Again assuming a laminar flow, we can involve the problem’s uniformity along the z-axis and its axial symmetry to infer that \mathbf{v}=\mathbf{n}_{z} v(\rho), and \(\mathcal{P}=-\chi z+f(\rho...Again assuming a laminar flow, we can involve the problem’s uniformity along the z-axis and its axial symmetry to infer that \mathbf{v}=\mathbf{n}_{z} v(\rho), and \mathcal{P}=-\chi z+f(\rho, \varphi)+\operatorname{const} (where \rho=\{\rho, \varphi\} is again the 2D radius-vector rather than the fluid density), so that the Navier-Stokes equation (53) for an incompressible fluid (with \nabla \cdot \mathbf{v}=0 ) is reduced to the following 2D Poisson equation: \[\eta \nabla_…
