assume 500 gpm 100 ft head 50% pump eff
hyd hp = 25.3 hp
use a 30 hp or 84% fl
vfd losses 3.5% or 0.88 hp
likely more since to get a control band you may run at 80-90% speed
if valve is size for 3 psi drop at 50% position and 500 gpm
7' head or 7% of the operating range
hp req for valve dp = 500 x 7 x 8.34 /(60 x 550) = 0.88 hp
as the valve moves off center point drop will increase with flow, basically offsetting
for the vfd as pump speed slows eff decreases
valve accuracy is typicaly better
pid 4-20 mA to I/P xdcr 3-15 psi to pilot positioner on pneumatic actuator
the choice valve vs vfd depends on many factors but usually favors a valve