A

The expression for (diV<pdV)/d is straightforward. It is dJ<pdV = dJv(<<p)avedV = dJy[X] dV = dmJydV = d[X]V = dJXX} dt dt dt dt dt dt

Substituting in Eqs. (92), (93), (94) into the Reynolds transport theorem,

V^m [ X ] - kd [ X]j = j V^p}+{-Q [ Xo ] + Q [ X]} (95)

This simplifies to

This may be compared with Equation (75). As shown, the difference is in the confusion as to whether to use the total derivative or the partial derivative. This difference may be dismissed as trivial, but, of course, the use of the total derivative is very wrong. Compare the two expressions:

From this comparison, it is very clear that d[X]/dt is not equal to d[X]/dt and one cannot substitute for the other.

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