Figure: Flow across a surface

represents the flux-density (mass per unit area per unit time) of the flow. Consider a surface in the flow. If is smooth, then the flux-density across a small patch of the surface at a point is given by the normal component of , i.e., Thus, the mass of the fluid flow across can be taken to be where is the unit normal at Thus, the total mass of the fluid crossing across the surface can be defined to be
                                                                ----------(68)