JimCasey,
Note that CRANE defines
beta = d1/d2
d1 = smaller diameter
d2 = larger diameter
beta is defined in page 2-11 Title: contraction and enlargement
mechanicaldup... in the Flow of Fluids Technical paper subindex 1 always refers to the smaller diameter and subindex 2 to the larger diameter...
so, K2 is referring to the larger diameter.
In case of a tapered contraction (your discharge nozzle), K2 refers then to the INLET (larger diameter).
the relationship between K1 and K2 is:
K2 = K1/beta^4
saludos.
a.