ABSTRACT
For simplicity's sake, let us consider a compressible amount of uid inside a tubular region (t) with volume V (t) at time t. (t) has an input face i with area Ai, and an output face o with area Ao = Ai. The outwardly directed unit normal to i and o are ni and no, respectively. This can be visualized using images of oil or gas pipelines. The uid is moving through such a pipe with a nonuniform velocity v(t) along its axis, but uniformly throughout each crosssection, so that particles are crossing i and o with velocities vi and vo, respectively, at time t. Consider the positions reached by the uid particles that were between i
and o at time t, after a time interval duration of t has elapsed (see Figure H.1.)
Figure H.1: Rectilinear tubular ow.
