But hovering, while it's a very useful characteristic, should not be confused with doing work in physical terms. While it may carry an impressive payload, a hovering machine has zero velocity and is thus doing zero work - i.e. zero HP generated to the payload.
Yup kow that... but the OP asked about thrust and horsepower. I mentioned a heli because the thrust will be equal to the weight in the hover - making the numbers easier to obtain.
Consider a turbine in a power plant, Since it isn't physically moving, or translating, by your definition, it's doing zero work
No that's incorrect. It doesn't have to move to do work - just moving something else is enough.
In the case of a stationary jet engine...
The basic equation is..
Work done = Force x Distance
Power = work/time
so
Power = Force x Distance/Time
Distance/Time = Velocity so
Power = Force x Velocity
I think the force can be calculated from the pressure after the turbine x the area of the turbine. Velocity is the velocity of the exhaust.