Velocity in both natural stream, canals, culverts, etc. is not uniform across the cross section and with depth.  When a current meter is used to measure velocity at various cross sections, if the flow is fairly shallow, the 0.6 depth is used with a top setting wading rod and it is generally the weighted average.  If water becomes deeper they use 0.2 and 0.8 depth and sometimes also add in 0.6 depth at each point of cross section.  Now with Doppler meters that can read this variances with depth at higher accuracy, the old school methods with a current meter and wading road is not used as much, especially for measuring high water or flooding where wading is impractical.  Small streams may still be waded.  Another use of the term might be made by some is to refer to mean velocity of a stream, channel of structure at a certain depth, and this can be calculated by cubic feet per second (or meters if you prefer) dividing by the area of the cross section in square feet or meters, to yield mean velocity in feet/second or m/sec. I think the primary use of the term is that velocity varies in flow channels and is affected by roughness and boundary friction.  Attached is lecture developed by Jim Best on sheer stress that includes some velocity references, and may give you more insights.