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So if we are looking at an aircraft with a ducted propeller (or a high bypass turbofan engine), does it matter how long the duct is? As an extreme example, would having a duct that extends 100 feet behind the prop give any added thrust (let's ignore drag/weight effects of the 100 foot duct)? Because from my understanding, thrust is applied directly at the propeller, so it shouldn't matter how long the duct is just as long as it prevents tip vortex effects.

So as a follow up, why do most high bypass turbofan engines have their bypass duct extend back to where the engine core ends?

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Generally, there are losses due to friction drag in any tube carrying a fluid; therefore, the longer the duct, the more energy is lost from the air stream (this loss appears as back pressure against the fan, so the same power is absorbed at the reduced flow rate).

The higher the flow velocity, the greater these losses, but in a high bypass turbofan, there are other considerations. Extending the bypass duct past the engine core allows the cool, relatively slow bypass air to mix with the hot, high velocity turbine exhaust, with the main effect of reducing exhaust noise. The loss with a duct 2-3 meters long rather than half a meter is small; the gain in noise reduction can be large, and mixing the bypass exhaust with the turbine exhaust inside the duct may also give enough augmentation effect to offset the duct losses.

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