Power needed to accelerate metal powder through two spinning wheels

I have a wheel which has a radius of 0.1m that needs to spin at 10000RPM. The outer surface of this wheel is pressed up against another free spinning wheel like a football or tennis ball launcher.

I am feeding metal powder through these two wheels, which I need to travel at 104.72m/s (basically the wheel needs to spin at 10000RPM while the powder is feed through). The powder is fed at a rate of 0.013 kg/s.

If I could work out the force on the wheel then I could work out the torque and hence power, however that is where I am not sure on what to do. The powder is being fed from almost standstill to a wheel traveling at over 100 m/s. It would seem the acceleration is almost instantaneous, but I know that's not the case. How would I work something like this out? Would I need the frictional coefficients of the wheels and powder?

(Assume this is operating in a vacuum and there is no air resistance)

• 10000 rpm is rather a lot, will it not cause dispersion of your powder? Depending how limited your budget is maybe you could measure torque Jan 13 '18 at 23:26
• non contact torque measurement. measurementsensors.honeywell.com/techresources/appnotes/Pages/… Jan 13 '18 at 23:26
• I belive torque is quantity you need to determine if you need to dimension driving motor. Maybe giving additional information and a sketch would get you better or more precise answers. Jan 13 '18 at 23:30

You actually don't need to know the force on the wheel to work on the power. Just look at the kinetic energy of the powder. Kinetic energy = $(1/2)mv^2$. For 0.013 kg of powder, the kinetic energy is $(1/2)(0.013)(104.72)^2=71$ Joules. You need to provide that much Joules every second, so the power is just 71 Joules/second = 71 Watts.