We exclude the derivation of the theorem from the present course; however discuss the significance and the application of the same. The theorem relates the rate of change of a property associated with a CV to the material or particle rate of change of that property. Consider a CV bound by the CS through which a fluid flows, described by the flow field,   relative to co-ordinates . As per the definition, CV is fixed in the flow field:

(Fig. 11a)

N is a property associated with flow field in CV. N could be either mass or momentum or energy or concentration of a species dispersed in the fluid. The theorem states:

where  is the specific property, N/M, where M = mass of fluid in volume .    or,         Note that if the property is mass, . If the property is momentum, . If the property is kinetic energy, .