# 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

## 1 Answer

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.

Of course, this assumes that the bearings in your wheels are frictionless. They are not. It will take some amount of power just to spin the wheels with no powder. This will depend on how good your bearings are. That's something that you could easily measure if you have the wheels already. If not, probably just round up to something like 100W and that should be more than enough.

• Thanks for that, I was looking at the question wrong. Jan 14 '18 at 4:30