Accounting for Pressure Drop in Propeller Calculations

[KarenRei]

I'm trying to optimize a system involving one or more propellers / fans driving air through a packed bed for scrubbing (compressed then expanded) and out the other side to achieve propulsive thrust. So there's going to be a pressure drop in the slipstream. I've already set up a system to do the calculations for a single propeller via blade element theory, to figure out how much shaft power equals how much flow rate at what speeds and so forth. However, it has no accounting for a pressure drop in the slipstream.

How does one work a pressure drop behind the propeller into prop calculations? I'm sure there's some set of formulae for accounting for such a situation.

Here's what I've been using so far for prop calculations: ewp.rpi.edu/hartford/~ernesto/F2012/EP/MaterialsforStudents/‌

If I plug in Bernouli's equation into the output (0.5 * rho * (Vinf^2 - Vslip)) I get a couple hundred Newtons pressure differential** But I need to reverse that, to work the pressure drop into calculating flow rates / speeds / etc. Hmm...

Ed: *** Seems unusually small. Multiplied by the disc area it comes out with far lower of a force than blade element theory calculates... Hmm... perhaps I just subtract from the force (pressure drop * disc area), since pressure is force over area? Surely that's right. Maybe I need to double check my Bernouli's formula...

Sorry, ended up sort of thinking out loud here. I'm pretty sure that's right, you can delete this.

 

[Baluncore]

Sorry, ended up sort of thinking out loud here. I'm pretty sure that's right, you can delete this.

Problem solved.