Axial-symmetric impinging streams

For axial-symmetric impinging streams, it is more convenient to use the cylindrical coordinates. The equations above then become the following  

A specific solution of the equations above is given in terms of the velocity potential 

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Champion and Libby analyzed both the planar two-dimensional impinging streams and the impingement of two co-axial-cylindrical jets in which the flow is axis symmetrical. Actually, the results they obtained are applicable for both the two cases, provided the two-dimensional coordinates in planar impinging streams are replaced by the cylindrical coordinates. 

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