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I have this theory about static and dynamic pressure generated by a propeller, but I might be wrong, so I could use some comments on this.

Its kinda long and whiney, but well.. here goes;

Lets say I have a motor with propeller, spinning at a certain rpm.

-In the first scenario, I put the propeller so that it can spin freely in the atmosphere. The volume flow in this situation is at its maximum (no static backpressure), and the generated pressure is a pure velocity pressure, equal to: ½ . Rho . v^2

Because no static pressure is generated, the total pressure equals Pvelocity.

(Ptot=Pvel + Pstat). Assuming Pvel = 2500 Pa => Ptot = 2500 Pa

-In the second scenario I take a sealed box, cut a hole in it with the same diameter as te propeller, and place the propeller so that it can spin in this hole. The prop will blow air into this box.

Initially the flow will be large (see scenario 1), but as the static pressure in the box rises, the airflow (think velocity pressure) wil decrease, eventually stalling the airflow (Pvel=0). At this point, the prop is purely maintaining the boxpressure, this being the maximum static pressure the prop can generate, and all kinetic energy has converged into potential energy (Pvel to Pstat). Analog but opposite to scenario 1, Ptot now equals Pstat. since Pvel is zero.

Now my question:

Since Ptot is constant, can I say that the static pressure in scenario 2 is equal to the velocity pressure in scenario 1, being 2500 Pa??

ps: Ignore small losses (This is ofcourse a simplified situation, but I need to get the concept)

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# Dynamic & Static propeller pressure

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