Exhaust stream velocity is not known, or at least beyond my ability to measure accurately.

For a bit more background, I want to measure the efficiency of an

Aeolipile. Mine is very similar to

this one, but it hangs from a bearing over a bunsen instead of being mounted on a turntable. I have done this in the past by trying to measure the angular acceleration as the thing spins up to speed. Knowing the moment of inertia, which I have measured, I can therefore work out the resultant torque (Thrust - friction). Measuring the angular deceleration as it comes to rest allowed me to estimate the friction. Then I just applied W=Fx while it was spinning up to speed.

I made the measurements with a light gate which registered every half rotation, which wasn't a very precise method as the thing is at full speed in a few rotations (<5). Plus the fact that letting the thing spin down to estimate the friction includes all sorts of assumptions about that friction that are probably dubious (e.g. that the friction is is constant and independent of rotational speed). Was there a better way of measuring the work done? I wondered whether it could be done by hanging the Aeolipile from a torsion spring, hence my original question.

However, I'm starting to think that I just don't have enough info. to solve this for the work done. The set up would allow me to measure the thrust of the Aeolipile, but not the power, right?

Could I then let the Aeolipile spin up to a constant angular velocity, measure that velocity, and then apply P=Fv using that measured thrust?

Thanks

p.s. - In case you are interested, the power input is measured by timing how long it takes to boil away a known quantity of water and working out the energy needed to boil that water using water's latent heat of vaporization.