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3.3 Determination of velocity and acceleration fields of ether streams of isolated sources and drains

Let us consider the mechanical models of velocity and acceleration fields of ether streams of isolated sources and drains, consistent with the views of Faraday and Maxwell.

Let us single out an isolated material system consisting of a source bounded by the surface of a sphere of radius R_u, And a space uniformly filled with ether particles.

Suppose that the source is characterized by a constant intensity -  Q_u, That is, a constant mass stream of ether particles per unit time passing through its surface.

Then, taking a positive direction - the direction from the center of the source, we get:

  (3.3.1)

Where:  - density of ether particles, in the filled space; 

 - an elementary increase in volume;

 - increment of time.

Elementary increase in volume is defined as the difference in volumes bounded by spheres. Spheres of radius R , Bounding the front of the ether streams emitted by the source in time , And a sphere of radius R_u, Limiting the source (Figure 3.3.1).

Fig. 3.3.1

 (3.3.2)

We define the derivative of the function  depending on the argument  .

    (3.3.3)

Substituting the value obtained  From (3.3.3), into equation (3.3.1), we obtain the dependence:

= (3.3.4)

From (3.3.4) we determine the field of distribution of the velocity vectors of ether particles in the streams emitted by an isolated source - :

  (3.3.5)

Differentiating the particle velocities in (3.3.5) with respect to time (3.3.4), we determine the field of distribution of the particle acceleration vectors in the streams emitted by an isolated source -  :

      (3.3.6)

Similarly, we define the field of distribution of velocity vectors of ether particles in streams absorbed by an isolated sink -  :

  (3.3.7)

where:   - intensity of drain;

- an elementary decrease in volume;

- increment of time.

Elementary reduction in volume is defined as the difference in volume of spheres. Spheres of radius R_c , Which limits the runoff and sphere of radius , Bounding the front of the ether particles absorbed by the runoff in time .

  (3.3.8)

We define the derivative of the function Vc depending on the argument R.

(3.3.9)

Substituting the value obtained  From (3.3.9), into equation (3.3.7), we obtain the dependence:

= (3.3.10)

From (3.3.10) define distribution field vectors ether particle velocities in streams absorbed insulated drain -   :

(3.3.11)

Differentiating the particle velocity (3.3.11) over time (3.3.10), we define the vectors of the field distribution in the acceleration of the particles streams absorbed insulated drain - :

(3.3.12)

3.4 General view interaction equation sources and drains

Analytical model define mechanical force interaction sources and drains.

Consider an element of a sufficiently small surface bounding material object - ,  In which the ether of particle velocity changes in the stream can be ignored.

We define the mass stream rate of the particles - through the element surface  per unit time in the direction  :

(3.4.1)

Where: - total velocity vector ether particles fluxes passing through the element surface ;

- the particle velocity vector ether in i-volume flow;

- the number of threads ether particles passing through the element surface ;

– the unit vector normal to the outer surface of the element .

Then the projection of the reactive force  in the direction , Exerted by the ether stream on the particle surface of the object , member  Will be proportional to the mass stream rate of the particles in the stream module потоках - , Emitted (absorbed) from the surface of the element , On total acceleration vector particles in these streams- the direction :

(3.4.2)

Where: - proportionality factor.

Integrating across the surface of the material object , in the direction of the projection  , Define the value of the force acting on the material object in the desired direction:

(3.4.3)

Equation (3.4.3) is the general form of equations describing the interaction of material objects in the physical fields in the case of emission or absorption ether flows.