Solution
= Solution
In <spherical symmetry>, the velocity is radial and constant over each sphere. Hence
$$
Q(R,t)=4\pi R^2u(R,t).
$$
Apply the <divergence theorem> to the fluid shell between radii $R_1$ and $R_2$. Since the flow is <incompressible flow>[incompressible],
$$
0=\int_{\text{shell}}\nabla\cdot u\,dV
=Q(R_2,t)-Q(R_1,t).
$$
\b[Thus $Q$ is independent of $R$ and is a function of time alone. This is the flux law for <spherically symmetric incompressible radial flow>.]