Again assuming a laminar flow, we can involve the problem’s uniformity along the z-axis and its axial symmetry to infer that v=nzv(ρ), 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 v=nzv(ρ), and P=−χz+f(ρ,φ)+const (where ρ={ρ,φ} is again the 2D radius-vector rather than the fluid density), so that the Navier-Stokes equation (53) for an incompressible fluid (with ∇⋅v=0 ) is reduced to the following 2D Poisson equation: \[\eta \nabla_…
