Final answer:
The water does not pour out of the bottle when a fine mesh screen is used because surface tension and the cohesive forces among water molecules are stronger than the force of gravity, effectively holding the water inside the bottle.
Step-by-step explanation:
When you put a fine mesh screen over the top of an open water bottle and turn it upside down, the water does not pour out due to a phenomenon known as surface tension. This is because water molecules have a strong attraction to each other, which is called cohesion.
Cohesive forces create a sort of 'skin' at the surface of the water, also known as surface tension, which can be strong enough to prevent the water from flowing out of the mesh's tiny pores, especially if the mesh has small enough openings to significantly interfere with this force. In this case, the cohesive forces of the water molecules are stronger than the force of gravity pulling the water down, thus the water remains in the bottle.