Why does a box fan blow out lesser air compared to a circular one?

Answer 1

The box shape provides corners and sides that restrict air flow. The smoother round shape provides less air restriction. When air moves just like water it can get turbulent, this turbulence causes resistance which creates noise and slows things down.

A round fan creates less turbulence so the air movement is the smoothest.

Another factor is the construction of the grill. Here to there is turbulence because the grid interferes with the air flow; the finer the grid the lower the noise level, the fewer vanes in the grid the less air restriction and so the faster air movement.

Answer 2

the tube directs the air with more velocity, so it seems like there's more air.
The box fans have more turbulence around the tips of the blades and it's less efficient.
For example, the shroud around your car's radiator fan directs the air more efficiently over the radiator. If the shroud wasn't there, or if it was a plain box, some of the air would escape around the sides and not be directed where you want it.

Answer 3

If you have the same number and type of fan blades, and it's spinning at the same speed, you'll get the same amount of airflow. The shape of the enclosure makes no difference.