Molecular Behavior Near Faucet: Exploring the Continuity Principle

[cjl]

cjl: Saying something multiple times does not make it true. Why are you referring to static pressures in what is obviously a dynamic situation?

Because the relevant pressure here is the static pressure. Perhaps you're confusing it with the stagnation pressure? The static pressure is absolutely relevant in a dynamic situation - in fact, the static pressure is really the only pressure you care about directly in a dynamic situation. The static pressure describes the pressure exerted by the fluid. Dynamic pressure is merely a method of measuring the kinetic energy of the fluid, and the dynamic pressure is always equal to 1/2*ρv².

To go into somewhat more detail, since the entire fluid column is exposed to the atmosphere, a force balance requires that the static pressure in the entire fluid column is equal to the atmospheric pressure surrounding it. The increase in velocity is coming from potential energy (or, as russ correctly put it using slightly different terminology, it comes from the gravitational head). This is causing an increase in the stagnation or total pressure, as the static pressure is staying constant and the dynamic pressure is increasing. Often, the Bernoulli equation is written in such a way as to reflect this term, specifically:

P+1/2ρv²+ρgh = constant

In this particular case, h is decreasing and v is increasing, while P is constant throughout the column.

From the standpoint of kinetics, there is no static pressure in moving water. There are only dynamic pressures that vary from time to time at any given place and from place to place at any given time. These variations allow streams to pluck heavy rocks from their beds.

Perhaps you should brush up on your fluid dynamics terminology.

To go back to the bernoulli equation as I have written it above, for an inviscid, incompressible, lossless flow, P+1/2ρv²+ρgh = constant.

This is typically broken down into three separate components. P is the static pressure, and it describes the actual pressure felt by an area at that location in the flow. 1/2ρv² is the dynamic pressure, and it describes the kinetic energy of the flow (or, to look at it another way, it is the amount of pressure that would be gained if the flow were slowed down to a stop with no losses). Finally, ρgh is an external force term describing the influence of an external force (in this case, gravity). If other external forces are present, this term can be generalized to include them as well.

When people using the bernoulli relationship talk about pressure dropping as velocity increases, they are typically referring to the simplified case where there is no external force term. In this case, the equation simplifies to P + 1/2ρv² = constant. In this case, as the velocity of the flow is increased (perhaps by running it through a constriction in a pipe), it is clear that the dynamic pressure term increases. Since the stagnation (or total) pressure is constant, this requires that the static pressure decrease. Since static pressure is in fact what most people are referring to when they refer to pressure, this allows for the rough generalization that pressure decreases as velocity increases.

Since this simplification relies on no external force however, it does not apply in this case.

Finally, the Bernoulli Principle is always in effect whenever you have a fluid in motion or an object in motion relative to and in contact with a fluid.

Well, the Bernoulli principle always applies when you have an inviscid, incompressible, lossless flow. However, in this case, those approximations are fairly valid. However, that doesn't mean that you are applying the Bernoulli principle correctly. In this case, you are neglecting the presence of the external force term, which is why you are getting incorrect results.


Chris
(Graduate student in aerospace engineering focusing on fluid mechanics and propulsion)

 

[arashmh]

Because the relevant pressure here is the static pressure. Perhaps you're confusing it with the stagnation pressure? The static pressure is absolutely relevant in a dynamic situation - in fact, the static pressure is really the only pressure you care about directly in a dynamic situation. The static pressure describes the pressure exerted by the fluid. Dynamic pressure is merely a method of measuring the kinetic energy of the fluid, and the dynamic pressure is always equal to 1/2*ρv².

To go into somewhat more detail, since the entire fluid column is exposed to the atmosphere, a force balance requires that the static pressure in the entire fluid column is equal to the atmospheric pressure surrounding it. The increase in velocity is coming from potential energy (or, as russ correctly put it using slightly different terminology, it comes from the gravitational head). This is causing an increase in the stagnation or total pressure, as the static pressure is staying constant and the dynamic pressure is increasing. Often, the Bernoulli equation is written in such a way as to reflect this term, specifically:

P+1/2ρv²+ρgh = constant

In this particular case, h is decreasing and v is increasing, while P is constant throughout the column.


Perhaps you should brush up on your fluid dynamics terminology.

To go back to the bernoulli equation as I have written it above, for an inviscid, incompressible, lossless flow, P+1/2ρv²+ρgh = constant.

This is typically broken down into three separate components. P is the static pressure, and it describes the actual pressure felt by an area at that location in the flow. 1/2ρv² is the dynamic pressure, and it describes the kinetic energy of the flow (or, to look at it another way, it is the amount of pressure that would be gained if the flow were slowed down to a stop with no losses). Finally, ρgh is an external force term describing the influence of an external force (in this case, gravity). If other external forces are present, this term can be generalized to include them as well.

When people using the bernoulli relationship talk about pressure dropping as velocity increases, they are typically referring to the simplified case where there is no external force term. In this case, the equation simplifies to P + 1/2ρv² = constant. In this case, as the velocity of the flow is increased (perhaps by running it through a constriction in a pipe), it is clear that the dynamic pressure term increases. Since the stagnation (or total) pressure is constant, this requires that the static pressure decrease. Since static pressure is in fact what most people are referring to when they refer to pressure, this allows for the rough generalization that pressure decreases as velocity increases.

Since this simplification relies on no external force however, it does not apply in this case.




Well, the Bernoulli principle always applies when you have an inviscid, incompressible, lossless flow. However, in this case, those approximations are fairly valid. However, that doesn't mean that you are applying the Bernoulli principle correctly. In this case, you are neglecting the presence of the external force term, which is why you are getting incorrect results.


Chris
(Graduate student in aerospace engineering focusing on fluid mechanics and propulsion)

Chris , that was awsome! now can u explain what forces the molecules to form a conic shape ?

 

[russ_watters]

Chris , that was awsome! now can u explain what forces the molecules to form a conic shape ?

Again, surface tension is the force. It acts against the differing velocity along its length.

This is similar to why a rubber band narrows when you stretch it.

The Bernoulli's explanation just doesn't fit: there isn't anything for static pressure to do and it doesn't add anything useful. Just consider what would change if you ignore the issue of pressure (answer: nothing). And consider that since pressure is a square function of velocity, it adds problems, such as why isn't the shape a parabola and is there enough pressure to move the water when it is only a few cm from the tap.

 

[klimatos]

OK, bernoulli works always . but we have to keep in mind that this experiment with paper leads to the same result even if there is no curve in water stream , i.e when the flow rate of water is so tremendous!
So i c that this bernoulli effect , affects the water stream , but it;s just one of contributers , i want to know others and the reason they contribute in pulling the molecules towards the center.

Since the Bernoulli Effect fully explains the tapering, what makes you think that there are other factors at work?

Let me add another argument to the hypothesis. The tapering of the stream is not uniform, but increases with an increase in the water velocity. This means that the force or forces that cause the constriction are functions of some power of the velocity. This automatically eliminates any inter-molecular force, since hydrogen bonding is independent of fluid flow. With the exception of the Van der Waals attraction (which is also independent of fluid flow) and possible ionic attractions (same independence) I know of no other inter-molecular bonding forces that you might offer to support an argument for internal molecular attractive forces.

The Bernoulli Effect, in contrast, is a function of the square of the velocity. It thus fully explains the increase in constriction with the increase in flow velocity.

By the way, the molecules are not being pulled toward the center, they are being pushed.

 

[russ_watters]

I'll respond in more detail later, but a clear counterexample: sand. If Bernoulli's principle were strongly at work here, a poured column of sand should form itself into a coherent stream.

 

[arashmh]

Again, surface tension is the force. It acts against the differing velocity along its length.

This is similar to why a rubber band narrows when you stretch it.

The Bernoulli's explanation just doesn't fit: there isn't anything for static pressure to do and it doesn't add anything useful. Just consider what would change if you ignore the issue of pressure (answer: nothing). And consider that since pressure is a square function of velocity, it adds problems, such as why isn't the shape a parabola and is there enough pressure to move the water when it is only a few cm from the tap.

ok, and what would have been violated if the stream didn't make a conic form with the presence of tension ?

 

[cjl]

Since the Bernoulli Effect fully explains the tapering, what makes you think that there are other factors at work?

Except that it doesn't. Read my last post for details (I'm not typing all of that out again).

Let me add another argument to the hypothesis. The tapering of the stream is not uniform, but increases with an increase in the water velocity. This means that the force or forces that cause the constriction are functions of some power of the velocity. This automatically eliminates any inter-molecular force, since hydrogen bonding is independent of fluid flow. With the exception of the Van der Waals attraction (which is also independent of fluid flow) and possible ionic attractions (same independence) I know of no other inter-molecular bonding forces that you might offer to support an argument for internal molecular attractive forces.

Actually, if you work out the details, I think you'll find that the tapering is such that the area follows a 1/v profile (actually, this must be true for continuity to be satisfied in an incompressible flow). Thus, the diameter should follow a 1/sqrt(v) profile. Since v is proportional to sqrt(h) for a freefalling object (or liquid in this case), the diameter should actually follow a 1/h^1/4 profile, and this only follows from the fact that the flow is incompressible, the flow is in freefall, and mass is conserved.

The Bernoulli Effect, in contrast, is a function of the square of the velocity. It thus fully explains the increase in constriction with the increase in flow velocity.

If your proposed mechanism increases with the square of the velocity, why does the actual profile go as the inverse square root (or directly as the inverse, if you want to look at area instead of diameter)?

By the way, the molecules are not being pulled toward the center, they are being pushed.

You really haven't shown that at all. You've simply asserted it extensively.

I'll give one more (very good) reason why your argument can't be true. If the real cause were that the static pressure decreased with velocity (which is the standard bernoulli effect), the water could never exceed a speed of approximately 14 meters per second. At 14 meters per second, the static pressure of the water would be zero, the water would boil off, and you'd be left with a cloud of water vapor (seriously). If the water were exchanging its static pressure for velocity (which is the entire idea behind the bernoulli effect), and it had a stagnation pressure of 1 atmosphere, the static pressure would be zero at just over 14 meters per second (and the dynamic pressure would be exactly 1 atmosphere). Since this clearly doesn't happen - water falls faster than 14 meters per second quite frequently (though not usually in most people's houses), the velocity must be coming from some other source (namely, gravitational potential energy or gravitational head).

 

[cjl]

ok, and what would have been violated if the stream didn't make a conic form with the presence of tension ?

Conservation of mass. The surface tension keeps the stream as a single stream rather than breaking up into droplets or several separate streams, and the conservation of mass requires that at any point, the product of the density of the fluid, the cross sectional area of the flow, and the velocity is constant (to put it more mathematically, ρ₁A₁V₁ = ρ₂A₂V₂). Since we're assuming water is incompressible, the density won't be changing, and the velocity is obviously increasing, so the only way for this to be satisfied is if the area has a corresponding decrease.

If you're wondering where that relation comes from? The cross sectional area of a flow multiplied by its velocity is the volumetric flow rate past that area (I can go into more detail if this doesn't make sense to you). So, if you take the rate of volume flow past an area, and then you multiply it by the density, you get the rate of mass flow past that area. Since mass is conserved, the rate of mass flow past an area near the top of the stream must be the same as the rate of mass flow past an area near the bottom, and that is where the relation arises.

 

[arashmh]

If you're wondering where that relation comes from? The cross sectional area of a flow multiplied by its velocity is the volumetric flow rate past that area (I can go into more detail if this doesn't make sense to you). So, if you take the rate of volume flow past an area, and then you multiply it by the density, you get the rate of mass flow past that area. Since mass is conserved, the rate of mass flow past an area near the top of the stream must be the same as the rate of mass flow past an area near the bottom, and that is where the relation arises.

Dear Cjl, i am a phd student of chemical engineering and i know every single detail about conservation of mass and I'm sure u know it too and in detail .

but my point is that , the molecules do not know any thing about conservation of mass as we do :) the thing that makes me confused is that , which forces exactly acts upon the molecules (and under what mechanism) that makes molecules behave in such a way that we can (from a higher level) describe the totality of their behaviour as conservation of mass (of water stream).

in other words, i want to know the exact mechanism in molecular level, so that if i run a molecular simulation of water molecules, I as an "observer" watch them forming a cone, did u get my point ?

 

[cjl]

But that has been explained to you several times. What keeps the water as a single, connected stream is the intermolecular attractive forces. The example of pouring sand is a great example to show what would happen in their absence - the column would remain at a constant diameter, and the density would decrease with height (you'll notice this is also a valid solution to the mass conservation relation given above). The intermolecular forces keep the water stream at a constant density, and thus they are the direct cause of the narrowing of the stream.

 

[256bits]

The flow of water exiting the end of the tube (faucet) has a velocity profile, and one has to take that into account.

http://www.engineersedge.com/fluid_flow/flow_velocity_profiles.htm

At the walls of the pipe the velocity of the water is basically zero, and depending upon laminar or turbulent flow, the velocity profile is as shown.

For laminar flow the streamlines do not mix when the flow is within the pipe, and from one section to next there is a pressure drop. At exit the pressure drop is non-existant, or we can say that the fluid surface is now at atmospheric pressure ( if exiting into the atmosphere ).

This is the part that you all have been missing:
There is a slight pressure gradient from the surface to the center due to the surface tension of the water. As the center is traveling faster than the outer surface, and due to continuity and the fact that the flow in incompressable, the flow constricts. This is most noticable on immediate exit from the pipe, where the velocity profile from the pipe continues on into the free liquid flow.

For a gravity situation, the liquid accelerates, and the flow further constricts due to continuity, the interior always at a faster velocity than that of the outer surface, until a state farther down in the flow is reached where the surface tension is able to pinch off droplets.

 

[klimatos]

I'll respond in more detail later, but a clear counterexample: sand. If Bernoulli's principle were strongly at work here, a poured column of sand should form itself into a coherent stream.

Sand is not a fluid. There are no hydrogen bonds between the grains of sand. In the water column it is the surface tension (hydrogen bonds) that keeps the stream coherent and the pressure differential that constricts the column.

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.

 

[256bits]

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

If you are taking a hot shower, the air within the shower stall is heated and rises - colder air moving in by pushing the shower curtain inward, would be my best explanation.

 

[klimatos]

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.

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.

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.

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.

 

[256bits]

From the viewpoint of the continuity principle, we know that the stream of water is fatter near the mouth of the faucet and skinner lower down.

The question is how single molecules understand when/how they should deviate from their perpendicular free fall to a deviated one ?

Your situation is similar to flow from an orifice.

2 other situations you may find interesting:

1. Oscillatory patterns in the flow. If you have ever noticed the flow seems to be twisted or having a noticable pattern, then this is caused by the surface tension attempting to bring the flow to a minimum surface ie a circular cross section. A harmonic is set up as the inertia of the water overcompensates and overshoots the circular form. A square exit will have the sides become the corners and the corners become the sides ( not exactly , but just to expalin what happens ), and this continues down the stream.

2. A flow exiting horizontally from will have the bottom part traveling faster than the top due to the pressure difference caused by the height of the orifice. The stream will flatten out as the bottom interferes with the upper layers.

Even though the pressure differences are small, the effects are visually noticable.

 

[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.