Based on the use of the complex potential of the vortex function, a mathematical model of the working process of the jet pump for the conditions of its symmetrical rotation in the well is proposed. The field of linear velocities is characterized by the trajectory of vortex lines, which are generated by a vortex point for a planar flow and a vortex conduit for a spatial flow. To characterize the vortex function, the vector circulation of the translational speed of the liquid movement along a closed circuit in the form of a double product of the flow rate by the area of the mixing chamber has been used. In the case of plane flow, the graphic representation of the vortex function has the form of concentrically placed streamlines and a set of equipotential lines passing through the coordinate center. For a three-dimensional flow, the equipotential surfaces and flow surfaces of the eddy function, as in the case of the leakage function, form a hydrodynamic mesh in the form of orthogonally placed coaxial spheres and radial meridional planes. The ratios obtained in the process of modeling the working process of the jet pump satisfy the CauchyRiemann conditions, which makes it possible to determine the absolute value of the velocity vector of the vortex flow in the form of the derivative of the characteristic function of the circulation flow. According to the obtained characteristic function, the speed of the circulation current is determined by asymptotic curves; in the case of zero values of the coordinate of the spatial vortex, the speed of the circulation current is equal to infinity, and with increasing distance to the origin of the coordinates, it approaches zero. The maximum speed of the circulation flow depends linearly on the rotation frequency of the drill string. It is directly proportional to the diameter of the mixing chamber of the jet pump
Received 27.04.2022
Revised 21.06.2022
Accepted 31.08.2022
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