# Glass with water

## Homework Statement

What is the velocity of the water at the top of a glass of water? Is it really 0?
For example, there is a lot of problems which asks with what velocity does the water would leave that glass if I make a hole on the bottom. For these, we consider the velocity at the top to be zero. Why is that? Is it approximately zero or really zero? I am thinking now, if it is an incompressible fluid, it must be zero, because if the water is confined to that volume, cannot have speed. Nevertheless, it is clear that the water molecules are randomly moving. Can you clarify my doubts? Thanks in advance.

I had an exercise on my book where I should show that the velocity at the bottom of the glass where there is a small hole is $$\sqrt{2gh}$$, h is the height of the water level. This is only true, if I consider the velocity at the surface to be zero, when applying Bernoulli's equation. Right?