Three-Dimensional Linear Flow of Finite Length with Uniform Intensity Distribution Along Length

New Approach to Investigation of Potential Flows with No Analytical Expression of the Velocity-Potential Function

“…It is demonstrated in [2] that the flow surfaces of a spatial linear flow of finite length are confocal hyperboloids (Fig. 2b ), but the equipotential surfaces are confocal ellipsoids.…”

“…Let us demonstrate this in an example of the calculation of the field of travel speeds of a liquid caused by a cylinder flow of finite length, which is located on an impenetrable cylinder in a boundless space filled with an ideal (non-viscous) liquid, based on the known velocity-potential function of a spatial linear flow of finite length [2].…”

“…Since r 1c.g increases continuously with increasing cosh ö 1 , velocity correction K v in the direction from the discharge cylinder also increases continuously, tending to unity. When moving along the streamlines, the continuity of K v , and its constancy for points falling on the equipotential surface, as well as the invariability of the form of the streamlines and the equipotentials for the initial flow and flow under investigation enable us to state that if the initial movement [2] is potential and continuous, the flow under investigation will also be potential and continuous.…”

“…Thus, the function of the velocity potential of the flow caused by the cylinder flow is written on the basis of [2] and (3) as…”

“…In the cylindrical coordinate system (r, z, È), this is written as where V r and V z are the radial and vertical velocity components, V avg are the average velocities on the equipotential surfaces, q 1 and q 2 are the flow rates of the first and second flows, respectively, and S 1 and S 2 are the areas of the corresponding equipotential surfaces of the first and second flows. If the flow rates q of the flows under consideration are similar, (2) and the function of the velocity potential Ö 2 of the second flow is expressed in terms of the function of the velocity potential Ö 1 of the first flow as…”