It is proposed to consider plane or axisymmetric incompressible flows when at a certain point in space a finite source of momentum is instantaneously created. This type of flow is characterized by the continuous setting in motion of new volumes of fluid with a simultaneous decrease in velocity. It is usual to associate this diffusional process with viscosity. Here it is shown that such processes can be described within the framework of an ideal fluid. The main concern is to prove the existence of four-parameter plane ideal-fluid flow. The method of constructing the solution is based on the conformal transformation of the dimensionless variable, so that from the relatively simple self-similar solution the unknown flow can be obtained.