How Do Molecules Behave Near a Faucet According to the Continuity Principle?

[cjl]

If the Bernoulli Effect were not in play, how do you explain the inward movement of the waxed paper in my previous post? How do you explain a shower curtain moving toward the shower spray? Absent the Bernoulli Effect, there is no other way to explain these movements.

Look up the coanada effect and become enlightened.

 

[cjl]

From his OP onward, arashmh has indicated that he is interested in why the phenomenon of water column tapering occurs. He has indicated that he is conversant with continuity equations, but does not want a macroscopic description of the phenomenon nor any mathematic equations explaining the parameter relationships. As he said in his OP, he wants to know WHY a surface molecule moves inward. What force or forces cause it to move? And he wants the explanation in molecular terms.

Hence the discussion of intermolecular forces related to continuity.

Many of the responding posts have contained equations. Some of these equations were verbal and some were in notation. Equations never explain why something happens, they only explain what happens. (“To make the equation come out right” is not an explanation. It is a cop out.) For example, Boyle’s Law doe not explain why the pressure doubles when we halve the volume of gas in a container (temperature kept constant). It only describes what happens. We must bring in kinetic gas theory and statistical mechanics to explain why.

Along this same line, continuity equations and other fluid dynamic equations and statements of principle do not explain why the surface molecules in a column of water move inward as the water velocity increases. They don’t mention molecules at all. And I have been as guilty as everyone else.

Continuity combined with the fact that intermolecular forces keep the density of water constant is more than sufficient.

Let me correct that omission. The ambient air pressure (frequency of molecular impact times the mean impulse per impact) of the air on the air-water interface is greater than the pressure of the flowing water on that same interface. Consequently the interface moves inward until the two pressures equalize. This interface is curved and receives two forces from the water. The first is from the parallel flow which diminishes the pressure on the surface in keeping with the Bernoulli Effect. This diminution allows the interface to be pushed inward. The second force is the direct impact of the water molecules on the upper part of the curved interface. This increases the pressure on the interface and tends to push the interface outward. This second force increases the closer you get to the center of the column because interior flow is faster than surface flow. The interface comes to rest when all three of these forces balance one another.

And this is completely wrong. I am starting to tire of correcting you, but suffice it to say, this is an incredibly flawed way of looking at the problem. Read my post above for a full explanation of why the bernoulli effect is not the correct explanation for this problem.

The waxed paper experiment (Post #31) demonstrates that the Bernoulli Effect is in operation. Explanations that ignore the Bernoulli Effect must still account for the inward movement of the waxed paper. If you carefully vary the flow rate, you will note that the faster the flow the greater the deviation. No explanation involving surface tension will produce this result.

Once again, look up the coanada effect. This fully explains the waxed paper motion.

 

[Phrak]

"Bernolli effect" sounds like pop-science. Shouldn't this be the Venturi effect?

 

[klimatos]

"Bernolli effect" sounds like pop-science. Shouldn't this be the Venturi effect?

No. The two principles are different. Let's use the old-fashioned automotive carburetor as an example. The constriction of the venturi in the throat of the carburetor increases the velocity of the flow through the throat. This is the Venturi Principle: constricting the flow increases the flow velocity.

This increase in the flow velocity drops the pressure on the fuel jet orifices in the carburetor throat. This drop in pressure sucks fuel from the float chambers. This is the Bernoulli Principle.

 

[klimatos]

If what many of the posters on this thread maintain is true, perhaps they should inform the teachers in the following videos that they are teaching falsehoods. Both videos involve a water tap and a ping-pong ball. Both videos attribute the attraction of the ball to the stream of water to the Bernoulli Principle.

http://www.youtube.com/watch?v=MThEtISRMPg&feature=related

http://www.youtube.com/watch?v=AUyczZ3EiZg&feature=related

 

[Phrak]

No. The two principles are different. Let's use the old-fashioned automotive carburetor as an example. The constriction of the venturi in the throat of the carburetor increases the velocity of the flow through the throat. This is the Venturi Principle: constricting the flow increases the flow velocity.

This increase in the flow velocity drops the pressure on the fuel jet orifices in the carburetor throat. This drop in pressure sucks fuel from the float chambers. This is the Bernoulli Principle.

There is a difference between a principle and an effect.

 

[arashmh]

Many of the responding posts have contained equations. Some of these equations were verbal and some were in notation. Equations never explain why something happens, they only explain what happens. (“To make the equation come out right” is not an explanation. It is a cop out.)

I can't agree more Klimatos. What i want to know is a description of what happens at the molecular level. These different explanations ( Bernoulli and molecular attraction) shows that we do not look for the origin of the forces. We know that each known force is exerted from something ON something. So whenever we identify the origin of the forces , we can describe the problem in full detail.

Lets look at the problem from beginning. assume that we have a bunch of balls (molecules) connected with fixed ropes (molecular attraction) on a flat horizontal surface. At a moment the flat plane is removed and they start to fall. The gravity force is exerted on all of them. Now the whole bunch of balls a bulk starts accelerating. Now consider two cases , case I in the absence of air molecules, and case II with air molecules.

Now what happens if the balls accelerate altogether without changing their relative position ( without being deformed into a conic shape)? Now you may want to add other forces by an analogy so that we force ourselves to keep in molecular level :)

 

[klimatos]

Look up the coanada effect and become enlightened.

Congratulations on your use of the Coanda (not coanada) Effect to explain the movement of the waxed paper toward the faucet stream! For the benefit of those readers who are not familiar with this obscure effect I offer the following description: The Coanda Effect describes the tendency of a jet stream to deviate toward a nearby fixed surface, to attach itself to that surface, and to follow that surface even when the surface deviates from the stream’s original path. If that surface is free to move, the surface will also move toward the stream. That certainly describes the experiment where the waxed paper moves toward the faucet stream.

However, a close examination of the Coanda Effect shows that it is simply a special case of the Bernoulli Effect. The Bernoulli Effect explains why the Coanda Effect does what it does. The Coanda Effect does not explain the Bernoulli Effect.

The free surface (e. g., the waxed paper) will not move unless the fluid pressure on the outboard side is greater than the fluid pressure on the stream side. And the fluid pressure on the stream side is diminished from the ambient pressure by the square of the fluid flow velocity: i. e., the Bernoulli Effect. Hence the paper moves toward the stream. In terms of the Coanda Effect, the free surface moves toward the stream. In most illustrations of the Coanda Effect, the stream also moves toward the surface. This lateral movement is not apparent in the experiment.

In the case of a fixed surface, the contact of the stream with the fixed surface creates a diminution of pressure in keeping with the Bernoulli Effect, and ambient pressure on the outboard side eventually moves the stream toward the fixed surface. Hold a breadboard stationary in close proximity to the faucet stream and that stream will affix itself to the breadboard in keeping with the Coanda Effect.

Since the Bernoulli Effect is the earlier and more general of the two Effects. I consider the Coanda Effect to be a special case of the Bernoulli Effect and not the other way around.

 

[klimatos]

There is a difference between a principle and an effect.

Point taken, Phrak. I'm afraid that my homey example of the carburetor led to some inexcusable sloppiness in terminology. Mea Culpa!

 

[klimatos]

I can't agree more Klimatos. What i want to know is a description of what happens at the molecular level. These different explanations ( Bernoulli and molecular attraction) shows that we do not look for the origin of the forces. We know that each known force is exerted from something ON something. So whenever we identify the origin of the forces , we can describe the problem in full detail.

Lets look at the problem from beginning. assume that we have a bunch of balls (molecules) connected with fixed ropes (molecular attraction) on a flat horizontal surface. At a moment the flat plane is removed and they start to fall. The gravity force is exerted on all of them. Now the whole bunch of balls a bulk starts accelerating. Now consider two cases , case I in the absence of air molecules, and case II with air molecules.

Now what happens if the balls accelerate altogether without changing their relative position ( without being deformed into a conic shape)? Now you may want to add other forces by an analogy so that we force ourselves to keep in molecular level :)

Case One - Vacuum: The water molecules vaporize almost instantly. At 25°, one square meter of water surface will vaporize some 3.41 kilograms of water per second in the absence of any surrounding gas. That is equivalent to a column erosion of some 3.42 millimeters per second, and a numerical vaporization rate of some 1.14 x 10²⁶ molecules per square meter per second.

Case Two - Air at Equilibrium Vapor Pressure: Firstly, let us replace your intermolecular ropes with fairly rigid springs. The angles at which water molecules form their intermolecular hydrogen bonds have preferred values. Any deviations from these values require the application of force. Secondly, water—being a fluid—has no rigid structure. The molecules cannot and will not keep their relative positions. Thirdly, hydrogen bonding is ephemeral. At 25°C, the average liquid water molecule breaks all of its hydrogen bonds with its neighboring molecules and forms new bonds with new neighbors many billions of times each second. Even a surface water molecule making up part of the surface tension network will vaporize and be replaced some ninety billion times a second. At equilibrium vapor pressure, the number of new arrivals and the number of escapees roughly balance. Fourthly, molecules are in random movement. At rest there are just as many water molecules moving in anyone direction as in any other direction.

As the water falls, more molecules will have a downward component of motion than in any other direction. Since pressure is the simple product of number of impacts per unit area and time and the mean impulse per impact, this reduction in lateral motions is reflected in the diminution of lateral water pressure (the Bernoulli Effect). Meanwhile, the air pressure remains the same. The consequence is increased relative lateral pressure on the water column and a diminished diameter.

Arashmh, did I give you the molecular explanation you were looking for?

 

[russ_watters]

A common misconception is that Coandă effect is demonstrated when a stream of tap water flows over the back of a spoon held lightly in the stream and the spoon is pulled into the stream. While the flow looks very similar to the air flow over the ping pong ball above (if one could see the air flow), the cause is not really the Coandă effect. Here, because it is a flow of water into air, there is little entrainment of the surrounding fluid (the air) into the jet (the stream of water). This particular demonstration is dominated by surface tension.

http://en.wikipedia.org/wiki/Coandă_effect

I suggest using waxed paper to avoid any chance of using surface tension to explain the movement. Wax and water repel one another, not attract.

Do you have any waxed paper at your disposal? I suggest you get some and actually experiment with it. Waxed paper might not have as much adhesion as other materials, but it does not repel water. You can clearly demonstrate this by wetting it and then flipping it upside-down. Some small droplets of water will cling to it, even when upside-down.

 

[arashmh]

Case One - Vacuum: The water molecules vaporize almost instantly. At 25°, one square meter of water surface will vaporize some 3.41 kilograms of water per second in the absence of any surrounding gas. That is equivalent to a column erosion of some 3.42 millimeters per second, and a numerical vaporization rate of some 1.14 x 10²⁶ molecules per square meter per second.

Case Two - Air at Equilibrium Vapor Pressure: Firstly, let us replace your intermolecular ropes with fairly rigid springs. The angles at which water molecules form their intermolecular hydrogen bonds have preferred values. Any deviations from these values require the application of force. Secondly, water—being a fluid—has no rigid structure. The molecules cannot and will not keep their relative positions. Thirdly, hydrogen bonding is ephemeral. At 25°C, the average liquid water molecule breaks all of its hydrogen bonds with its neighboring molecules and forms new bonds with new neighbors many billions of times each second. Even a surface water molecule making up part of the surface tension network will vaporize and be replaced some ninety billion times a second. At equilibrium vapor pressure, the number of new arrivals and the number of escapees roughly balance. Fourthly, molecules are in random movement. At rest there are just as many water molecules moving in anyone direction as in any other direction.

As the water falls, more molecules will have a downward component of motion than in any other direction. Since pressure is the simple product of number of impacts per unit area and time and the mean impulse per impact, this reduction in lateral motions is reflected in the diminution of lateral water pressure (the Bernoulli Effect). Meanwhile, the air pressure remains the same. The consequence is increased relative lateral pressure on the water column and a diminished diameter.

Arashmh, did I give you the molecular explanation you were looking for?

You are very detailed in your explanation. I appreciate it. Ok, we know that if the stream of water has enough path to fall freely , after some time , it will break down to some branches and finally into a spray. how this ball-spring model explains this in molecular level . by the way, feel free to call me Arash :)

 

[russ_watters]

This thread has become somewhat of a mess, so I'm locking it pending moderation.