Ok, upon further reading, HDS-5 does discuss approach velocity. (It may not be sufficient for the conditions being discussed).
"HWo+Vu^2/2g=TW+Vd^2/2g+HL
HWo is the headwater depth above the outlet invert, m (ft)
Vu is the approach velocity, m/s (ft/s)
TW is the tailwater depth above the outlet invert, m (ft)
Vd is the downstream velocity, m/s (ft/s)
HL is the sum of all losses including entrance (He), friction (Hf), exit (Ho) and
other losses, (Hb), (Hj), etc., m (ft)
Note: the total available upstream energy (HW) includes the depth of the upstream water
surface above the outlet invert and the approach velocity head. In most instances, the approach
velocity is low, and the approach velocity head is neglected. However, it can be considered to
be a part of the available headwater and used to convey the flow through the culvert
Likewise, the velocity downstream of the culvert (Vd) is usually neglected."
HY-8 indeed does not account for approach velocity "Entrance limitations -Since HY-8 is not primarily a water surface profile computation program but is a culvert analysis tool, it assumes a pooled condition at the entrance to the culvert."
My experience has been entirely in a coastal plain where I have never encountered significant approach velocity. I alway appreciate getting an education.
