What is the expression for when the surface is curved? See the figure below.

and the water flow
is specified by
. Then, by
applying equation (2), the small flux
through the
ith segment is 
where is the angle between the vectors
and
.
The total flux through the curved surface can be obtained by summing
all the
's from i=1 to
i=n.

(Remember, i is an integer.)
In the limiting case,

we obtain
|
(3) |
Notice that this is an area integral. In general, evaluating this integral will be rather complicated, but in this module we will use it only in cases of simple geometry.
Once you're ready, go on to our discussion of flux through a Gaussian surface.