For the design of a pipeline chemical injector device that depends on energy of the flow velocity, I think you should be concerned about determing the minimum flowrate to completely fill a pipe of any diameter and figuring out what the fluid velocities are in partially filled pipes at lower than filled-flowrates. Seems like you should also be concerned about piperun orientation (horizontal, vertical, canted) to ascertain the correct radial positioning of the device for flowrates less than filled flowrate. The only input I can provide to these problems is to pass on an unproven (to me) equation for minimum filled flowrate found in Costa,,D.P., 1963, Design News Reprint RS 528, Vol. 18, No. 10, 5/15/63. The equation is attributed to Greve,F.W., 1929, Bulletin of Purdue University, Vol.12, No.35.
The equation is Q=7.3*D^2.56*K^1.84 where Q is in GPM, D is inside diameter of standard iron pipe of 2 to 6 inches diameter and K is fraction of ID under fluid from 0.2 to 0.6. I ran some numbers for several pipe diameters in and out of the ranges specified and got results for a near 12 inch ID pipe that seemed plausible from my experience with reactor coolant pumps and piping. For 2, 6 and 12 inch IDs the equation results for K=1.0 are Q=43.05, 716.79 and 4226.95 GPM with respective full-flow velocities of 4.40, 8.13 and 11.99 fps. I can't offer anything reliable at this time on how to get in-fluid (not area averaged) velocities for partial fill fractions but it looks like a possibly simple circular segment geometry problem. Gas-water flow technology may provide an answer to the part-filled pipe orientation problem.