Why does a drop wear away a stone?

An ordinary drop is fraught with many interesting problems. You have probably paid attention many times to the recesses that water falls from roofs during rain gouges in asphalt, concrete, granite and other hard materials. If you didn’t pay, take a closer look, in any city you can find as many such places as you like.

The ability of water drops to destroy solid obstacles was noticed a very long time ago and is reflected in the saying a drop wears away a stone

The ability of water drops to destroy solid obstacles was noticed a very long time ago and is reflected in the saying "a drop wears away a stone". At first glance, there is nothing in this phenomenon that deserves special attention: moving water carries energy and momentum, and therefore it is not surprising that it has a destructive effect on the barrier. However, a closer examination reveals a not entirely clear side of the destruction process.

Let us consider the case when drops fall onto an obstacle from a certain constant height and the velocities of all drops at the moment of impact are the same. We will gradually increase the frequency of falling drops. It is clear that the more often the drops fall on an obstacle, the faster they destroy this obstacle, since the energy and momentum transferred to the obstacle per unit time increase. Let us further increase the energy and momentum carried by water – let's open the dropper valve so much that the individual drops merge into a continuous stream.

From energy and momentum considerations, it is natural to expect that a continuous jet of water should destroy a solid obstacle faster than a succession of drops.

Experience shows just the opposite. In fact, a continuous jet destroys the barrier much more slowly than a succession of drops. In the transition from individual drops to a continuous jet, the destruction rate can drop by hundreds and thousands of times. It seems incredible and inexplicable, but, nevertheless, it is true.

What's the matter here? Why do individual droplets carrying less energy and momentum destroy the obstacle faster than a continuous jet?

The answer is very simple, and, probably, many immediately guessed what it was. When a drop hits an obstacle, a sudden contact of the drop surface with the obstacle surface occurs. When such a contact occurs, pressures develop that are many times greater than in the case of a falling continuous jet.

This phenomenon is called water hammer, and it is water hammer that causes a succession of individual drops to have a greater destructive effect than a continuous jet. This is a qualitative answer to the questions posed earlier.

Let's now move on to a more detailed discussion of water hammer. If a drop hits an obstacle with a speed of 5 m/s, then a pressure develops that is 300 times greater than the pressure of a continuous jet of the same speed. And with an increase in pressure by a factor of 300, the rate of destruction can increase by more than 300 times. This is due to the fact that the destruction of the material begins with a certain threshold pressure.

If the pressure is less than the threshold, then a simple elastic deformation occurs, but the material does not collapse. Therefore, if the pressure of a continuous jet is in the region of elastic deformations, and the pressure developed during the impact of drops (it is hundreds of times greater) is beyond the destruction threshold, the destruction rate increases not by hundreds, but by thousands of times. That is why drops destroy what a continuous jet cannot destroy.

The phenomenon of water hammer is widely used in technology, since it allows relatively simple methods to obtain high pressures. This phenomenon, for example, is used in a very ingenious device for pumping water to a great height. The device is called a hydroram, and its peculiarity is that it does not consume energy from outside to raise water. The energy of a large mass of water flowing from a low height is transferred in a hydroram to a small part of the same water, and this energy is enough to raise a small amount of water to a great height.

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