Here are the airflow efficiencies I found in a library book for smooth duct openings with different shapes. (Ignore all the dots, I had to add them to get the solid lines to position correctly.)

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Plain opening with sharp edge, efficiency = 72%

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Flanged opening, efficiency = 82%

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Funnel-like tapered opening, efficiency = 90%- 98%
Angle of taper 20° to 65°

Curved "Bellmouth" shaped opening, efficiency = 98%

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Can type opening, efficiency = 82%

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Can with funnel-like tapered bottom, efficiency = 90% to 96%
Angle of taper 20° to 65°

Can with curved bellmouth shaped bottom, efficiency = 97%


The sharp edged plain opening is the least efficient because most of the air is sucked in from right next to the duct. As it makes the sharp turn into the duct, its inertia makes it overshoot a little bit and the flow constricts to as little as 70% of the duct diameter a short distance inside the end of the duct.

 

Do you think it's a coincidence that the third example looks a lot like an exhaust valve? Or that your last example looks a lot like the TB opening on a TPI or LT1 engine? Those guys at the factory must've read the same book....