2 7 0 D O C . 3 3 9 A N I S O T R O P I C P R E S S U R E F O R C E S , where f means a sought function of the velocity components and means the element of the velocity space. The secondary conditions apply:[6] . . . (5) (per the definition of the probability function f ) . . . (6) . . . (7) (condition of the freedom of flow) . . . (8) (given heat flow) m means the mass of the molecule, n the number of molecules per unit volume. Executing the variation yields , . . . (9) where C, h, A, B are independent of . This solution cannot apply to arbitrarily large positive . Nevertheless, for a small A and B it is still useful in velocity ranges, at the limit of which the factor practically vanishes. We can, of course, confine our entire consideration to this range of the velocity space. For finding the constants C, h, A, B we note that we may substitute (9) to second approximation with . . . (9a) With this taken into account, (5) yields . . . . (10) Furthermore, from (9a) and (7) we get . . . (11) Finally, from (8) follows: . . . . (12) To first approximation it is also known that[7] , . . . (13) where M denotes the molecular weight with reference to the mole, R the gas con- stant, T the absolute temperature. Now after function f of the velocity distribution has been obtained, the pressure components can be calculated by means of the formulas: f lg fdτ ξ η ζ , , fdτ 1= [p. 2] m 2 --- -( ξ2 η2 ζ2)fdτ[ + + ] L const. = = ξfdτ[ ] 0= n m 2 --- -( ξ2 η2 ζ2)ξfdτ + + fx = f Ce h( ξ2 η2 ζ2) + + Bξ( ξ2 η2 ζ2) + + + + = ξ η ζ ,, ξ η ζ e–h( ξ2 η2 ζ2) + + f Ce–h( ξ2 η2 ζ2)[ + + 1 Bξ( ξ2 η2 ζ2)]. + + + + = C h3 /2π 3 2 -–-- = 2Ah 5B + 0. = [ ]mnAh 2– fx = h M 2RT ---------- =
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