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
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.
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.