= Laminar skin-friction scaling along a slender swimmer
{title2=$\tau_w\sim\rho\sqrt\nu\,u_t^{3/2}s^{-1/2}$}
A steady attached laminar <boundary layer> with slip speed $u_t$ and downstream distance $s$ has thickness $\delta\sim\sqrt{\nu s/u_t}$. The wall shear is $\tau_w\sim\mu u_t/\delta$, giving the displayed scaling, where $\mu=\rho\nu$ is <dynamic viscosity>. Multiplying by a nearly constant wetted perimeter gives local drag per unit length proportional to $u_t^{3/2}s^{-1/2}$, and integration gives drag proportional to $u_t^{3/2}\sqrt L$. A force density weighted by $s^{1/2}$ instead produces $L^{3/2}$; it can be a separately prescribed phenomenological model but is not this local laminar shear law. Strong curvature, unsteadiness, separation or turbulent transition can invalidate the estimate.
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