Wall-shear and pressure-drop balance in a tube
= Wall-shear and pressure-drop balance in a tube
An axial force balance on fluid between two remote cross-sections of a cylindrical tube gives
$$
a\int_{x_1}^{x_2}\int_0^{2\pi}\sigma_{rx}(a,\theta,x)\,d\theta\,dx
=\pi a^2[p(x_2)-p(x_1)]
$$
when every immersed body between the sections is <force-free>.