Does a scale weigh a bee flying inside a box? This question is very similar to this one or even this one except some minor differences. 


*

*The box is much larger than the bee.

*The box has no top cover.

*The bee is flying still in the middle of the box.

*The scale has an infinite precision.

*The scale is lying on the ground floor.
Does the scale weigh the bee whether it is inside or outside the box?
Does it change anything if the box has a top cover or not?
|                 |
|                 |
|                 |
|                 |
|         (flying |
|       o  bee)   |     (air)
|                 |
|                 |
|                 |
'-----------------'
    | (scale) |
----'---------'--------- (ground)

 A: the bee makes movement of air that causes air pressure, and this pressure is distributed around, 
if the box is closed, the amount of lift above because low pressure is equal to the weight below caused by air pressure, so no change on weight 
but if the box is open, i think that the air outside the box will flow in and the air below will 'hit' the box, basically, the lift will be lost to the ambient, and the weight will change.
in a nutshell:
with a top cover: no change
open box: the bee makes a little amount of weight, depending on its flying height
edit:i'm saying here that not all the bee weight will be measured, in fact, the system will weight less than (box mass + bee mass)
A: In an open box, it depends on how high the bee flies. In aviation, this is called the ground effect - if you're flying low enough, you have extra lift, because you're not only pushing against the air, you're pushing against the ground (the air flow below you dissipates and spreads out before reaching ground, if you're high, but not if you're low). A typical example is a hovercraft which obviously does push down on the ground directly.
In essence, the measured weight in the open box will start diminishing when the bee rises higher and higher, ultimately going down to the weight of the empty box. The characteristic height when the bee is no longer relevant, is probably of the order of magnitude of the size of the bee itself.
