Submerged Jet of a Power-Law Fluid

Let us consider the plane problem about the outflow of an incompressible power-law fluid from a narrow horizontal opening into an infinite space filled with the same medium. We introduce Cartesian coordinates X, Y with the X-coordinate measured from the opening along the jet. 

We assume that the opening is infinitely narrow and the outflow velocity of the fluid is so large that the longitudinal momentum of the jet remains finite, 

The velocity profile in the jet is described by the boundary layer equations (6.7.2), (6.7.3) together with the boundary conditions stating that the velocity profile is symmetric about the flow axis, 

By using the self-similar variable 7] and an auxiliary function F = F(rf), we can represent the velocity components as follows [443,445]  

The solution of problem (6.8.5), (6.8.6) satisfying the additional normalization condition F (0) = 1 can be represented in the implicit form 

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