>>Сабинин Г. Х. Теория идеального ветряка
Уникальное открытие. Ерохин В.В. из Тореза нашёл продольную силу в магнетизме Подробнее
Сабинин Г. Х. Теория идеального ветряка
The Theory of an Ideal Windmill.
The theory of an ideal windmill, developed in the present paper, is tased an application of the vortex theory of drag of laminae in three -dimensional flow, which vas given by Prof. N. E. Joukowsky, to the phenomenon taking place during the working of ideal windmill.
The ideal windmill is defined by the author as heving the following characteristics: 1) The aerofoil rasistance of the blades is zero; 2) the circulation of velocity around the blade outline is constant for the whole length of the blade; 3) the angular velocity of rotation tends to infinity, and the number of blades is very large; 4) the vortex solenoid which descends from the blade tips, and which represents continuous sheet of vortices, of infinitely small thickness, at a certain distance from the windmill takes a . cylindrical shape, the result being that the currents both inside and outside the solenoid become parallel to its axis, the pressures at all points sufficiently distant from the windmill are constant, and the velocities are equal over the whole cross-section of the current.
The pressure on the windmill is equal in magnitude, and opposite in sign, to the increment of the momentum produced by the cylindrical portion of the solenoid formed in unit time.
The circulation of velocity around the contour abed (fig. 2) for unit length of the solenoid
The momentum produced by unit length of the vortex solenoid is
where: F2 = area of cross-section of the current (fig. 2);
The increase in length of the solenoid per one second is
The pressure on the windmill
The entire system is given the velocity V — v2 in the direction opposite to that of velocity ot the flow (fig. 5), and the equation of the balance of energy writes for the whole flow to the left of the plane CC. The work performed by the external force P
The loss in kinetic energy of the current after passing through the windmill
The work absorbed by the vindmill
The equation of the balance of energy
The equation of discharge (see fig. 2)
Equating together (3), (9) and (9a) we get
The summation of (12) and (13) gives
Thus the swept area is the mean of the areas of cross-sections of fhe current before and after the windmill.