= Solution
The <stress tensor> of the incompressible <Newtonian fluid> is $\boldsymbol\sigma=-pI+2\mu e$, where $e=(\nabla\mathbf u+\nabla\mathbf u^T)/2$ is the <rate-of-strain tensor>. The homogeneous <Stokes equations> give $\nabla\cdot\boldsymbol\sigma=0$. Apply the <divergence theorem> to the fluid between the body and a surrounding sphere $S_R$. If $\mathbf n_B$ points from the body into the fluid, the fluid-domain normal on the inner boundary is $-\mathbf n_B$. Hence
$$
0=\int_{S_R}\boldsymbol\sigma\mathbf n\,dS-\int_{\partial B}\boldsymbol\sigma\mathbf n_B\,dS,
\qquad\boxed{\mathbf F=\int_{S_R}\boldsymbol\sigma\mathbf n\,dS.}
$$
This is the <force flux at infinity in Stokes flow>. A nonzero resultant <force> must be supported by a stress of order $R^{-2}$ on a surface of area of order $R^2$. More precisely, the leading exterior solution is a <Stokeslet> with force on the fluid $\mathbf f=-\mathbf F$:
$$
\mathbf u(\mathbf x)\sim\frac{(I+\widehat{\mathbf x}\widehat{\mathbf x}^{T})\mathbf f}{8\pi\mu R},\qquad
p(\mathbf x)-p_\infty\sim\frac{\mathbf f\cdot\widehat{\mathbf x}}{4\pi R^2}.
$$
Thus $\mathbf u=O(R^{-1})$, $p-p_\infty=O(R^{-2})$ and $e=O(R^{-2})$. These are leading generic orders for a translating body with nonzero drag; the integral alone does not determine every angular component, and force-free disturbances may decay faster.
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