# Fluid Dynamics Question

by Lucus
Tags: dynamics, fluid
Nice problem, although the statement makes no sense. You can't use Bernoulli equation to determine the axial pressure assuming viscous flow as you are doing. The jet core developed in a non dimensional distance of order $$Re_j^{-1}$$ is dominated by viscous forces. You only can apply Bernouilli to calculate external boundary layer pressure, but as it is an stagnant atmosphere, this pressure is trivially constant $$P_a$$.
Usual calculations of incompressible jets assume negligible pressure gradients, in part because the boundary layer is so thin at large $$Re$$ that transversal pressure gradients are very small, and also because by this argument the external pressure impose an uniform pressure across the symmetry axis.