= Viscous force
{title2=$\mathbf F_{\mathrm{visc}}=\int_{\partial V}\boldsymbol\tau\mathbf n\,dS$}
The viscous force on a fluid region is the resultant of the <traction> supplied by the <viscous stress tensor> $\boldsymbol\tau$. With $\mathbf n$ the outward <unit normal> of the region, its surface contribution is the displayed <surface integral>. For an incompressible <Newtonian fluid>, $\boldsymbol\tau=\eta[\nabla\mathbf u+(\nabla\mathbf u)^T]$, where $\eta$ is <dynamic viscosity> and $\mathbf u$ is <velocity>. A force scale is $\eta UL$ for a body of size $L$ moving at speed $U$, while the inertial force scale is $\rho U^2L^2$; their ratio is the <Reynolds number>. Total hydrodynamic <drag> on a body includes both viscous traction and the pressure traction induced by the flow. For example, the full <Stokes drag law> gives $6\pi\eta RU$ for a no-slip sphere, rather than just the viscous-traction part alone.
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