Consider the motion of a fluid in a region in which there are no sources or sinks, i.e., neither the fluid is being produced nor is destroyed. Let  denote the density of the fluid at a point  in the region at time  In other words, we are assuming that the fluid is compressible . Let
be the velocity vector field of the fluid . Then, the quantity
is called the flux of the fluid at the point  at time  Note that,  is a vector having same direction as that of  and the magnitude of  represents the flow of unit mass of the liquid per unit area, per unit time. This comes from the dimension considerations of  which are
One would like to write the equation of the fluid flow. For this, consider a small portion, a rectangular parallelepiped  of dimensions  with sides parallel to axes, in the fluid. We calculate the change in mass in the region  by computing the outward flow.
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