I don't have a copy of API 14E here but that equation is the same as the erosional velocity formula that I believe comes from 14E:
Vmax = C / (rho)^1/2
C is typically taken as a 100 by a lot of companies with short term excursions by some for intermittant operation. I haven't seen the 183 figure. For clean fluids you can push the 100 quite a bit.
There's also a rho*v^2 limit that some companies use that is simply another form of C/(rho)^1/2. I worked for one company that used the rho*v^2 limit for velocity in their flare system. I was doing some capacity testing and for some reason was curious how it compared to the 14E equation and found I got the same velocity with each (rho*v^2 worked out to a C of 370 I believe). With a little manipulation, it's easy to show they are the same equation expressed differently.
What are you trying to do? Back calculate the flowing velocity? This is not going to give it to you.