Divergence & flow integral

robban96

New member
Joined
Oct 27, 2014
Messages
3
Hi! I got this task:

S = the mantle area of the cylinder.
F = the vector field.

x^2+y^2=4
-2<= z <=2

F(x,y,z) = (x, 2y, 1-3z)

As div(F) = 0,
shouldn't the flow through the mantle area S also 0 ?

Because in one solution I got, which I don't really believe in, the take:
flow(total cylinder) - flow(top part cylinder) - flow(bottom part cylinder) = flow(mantle cylinder)

I get why they subtract like that, but shouldnt it be zero as div(F) = 0 ?
 
Top