# Can water drip from a capillary tube top? Perpetual motion?

In a normal capillary tube (ex: tube A), where the water doesn't travel as high as the tube's height, h, the meniscus formed is "normal" (concave, as seen in tube A).

From previous posts, I determined that if the tube's height is lower than the height that the water can travel, the meniscus becomes less and less concave, and will become almost flat (as seen in tube B).

Furthermore, I learned that if the tube is bent downward, the gravitational force will result in the meniscus becoming convex (as seen in tube C). This force of gravity isn't strong enough to "pull" the water away and make it drip, because the force from the surface tension is greater. And this fact has killed many perpetual machines dreams.

However, I began wondering, if many bent tubes were positioned so that their top ends are very close together, allowing the meniscuses (or menisci?) to touch (like tubes D and E, except many more), would the meniscuses combine to create a water drop that will become large enough so that the surface tension force will be insufficient to hold the water up? And thus the water will drip down?

(Let's assume that the tubes are bent almost vertically down, so there is little chance that the water drop, if it forms, will attach to the outer edges of the tubes).

Any help is appreciated. Thanks in advance.

• Since we know that the Second Law forbids an engine operating in this way, and since all that's left is the geometrical and energetic details of how it wouldn't work, I think the onus is on you to (1) do the experiment and/or (2) calculate the surface areas yourself (single tilted capillary, multiple adjacent tilted capillaries, and the hypothetical situation of a drop detaching). Aug 1, 2018 at 0:41
• Don't think that surface tension is preventing the water from continuously dripping out of the tube in Figure C. Suppose you touch your finger to the exposed water drop at point h in Figure C so that you negate any surface tension effects which inhibit the water from dripping out of the tube. (Try it.) Don't think that it's energetically favorable for water to continuously drip out of the tube at point h while continuously pulling water up the tube.
– user93237
Aug 1, 2018 at 5:46
• Hmm, @SamuelWeir that's the idea I was going for. If we touch the water drop, it negates the surface tension effect, and the water drop becomes "independent" from the water in the capillary. So, if we can put many capillary tubes such that all of the water drops touch, can we get a drop of water to fall down? Aug 1, 2018 at 13:13
• @Chemomechanics thanks for the ideas, but unfortunately I don't have tools to do this experiment, and I'm not sure what the math is behind two drops (or more) combining to form one larger one. Aug 1, 2018 at 13:22
• You seem to be assuming that the droplets only have one tube it can interact with. Note that, as you add more tubes, there is also a greater area the droplets can "attach" to.
– user195162
Aug 16, 2018 at 21:47

## 1 Answer

Assuming that the gravitational field is uniform in the region of the setup, and that the tubes don't gradually deform, it is simply impossible to be perpetual, because the total energy increases over time, since some is lost to air resistance and sound and heat when each droplet falls. Precisely why it fails to run may not be worth investigating, much like what to do when the trisector comes.

Nevertheless, some things ought to be mentioned. The capillary action in the first place is driven by adhesion. That is why it is flat (not bulging upward) when the (straight) tube length is shorter than the reachable height. So when you bend the tube downward, it is NOT going to bulge downwards in the way you expected. If it was pointing perfectly downwards, it will be flat for exactly the same reason as before! If not perfectly downwards, then there will be an outward bulge at the lower part of the hole but an inward bulge at the upper part of the hole, otherwise the net force would suck the liquid back into the tube exactly as in the upright case! So you cannot 'increase bulging' by merging multiple downward-bent tubes.