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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 ?

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Suppose the height of capillary tube initially was sufficiently high and water rises to a height h and while it is submerged a part of it is cut off including a portion of water in capillary of height d. Then portion of tube underwater is unchanged but now water rises only to a height h-d as that is the length of tube above the surface of water. As capillary rise is due to surface tension water does not overflow or come out of the tube like a fountain. enter image description here

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  • $\begingroup$ part of it is cut off including a portion of water in capillary of height d. Then portion of tube underwater is unchanged but now water rises only to a height h-d what is $d$ ? and If we consider the part of the tube is cut at the surface so the water would definately rise up so I think I mistook in understanding the words of the text. $\endgroup$ – Physicsapproval Dec 31 '16 at 6:41
  • $\begingroup$ "What is d?" d is part of water in cut off portion."water would definitely rise up"?When?After cutting?I didn't understand your comment $\endgroup$ – Sriram Cummaragunta Dec 31 '16 at 6:48
  • $\begingroup$ yeah after cutting but then can you edit your answer elaborating more about the h-d part $\endgroup$ – Physicsapproval Dec 31 '16 at 8:23
  • $\begingroup$ I've added a picture $\endgroup$ – Sriram Cummaragunta Dec 31 '16 at 8:33
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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 $h$.

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