Mathematical model of a droplet EPR

In the simplest case, all the droplets are of the same size and the droplet canopy affects the wind flow like an easily penetrable roughness mathematically expressed by the conjugation problem (3.33)—(3.35). The boundary layer approach is thus accepted. The distributed mass force / should depend, however, not on the local velocity P of the carried medium alone, but on the relative velocity between the two media V - T. To get /, the individual force (1.14) should be multiplied by the concentration of droplets n. 

The droplet medium is precisely governed by equations (1.15) and (1.16) which are linked with each other and are very difficult for investigation. Bearing in mind that only heavy droplets should be accounted for, let us use the appropriate law of vertical droplet motion instead of the second equation for the vertical droplet speed v. Imagine the simplest situation that the droplets are constantly generated at the height of fountains z = h with intensity q, /(m2s). 

After being born, all the droplets fall down towards the water collection surface z = 0 with the velocity v = v(z). Several assumptions can be suggested. 

Constant fall-down speeds (light droplets) 

The motion of a mass in the resistive atmosphere was well studied in connection with rain droplets and cannon shell trajectories. It is known particularly that any body reaches its constant fall-down speed, v(t) - v, the pancake speed . If a droplet of radius r with the frontal area S = nr2 moves in the vertical direction Oz only, Eq. (1.16) takes the form3 

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