Incompressible Viscous Flows

Plane Stagnation Flows

Potential axisymmetric stagnation flow is described as

The steady state Navier-Stokes equation for axisymmetric flows is given as

where

Similar to the plane flow case we look for a solution of the form

with

Using (25) and (26), Equation (22) reduces to

or

The boundary conditions are

or

Integrating (28) we find

For equation (31) to be valid at large z,

Introducing a change of variables

Equation (31) becomes

subject to

The numerical solutions of the flow filed are very similar to the plane stagnation flow case shown in Figure 2 with a slightly fuller velocity profile. The details of the numerical solution are discussed by Schlichting (1960).