Determining the flux of an arbitrary vector function

[DarkBabylon]

Hello there. I've been working on trying to re-derive a certain physical formula using vector calculus, and came to a conclusion that in order to derive it, I'll need a way to determine the nature of a certain expression.
Specifically:
∯f(v)·da - v={x₁,x₂,x₃,...,x_n} and f(v) returns a vector in the same space of v.
Is there a way to determine if a certain arbitrary function f(v) has a constant Flux, as one would call it, on a closed surface using some other information about f(v) such as its potential (∮f(v)· dv), divergence, etc.?

 

[Stephen Tashi]

if a certain arbitrary function f(v) has a constant Flux,

What flux do you want to be constant? The flux of a given function over a given surface has some numerical value - i.e. it is a constant.

 

[DarkBabylon]

i.e. it is a constant.

Oh, right. Thanks.