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_…
