RTFQ....
Not correct, I'm afraid. The governor is there to govern the RPM - and that is what it does. reduce power on a fixed pitch prop, and the RPM drops. Reduce power on a constant-speed prop, and the RPM remains the same (the hint is in the name!)
But that is not what he was asking....
a non-aircrew colleague of mine that on large supercharged piston engines with constant-speed-propellers, if you lost an engine during cruise due to fuel starvation, it would continue to windmill at the selected rpm with accompanying boost (manifold pressure) and oil pressure
And to refer to my link...
How Is the RPM Controled?
It is done by varying the pitch of the propeller blades. The pitch is the the angle of the blades with relation to the plane of rotation. As the blade angle is reduced, the torque required to spin the propeller is reduced and the airspeed and RPM of the engine will tend to increase for any given power setting. Convesely, if the blade angle increases, the required torque increases. Then the engine and the propeller will tend to slow down Thus, we can control the RPM by varying the blade angle or pitch of the propeller.
His question is "if you lost an engine during cruise due to fuel starvation, it would continue to windmill at the selected rpm"
The answer is:
No, the engine is producing a negative torque (windmilling) by virtue of the air passing accross the blades. A Governor is only designed to respond to POSITIVE TORQUE to achieve a selected rpm, since the torque is now a negative the result is a reduced blade angle to the flattest blade pitch position (Mechanical stop).
The question is not how a governor works, but how a prop responds in respect to the available torque with an engine failure.
And again, the answer is that the rpms will decrease as a result of negative torque and the governors response to that negative torque is reducing blade pitch resulting in lower rotational rpm from the flatter pitch and reduced blade angle. And again this is why the prop will need to be feathered since the drap rise with a flatter pitch will exceed the residual thrust available from the other engine and you WILL lose altitude ( loss of airspeed then lift, remember that equilibrium thing from your private pilot days?)