If the mass of the system is m at the initial instant of time, then its mass is preserved for all time afterward unless there is a process involving this group of particles that changes part of its mass into energy. This could happen if, for instance, nuclear processes occur in which mass is converted to energy. We do not consider such processes in this book; so, for all cases of interest, we can state with confidence that the mass remains constant. Thus, in rate form, we write:
for the specified system of fluid particles. The mass can be expressed conveniently as an integral over the volume containing only the identified particles:
m= J dm = JJJ pdV, (3.2)
where system mass is always meant to identify the mass of the particular glob of particles constituting the defined system; and system volume, V, is that volume of space enclosing the system glob at any given instant of time. Notice that the system volume might be required to change with time (although the mass remains constant) if the density of the glob, p, changes from point to point in the flow field. If Eq. 3.1 is satisfied, we ensured that system mass is not created or destroyed; in other words, mass is conserved. All other required laws of motion are expressed in similar rate form in the following subsections.