Lieber and Yajnik 

 Substituting Eq. (7) in Eq. (3), we obtain 



"i.t + "j^i.j = -P% - P?i +^V2u. . (8) 



Consequences of Symmetry 



Let us now consider symmetrical flow. The even and odd terms in Eq. (8) 

 are indicated by e and o: 



e e e e e o e 



"2,t + ^2^2,1 + "2^2,2 + "3^2,3 = '^U ' ^^ + ^^'^2 = 



o o o o o e o 



"3,t + "'"3,1 + "2^3,2 + "3^3,3 " -"^U " P% + ^^'^3 = 



e e e e e o e 



"l,l + "2,2 + "3,3 = . 



Since even and odd parts must vanish individually, we get 



"i,t + "j"i,j " -P'i + ^^'"i (9) 



p^. = (10) 



u. . = . (11) 



Since P^ does not vary with x-, 



P^(x,,X2,X3,t) = P^(Xj, -Xj.Xg.t) . 



Hence, by virtue of Eq. (6), P^ vanishes everywhere. In other words, 



P(Xj,X2,X3, t) = P(Xj, - X2,X3, t) . 



Thus, pressure must be symmetrical in a symmetrical flow. 



Consequences of Antisymmetry 



Now let us consider antisymmetric flow. The even and odd terms are indi- 

 cated below by e and o respectively: 



684 



