Toilet Tissue Held by Air Velocity or Pressure?

[Futsal1st]

a piece of toilet tissue is held against a ceiling grille. Is it held there by air velocity or differential pressure.

If the grille exhausting 50l/s through a 100x100mm egg crate opening the tissue may be held up.

If however the same air flow gives through a 500x500 mm grille, it will fall down.

For me the difference is velocity. So is the tissue held there by velocity?

 

[BvU]

No. The Earth is pulling it down by gravitational force. To prevent falling, some other force is needed to offset that. So it is held in position by a force, which of course depends on this air flow. And you are close with your hypothesis: the higher over-all velocity in the first case leads to higher velocity differences and that causes a pressure difference that keeps the tissue in place. The place to look for a description is in the Bernoulli equation.

A nice example of the same phenomenon is the bulging of a truck cover sail at the front end (behind the driver cabin): the air is pushed aside by the truck and has to move faster to get out of the way. That higher speed creates a lower pressure which 'pulls out' the cover in a bulge.