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1: How is this going to effect the required volume over time he has to adhere to?
It's not. A VAV (Variable Air Volume) system could measure the volume moved over time, but that is separate from the speed controller itself. There are BMS (Building Management Systems) available that do things like this, but that is an industry into itself. This part of it is not a simple electrical solution, there is a LOT that goes into it. One thing that pops up in my mind is air balance. When you exhaust, you have to supply return air at the same rate, otherwise you create a vacuum and can't open the doors, or too much return air and you create positive pressure so you can't keep the doors closed. If he has air balance now, changing speed on only one side will mess it up. There also might be health codes relating to minimum air volumes he has to move, and fire codes related to exhaust hood air flow. Do you know if all these issues are being addressed?
2: Is there a motor control that can be used for a single phase motor at 10 to 20 amps I might consider for this?
Maybe, but it depends on exactly what type of single phase motor it is. There are VFDs that can work on PSC (Permanent Split Capacitor) and Shaded Pole AC motors, but most motors for things like vent hoods that size are Capacitor Start / Capacitor Run or Split Phase motors and they cannot be speed controlled. You could replace the motor with a 3 phase 230V motor and use a VFD sized for twice the HP to convert a single phase supply to 3 phase, but that is going to be very expensive.
If he insists on having you do it, I would start by asking the Fire marshal if it's OK to do this. Then I would consult with an HVAC engineer on the air balance issue. You may end up with a nice project, but it may be a lot more than what he was thinking, at least that's my experience with things like this.
