I found some references, but no nice equations.
http://www.delta-tcompany.com/nozzles/equations.php
http://63.174.18.220/literature/docs/ssor002.pdf
http://www.daniel.com/products/gas/N...37%20457KB.pdf
That last one gave me this:
I don't believe that the straight section would be of any benefit, so if we exclude it, the nozzle length would be 3/8 (assuming a 3/4 inlet).