The divergence theorem states that the integral of the divergence of a vector field within a volume equals the flux of the vector field through the surface enclosing the volume. To understand this, consider the velocity field of a fluid flowing smoothly in a pipe. If a hole is poked through its surface, the fluid flows through it. The velocity field then has a positive divergence near the hole. The total amount of fluid flowing out from the pipe per unit time is equivalent to the net divergence of the velocity in the entire pipe volume. Stokes' theorem states that the surface integral of the curl of a vector field over a closed surface equals the line integral of the vector field around that surface. The curl of a vector represents the circulation of that vector along a closed loop. On the surface, the adjacent loops have opposite circulation and cancel each other out. So, the net circulation is only around the edge of the loops.