0
$\begingroup$

The problem I pose is about an application of the Pascal law and capillary action. It is based on a plot which I describe hereafter. Imagine a one side sealed cylinder with a piston on the other side. The sealed side is up, so the piston can move downwards. The cylinder is filled with water. Now the piston must move down and fall out due to hydraulic pressure p=rogh. But suppose now there is a tiny opening of diameter of the order of few nanometers on the top. It delivers a curved surface which leads to a Laplace pressure under a curved surface p1=2 s/R where s is sigma – the surface tension (it can be around 10 atm if the opening is 0.3 micrometer). This pressure must be delivered everywhere in the water according to Pascal low and hence on the surface of the piston. This pressure is negative against the hydraulic pressure and hence the full pressure will be P=p-p1. While p1 is much greater than p the piston would not fall down and even would be able to support a huge load. Now while it seems reasonable I haven’t seen it described in textbooks. My questions are: 1. Is this physically true and ---if yes 2. Has anyone seen this described in a textbook and ---- 3. Has anyone seen the experiment described to be performed --- 4. If we have N openings with the same radius will this give p1=2sN/R

$\endgroup$
  • $\begingroup$ This is a solid block of text, not easy to read. $\endgroup$ – sammy gerbil Nov 24 '16 at 4:54
0
$\begingroup$

I have no idea about actual calculations you are getting into, but all the trees grow via capillary action. That means, it lifts tons of weight, dozens of meters above the ground, but over a period of time.

If you sit on a tree, the tree is not going to stop growing. It will lift you but very slowly.

$\endgroup$
  • $\begingroup$ My concern are the actual calculations and not observations from nature. $\endgroup$ – Mercury Nov 22 '16 at 9:05
0
$\begingroup$

In the first case when the cylinder is closed, a sub-atmospheric pressure must develop inside the cylinder so that pressure difference across the piston may be able to support the weight of water+piston. When you open a hole into it, you provide a vent to atmosphere, and because of this sub-atmospheric pressure cannot develop inside the piston (if it did, air would rush in through the vent), and so the piston would continue to fall forever (along with water on top of it). So, contrary to what you said, if you wanted to support large weight by this method you must take care to seal off any vent to atmosphere.

$\endgroup$
  • $\begingroup$ I am not interested in the first case at all. Nevertheless you neglect the weight of the water. Water + piston will eventually make more pressure than athmospheric pressure from below, even than vacuum is build above. $\endgroup$ – Mercury Nov 22 '16 at 8:50
  • $\begingroup$ Unable to understand your comment. $\endgroup$ – Deep Nov 22 '16 at 9:00
  • $\begingroup$ What I mean is that pressure from the opening of 0.3 micrometer is 10 atm if it is transmitted according to Pascal law in every part of the liquid. Plus the 1 atm from below of the piston its 11 atm up. 1 atm from the air through the opening its 11-1 = 10 atm up. When you have no opening you have just 1 atm from below and zero from above = 1 atm up. So the meaning of all this is that the opening can hold a tenfold load compared to cylinder without opening. And more I think that 2 openings can hold 20 times more. $\endgroup$ – Mercury Nov 23 '16 at 9:04
  • $\begingroup$ Maybe I should mention that when I mean water I mean that it is free from dissolved air. Otherwise there should be cracking under the pressure. This as I think is the idea of the so called cohesion tension theory (about the ascent of water in the plants) devised 100 ago by Dixon and Joly but it was not based strictly on any physical law (just qualitative suggestions and experimental). $\endgroup$ – Mercury Nov 23 '16 at 9:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.