I am designing a potato peeler which is practically a bucket that has a rotating disk (figure below) at the bottom driven by a motor. Water and potatoes are put inside the bucket and the disk rotates creating a swirling motion and peeling the potatoes by rubbing them against an abrasive surface. How do I calculate the power required by the disk to rotate a given weight of water plus potatoes (in kgs) at a given rotational speed (in rpm)?
We have a fair share of questions about how to calculate maximum speed, but the fact remains that this is extremely hard calculation to make. See a mass will continue to accelerate until the losses are equal to the gains.
Estimating the losses is hard, if not impossible in practice. That is because friction of your system is extremely hard to predict. Friction depends on nearly everything, from tolerances to how the actual micro surface geometry, chemical reactions at the surfaces and total energy in system etc.. So the easiest answer is build and see. Bear in mind that you have to win at least known forces by some margin.
You can however make a simplified model and estimate each interface by finding a somewhat corresponding case for each thing. Its still just a guess though. Without the resources of a big engineering company its most likely easier to exaggerate engine size then build and see. But do measure the frictions and estimate them this will come handy next time you do something similar.