I'm trying to find the average velocity of a spinning propeller.(adsbygoogle = window.adsbygoogle || []).push({});

v(r) = RPM C(r) / t ; C(r) = 2πr; t=(1 min)

v(r) = RPM 2πr / (1 min)

I'm not quite sure what to do next. I need the answer in units of velocity, but if I integrate that last equation, I won't get units of velocity.

My rough guess at a next step would be:

lim(n→∞) (Ʃ(from r=0 to r_f) RPM 2∏r / (1 min)) / n

where "r_f" would be the "final radius," the "radius" being the "distance from the center"

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For anyone who wants to know what I'm trying to do, exactly, I'm trying to plug a value for velocity (for a spinning propeller) into an equation for lift - a force.

If you want to see the math I did for that, it involves a bit of physics, but here;

We start with a "paddle in a river" analogy. A paddle of area, A, is held in a river, with water moving at velocity, v, the paddle held at an angle, a, to the direction of the motion of the water. The water has density, D.

What is the force exerted on the paddle by the water?

m=mass, p=momentum, t=time, F=force, D=density, V=volume, v=velocity, x=distance(in the direction of the water's velocity), A=Area, and a=acceleration in "F=ma" and a=angle in "sin(a)"

AvD = AxD/t = VD/t = m/t

∴ Av^2D = mv/t = Δp/Δt = F

Note momentum (p) = mv, so Δp/Δt = mΔv/Δt = ma = F

So (adding in sin(a), using the principle of vector components),

F_Lift = A v^2 D sin(a)

Note: this equation does not include a friction coefficient or any other coefficient to account for losses. You could add a multiplied by .75 or so or whatever to the end to account for losses.

Again, though, however, I'm on the step after that, trying to get the value for the velocity (of a spinning propeller) to plug into that equation.

Thanks,

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# Integral? Average Velocity of a Spinning Propeller

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