The following is a problem in "Transport Phenomena" by Bird et al :
"A mathematical plane surface of area $S$ has an orientation given by a unit normal vector $\bar{n}$, pointing downstream of the surface. A fluid of density $\rho$ flows through this surface with a velocity $\bar{v}$. Show that the mass rate of flow through the surface is $w=\rho(\bar{n}\cdot\bar{v})S$"
Certainly this plane is some flat two-dimensional plane in $\Bbb{R^3}$. The orientation refers to one of two sets of normal vectors, corresponding to the two sides of the plane. What confuses me is the "downstream of the surface" phrase. I cannot see how any surface has a "downstream". What are the relevant facts one should understand from the quote above?