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Say I have an air turbine with diameter $d$, number of blades $N$, and moment of inertia $\frac {d^{2}*M_{Blade}^{**1}}{4}$ (at the tip of the blade). How do I calculate the power required to spin this turbine at a constant $RPM$, ignoring all the dissipative forces, except for the air drag on the blades$^{**1}$?

$^{**1}$: $M_{total} = M_{Blade}+M_{Air}$

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You need more information than this to solve the problem. Here's how you get started:

You model the fan as a black box that takes in air at a known mass flow rate and pressurizes it from ambient to a known pressure rise (i.e., the delta p across the fan disc). From this you can figure out the rate at which work must be expended to accomplish this task.

The rate of work is power, and so you convert units of the airflow power to shaft horsepower; this tells you the size of the electric motor needed to spin the fan.

This furnishes an estimate of the horsepower requirement as it ignores efficiency losses in the fan blades. It also does not tell you exactly how to design the fan (blade number, pitch, diameter).

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