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I am attempting to construct a model plane using Custer channel wings. In order to calculate (or at least approximate) the lift generated I need to find the speed of the air through the channel due to the propellers. Is there an equation I can use to do this given pitch, diameter, rpm, etc?

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Well, the textbooks tell you how to design a subsonic shroud for a turbofan and a propeller, but they usually don't tell you how to design half a shroud for a propeller. Besides, you need to pick a profile for the wing section in the channel also.

There are theoretical equations and heuristic ones for a propeller with not too many blades, but these are not nearly as useful as a run of CFD. The key part is to translate the number of blades and RPM, given pitch, chord, span, wash, and wingtip device into $\Delta p$ across the plane of the propeller. This is better done through simulation and experimenting than working with pen, paper and slide rule.

The roughest of the rough approximation is, of course, assuming $\alpha\approx0$ for each of the blade and $v_\mathrm{i}\approx\frac{1}{2}\cdot\omega\cdot\left(r_a\tan\theta_a+r_b\tan\theta_b\right)$ and assume $v_\mathrm{o}\approx v_\mathrm{i}$, where point $a$ is the point where the blade starts near the rotating axis, and $b$ the wingtip, $\omega$ the angluar velocity of the propeller, $r_{(\cdot)}$ the distance from the rotating axis and $\theta_{(\cdot)}$ the pitch angle.

The pusher configuration means the air hits the engine nacelle before it meets the propeller, and the propeller, therefore, works in disturbed air, if it's got a gas engine it will work also in the pulsing exhaust of the engine.

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