While studying fluid mechanics I came across a section which say:
If a tube is submerged in water and some part is empty
Water rises in a capillary tube say to height $ h$ .Now changing the length of the capillary tube above the surface of water to less than $ h $ would make water rise in the tube and also without overflowing.
My thoughts are as follows:
now if I assume question asks about If a tube is submerged in water and some part is empty
Firstly I think that water would not rise as if once it has risen to a height $h $ why would breaking the part above it make any difference? I think height of the water column changes on altering with the radius of the tube as $h$ is proportional to $ \frac {1} {radius} $ so then how the first statement is correct ?
Best Answer
I wonder whether the book or other source you are using has expressed the situation unclearly. You are right that the amount of tube above $h$ does not affect the capillary rise. The height $h$ is determined by the adhesion to the surface (and by any ambient pressure difference above the surfaces if there is one; usually we treat the case where that pressure is equal everywhere so we don't have to worry about that).
My guess is that the person writing the statement had in mind the idea of lowering the capillary tube further into the water (without breaking it or anything like that). In this case the capillary height stays fixed at $h$, and therefore the water is staying at the same height as the walls of the tube move in the downward direction; in this sense the water is `rising up the tube' although in fact it is not moving in the vertical direction, but rather the tube is going down. As I say, this is a guess at the intended meaning of the author. The main point is that the capillary height is independent of the part of the tube that is not involved, i.e. the part above $h$.