Do you know why the faucet is turned on, the smaller the water column is, the thinner it becomes, an

Ignore the effects of air for a moment. Let the size of a single water droplet remain unchanged in the process of falling, let its volume be and its length can be thought of in reverse, the faucet is slowly opened, and the water first gathers into water droplets, and then becomes a water column. Let's take the critical state from the water droplet to the water column like this, the smallest water column is the water droplet connected in a line.

For the sake of simplicity, let's assume the length of the water droplet, that is, when the distance of one drop of water from the faucet is l, the next drop will be generated and just start falling. This is a column of water, but let's start with a column of water consisting of only two drops of water. Why does the water column become broken?

As the velocity increases, both drops of water are doing acceleration.

But the speed is not the same, the speed of the water droplet that comes out first is greater than the second drop because of the long acceleration time, and the distance from the second drop is getting larger and larger, and the water column will break. To sum up, to calculate when the water flowing out of the faucet can turn from a drop of water into a column of water. For simplicity, we don't consider air resistance.

impact. In order to ensure that the water column in the critical state will not break, when one drop falls at a distance, the size of the water flow rate is just the second drop, the water flow. When the first drop of water drops by one more, to ensure that the water column continues, it is necessary to ensure that at least two drops of water fall, and the three drops of water are just lined up in a straight line, and so on.

Because the influence of air is ignored, the rate of descent of water droplets at each time is a temporal parameter, and the value range is determined by the height of the faucet from the ground, and the flow rate can be reversed. The water column is a function of the time it takes to break, the faucet according to the height of the ground, and the flow of water. In reality, the water flows out of the faucet, the speed is slow at first, the water is all gathered together, that is, the continuous water column, as time goes by, the water that flows out first becomes faster and faster, and when it reaches a threshold, it breaks away from the large lump of water and becomes a droplet, at this time, the water column bursts.

If the water hits the ground before the velocity reaches a critical velocity, it is a complete column of water. <>

This is due to the influence of the earth's gravity, the speed of the water will fall faster and faster, under the action of gravitational acceleration, so that the water column will be thinner and thinner, and finally break This is a physical phenomenon. That is, the distance passed in the unit time becomes larger, and the amount of water flowing out per unit time is certain, that is, the amount of water flowing out per unit time is fixed, that is, the thinner you are talking about, so it can only reduce the cross-sectional area, and because its gravitational potential energy is converted into kinetic potential energy in the process of its falling, but the volume is certain, that is to say, it is falling faster and faster, that is to say, the volume is certain. Because the amount of water flowing through the same period of time is the same, and the lower the water goes, the faster it flows, the longer the same amount of water, and therefore the finer it is.

Since the liquid spontaneously develops in the direction of decreasing Gibbs free energy, the surface tension tends to reduce the surface area of the liquid. This explains the fact that when water falls from the tap, the surface tension pulls the flow into small droplets in order to reduce the total surface area. In fact, letting water drop down is a classic method of measuring surface tension, which can refer to the hanging drop method to determine the surface and interfacial tension of liquid, and when water flows along the solid pipeline, its contact interface has two interfaces, gas-liquid and solid-liquid, and because the surface energy of the solid is much higher than that of gas, the liquid will spontaneously spread at the solid-liquid interface, and it is easy to form a continuous water flow.

So if you add surfactant to the water and reduce the surface tension of the water, it may be possible to form a continuous flow of water from the tap. And if you replace the surface of the vertical pipe with a superhydrophobic surface, the water flow will also become small droplets. <>

After the faucet is turned on, the main reason why the water column is always thick at the top and thin at the bottom is that it is mainly affected by the main action from gravity, which is the so-called law of conservation of mass.

Therefore, the water column can always appear in such a state of thickness at the top and thin at the bottom. <>

When people at home turn on the faucet, they can find that there is a state of thick and low lines on the whole, mainly because of the influence of gravity. The phenomenon that gravity is accelerating and the overall flow of water is becoming thinner and thinner, mainly due to the law of conservation of mass, and the knowledge of pressurized fluids for a long time. This water flow will not be broken for a variety of reasons.

Therefore this is the knowledge about physics. The water flow itself is capable of long-term stability, ostensibly allowing the water to flow normally through prolonged pressure and pushing. So it's a very interesting mechanical problem, so you can have a big and small situation, but the overall flow can be like this.

The gradual resistance of the water is also a major factor, and the movement of the water droplets through free fall can keep the overall water volume constant. The falling speed of the water can also continue to increase, and the area of the water column itself will become smaller and smaller, so various forms of water states will be formed. It is very interesting to have a factor for the overall mechanics of water, which can appear from large to small through its own surface and finishing, so that it can be effectively stretched.

Therefore, as the whole is very thick at the top and very fine at the bottom, so that a normal operation effect can achieve a good gravitational effect, so that the water can flow down normally, for such an image and a normal phenomenon in the physical life of water. Under the action of gravity for a long time, it is a state that can accelerate for a long time, so the water is getting thinner and thinner, and we should be aware of this in our daily life. <>

In the process of water flow, the behavior of the water being thicker on the top and thinner on the bottom is caused by the laws of intelligent life and the effect of gravity over a long period of time.

Because the speed of gravity increases, the velocity of the flow increases, and the pressure decreases. So the water column below is squeezed and thinner by the atmospheric pressure.

Because the water below spreads out when it encounters the wind in the air, it looks thinner.

"That's because the volume of water v = SVT (s is the cross-sectional area of the faucet outlet, v is the flow rate of the water, and t is the time). s and v are fixed values, so the volume of water flowing out per unit time is also a fixed value, but a certain amount of water does a uniform acceleration linear motion after flowing out s=vt+1 2gtt. The length of the water column has increased, but the volume has not changed, so the cross-sectional area has become smaller.

As it continues to accelerate under the action of gravity, the water column must become thinner and thinner (agree here @Diao Shihan) due to the conservation of mass. This is easy to understand with the knowledge of non-compressible fluids. But the water column does not break for this reason (here against @DiaoShihan), in this case, the water can be considered continuous.

The fracture of the water column is a stability issue, (here agrees with @金chenyu, and thanks to him for the details).

Surface tension. Shrinking the surface of a fluid is such that for a continuous fluid, two isolated water droplets do not spontaneously coalesce into one, even if the surface area of the latter is possible.

Smaller. <>

For this interesting mechanical problem, we can consider it this way: if we do not take into account the interaction forces between the various water columns.

Then each section of the water column is in free fall.

Since the amount of water flowing through each horizontal section per unit time should remain constant, i.e., constant. Here V is the flow velocity of the water column and S is the cross-sectional area of the water column. Obviously, as the speed of the water column increases, the cross-sectional area of the water column will become smaller and smaller - the water flow will become thinner, or even become water droplets.

When the water is small, we see water droplets, and when the water is large, we see water columns. This is a gradual process, so there must be a linear relationship in between.

Then I think this linear relationship should have two parameters, one is to change with the size of the water flow, and the other is to maintain the water column in the opposite direction.

So it can be guessed that the water tension is related to the surface area, and the gravitational acceleration per unit of water.

is constant, then when the water flow is large enough, the tension surface area is greater than a certain critical point.

You can connect the water units and vice versa.

At the beginning, there is water pressure, but after leaving the faucet, the water falls due to gravity, and the force given by the earth makes the thick water column thinner, and then disperses into water droplets.

As it accelerates under gravity, the water column becomes thinner and thinner.

The problem of the decline of water flow stems from the gravitational pull of the earth, so any matter falls vertically. This stems from the design of the faucet, and the water flow from large to small is of course from coarse to fine, and the problem of water flow falling comes from the gravitational pull of the earth

Water has gravity, under the action of the earth's gravity, due to the acceleration of gravity, the speed of the water flow will become faster and faster, the longer the water beam will become, the thinner and thinner it will be, and the water masses will collide with each other to form water droplets and scatter.

In the same way, the water flowing out of the water changes from coarse to fine.

This stems from the design of the faucet, the water flow from large to small, the same water flowing out of the same way, of course, is also from coarse to fine, the problem of water flow falling, stemming from the gravitational pull of the earth, so any matter is falling vertically. This stems from the design of the faucet, the water flow from large to small, the same water flowing out of the same way, of course, is also from coarse to fine, the problem of water flow falling, stemming from the gravitational pull of the earth, so any matter is falling vertically.

There's dirt in your faucet, you can clean it up.

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The main reason for the breakage of the water column is that after breaking into droplets, the surface area is smaller than that of the water column. Contrary to intuition, but it's true. Please focus on the second part of the calculation.

This phenomenon is called plateau rayleigh instability, a column of water of sufficient length of any diameter, will break over a period of time, the time of breaking depends on the diameter of the water column, the smaller the diameter, the faster the fracture will occur. The relationship is Chinese. The reason is that there are various disturbances inside the water flow, and whether these disturbances are enhanced or attenuated depends on the number and diameter of the wave, and the relationship is the Chinese formula, and the maximum rate of disturbance enhancement is seen in Figure 4 at kr = (k is the wave number, r is the diameter of the water column).

This gives the formula. The effect of gravitational acceleration here is to increase the flow velocity and decrease the cross-section (the specific calculation is in the first part of the lesson plan, using Bernoulli's equation), so that the fracture occurs faster. So when we turn off a small faucet, or use a capillary faucet, why don't we see a thin column of water that has been stable for a long time, here is another problem, the situation is more complicated, there is no process of water droplets accumulating into a water column in this phenomenon.

Moreover, this assumption makes the cross-section of the water column unchanged, which is not consistent with the conservation of flow. The velocity and cross-section size should be calculated strictly according to Bernoulli's equation, although when the Weber number tends to infinity, the velocity at a certain height can be simply calculated by approximating the acceleration chain of the heavy Chang Bisun force. Please don't say that surface tension is the force that makes water "come together and not disperse", it is the cohesive force between water molecules, strictly speaking, the van der Waals force and hydrogen bonds that attract each other.

The surface tension occurs due to the fact that the surface molecules lack a "cohesive interaction object" that makes the energy higher, while the spontaneous process becomes lower energy, so the surface of the liquid tends to be minimized. This fracture process is a process in which the surface area of a liquid becomes smaller.

In this problem, the water flow outside the pipe is still cylindrical, and the Reynolds number can be calculated, but I think that whether the turbulent state is the same as the air resistance is not the determining factor. The main application of this phenomenon is the printhead design of inkjet printers.

to calculate when the water coming out of the faucet can turn from a droplet to a column of water. For the sake of simplicity, we do not consider the effect of air resistance. In order to ensure that the water column in the critical state in 1) is not broken by the first observer, when the drop distance is l (time t0), the size of the water flow rate is just the second drop, and the water flow rate is v t0.

When the first drop drops by one more L, it takes t1, t1 <>