  The conformal mapping problem for the section of a channel filled with porous
material under a rectangular dam onto the upper half-plane is considered.
Similar problems arise in computing of fluid flow in hydraulic structures. As a
solution method, the representation of Christoffel-Schwartz elliptic integral
in terms of Weierstrass functions is used. The calculation is based on Taylor
series for the sigma function, the coefficients of which are determined
recursively. A simple formula for a conformal mapping is obtained, which
depends on four parameters and uses the sigma function. A numerical experiment
was carried out for a specific area. The degeneration of the region, which
consists in the dam width tending to zero, is considered, and it is shown that
the resulting formula has a limit that implements the solution of the limiting
problem. A refined proof of Weierstrass recursive formula for the coefficients
of Taylor series of the sigma function is presented.
