Solution
= Solution
The <scalar> integrand still equals $10e$ throughout the unit <sphere>, and the upper <hemisphere> has the same <surface area> $2\pi$. Excluding its equator changes no <area>. Therefore
$$
\boxed{\int_{S'}(\nabla\cdot\mathbf v)\,dS=20\pi e}.
$$
There is no sign reversal between hemispheres because this <scalar> <surface integral> has no choice of normal orientation.