [19,20].
For studying of the specified currents in the presence of evaporation
or infiltration on a free surface the mixed multiple parameter
boundary value problem of the theory of analytic functions
which solution is carried out with use of the method of PYa Polubarinova-
Kochina [2-7] based on application of the analytical
theory of linear differential equations of a class of Fuchs are formulated.
And also [21-24] ways of conformal mapping of a special
type of circular polygons developed for areas which are very typical
for tasks of the theory of filtering. Accounting of characteristics
of the considered classes of areas of the hodograph of speed
allowed to present solutions of tasks in the closed form through
elementary functions that does their use the simplest and convenient
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