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

[arashmh]

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 ?

 

[I like Serena]

Welcome to PF, arashmh!

The molecules in the middle have no choice, they're just along for the drive, mostly driven by gravity through which they have to accelerate.

The molecules on the edge are drawn in by the adhesion force.

 

[arashmh]

Welcome to PF, arashmh!

The molecules in the middle have no choice, they're just along for the drive, mostly drive by gravity in which they have to accelerate.

The molecules on the edge are drawn in by the adhesion force.

Thanks Serena , I know that the only available force for molecules at the edge is adhesion force , but why the adhesion force gets stronger as the molecules go down (and get more speed ) ?

 

[I like Serena]

Thanks Serena , I know that the only available force for molecules at the edge is adhesion force , but why the adhesion force gets stronger as the molecules go down (and get more speed ) ?

Uhh... The adhesion force get weaker as the molecules go down.

It has to, since the molecules on the edge can never reach the center.

 

[rcgldr]

The mass flow across any horizontal plane is constant, so the cross sectional area of the flow decreases as the flow speeds up. If there's enough adhesion, the flow just narrows, if not, the flow breaks up.

 

[klimatos]

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 ?

One factor you might consider is Bernoulli's Principle. As the speed of the falling water increases, the pressure differential of the surrounding air increases. This forces a smaller diameter column.

 

[cjl]

One factor you might consider is Bernoulli's Principle. As the speed of the falling water increases, the pressure differential of the surrounding air increases. This forces a smaller diameter column.

This isn't really relevant to the problem - in this case, the static pressure of the water won't change (even though it is speeding up). The water is speeding up by converting gravitational potential energy to kinetic, so no loss of static pressure is necessary (and in fact the pressure inside the column will be effectively equal to the ambient pressure the whole time).

Instead, the reason is simple continuity. The mass (and volumetric) flow rate of the water must be the same near the bottom of the column of water as it is near the top, since clearly water isn't being generated out of thin air in the middle of the column. Since the water is speeding up due to gravity, the cross sectional area must decrease to keep the flow rate the same. The surface tension of the water is what keeps it as a single column, rather than splitting up into several separate streams or drops.

 

[arashmh]

One factor you might consider is Bernoulli's Principle. As the speed of the falling water increases, the pressure differential of the surrounding air increases. This forces a smaller diameter column.

klimatos , how about when we repeat this with all surrounding air removed ? I guess it's not related to the air velocity or air pressure surrounding the water stream

 

[arashmh]

This isn't really relevant to the problem - in this case, the static pressure of the water won't change (even though it is speeding up). The water is speeding up by converting gravitational potential energy to kinetic, so no loss of static pressure is necessary.

Instead, the reason is simple continuity. The mass (and volumetric) flow rate of the water must be the same near the bottom of the column of water as it is near the top, since clearly water isn't being generated out of thin air in the middle of the column. Since the water is speeding up due to gravity, the cross sectional area must decrease to keep the flow rate the same. The surface tension of the water is what keeps it as a single column, rather than splitting up into several separate streams or drops.

Dear Cjl, we all have the same knowledge about a mathematical principle called continuity or mass conservation. i c what u mean but I'm asking about what happens at the molecular level. all molecules at one horizontal cross section of the water stream have the same velocity at the beginning of the fall. The effect of gravity continues to affect all molecules. the point is about the molecules near the edge being deviated from their path to be more closer to the center to make a cone. How they "know" that they have to be deviated ? u know we are not talking about the rules, instead the basic behaviour of molecules is of interest .. now can u help in this manner?

 

[klimatos]

klimatos , how about when we repeat this with all surrounding air removed ? I guess it's not related to the air velocity or air pressure surrounding the water stream

There would be no stream. Instead, all of the water would instantly vaporize.

 

[klimatos]

This isn't really relevant to the problem - in this case, the static pressure of the water won't change (even though it is speeding up). The water is speeding up by converting gravitational potential energy to kinetic, so no loss of static pressure is necessary (and in fact the pressure inside the column will be effectively equal to the ambient pressure the whole time).

I'm not talking static pressure. I'm talking dynamic pressure. The water is moving with regard to the surrounding air. Hence, the dynamic pressure of the moving water against the static surrounding air is reduced. This pressure differential causes the surface water to move inward. It will not do so without the application of some force. What force do you suggest causes this movement?

[/QUOTE]Instead, the reason is simple continuity. The mass (and volumetric) flow rate of the water must be the same near the bottom of the column of water as it is near the top, since clearly water isn't being generated out of thin air in the middle of the column. Since the water is speeding up due to gravity, the cross sectional area must decrease to keep the flow rate the same. [/QUOTE]

This is certainly good classical fluid dynamics. It explains what happens, but it doesn't explain why. The question remains what force causes the water to move inward? Surface tension? I don't think the magnitude is sufficient, but I'm willing to be convinced.

 

[arashmh]

I'm not talking static pressure. I'm talking dynamic pressure. The water is moving with regard to the surrounding air. Hence, the dynamic pressure of the moving water against the static surrounding air is reduced. This pressure differential causes the surface water to move inward. It will not do so without the application of some force. What force do you suggest causes this movement?

Instead, the reason is simple continuity. The mass (and volumetric) flow rate of the water must be the same near the bottom of the column of water as it is near the top, since clearly water isn't being generated out of thin air in the middle of the column. Since the water is speeding up due to gravity, the cross sectional area must decrease to keep the flow rate the same. [/QUOTE]

This is certainly good classical fluid dynamics. It explains what happens, but it doesn't explain why. The question remains what force causes the water to move inward? Surface tension? I don't think the magnitude is sufficient, but I'm willing to be convinced.[/QUOTE]

uhu Klimatus! that's it! I'm looking for the force that causes the molecules to move inward !

 

[Drakkith]

Two forces combine to cause this effect. First, there is an attractive force between water molecules due to hydrogen bonds. Then we have gravity of course. As the water exiting the tap begins to accelerate due to gravity, it pulls on the water behind it through the intermolecular forces. Imagine you have two balls attached by a piece of rope. Set the balls as far apart on the ground as the rope will allow and then go and pull the middle of the rope in perpendicular direction to the rope. What happens? The balls don't move parallel to your pull, they move inward until the contact each other! A similar effect is happening here.

 

[cjl]

I'm not talking static pressure. I'm talking dynamic pressure. The water is moving with regard to the surrounding air. Hence, the dynamic pressure of the moving water against the static surrounding air is reduced. This pressure differential causes the surface water to move inward. It will not do so without the application of some force. What force do you suggest causes this movement?

Unfortunately, you seem to be mixing up dynamic and static pressure here. As the speed of motion of a fluid is increased, the dynamic pressure increases. In fact, this is the reason behind the typical bernoulli relation - in the absence of external forces, the total or stagnation pressure (which is static pressure plus dynamic pressure) is constant. So, if the flow speeds up, the dynamic pressure is increased, which necessarily causes a reduction in static pressure. However, in this case, there is an external force - gravity. The work done by gravity is the cause for the increasing dynamic pressure, and the static pressure stays constant.

As for the force? I already said - the reason is the surface tension of the water.

 

[mrspeedybob]

Water molecules are polar, they have a + charged end and a - charged end. If you put 2 of them next to each other they will try to align so the + end of 1 sticks to the - end of the other. If you put a bunch of them together they will all try to align into positions that cause them to attract, this is what causes water to have surface tension. A water molecule on the edge of the stream doesn't separate because it is electrostaticly attracted to the next one in, which attracted to a few others further in, and so forth.

 

[PatrickPowers]

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 ?

The water falls faster, so the same amount of water has to stretch to fill more length. That is, the amount of water per second stays the same, but the length goes up with the square of time.

You see the same thing in a river. Rapids are always shallower and/or narrower than the rest of the river, and slow-moving portions are deeper and/or wider.

 

[PatrickPowers]

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 ?

Aha, I haven't answered your question. How does a single molecule know? It has to do with

1) water molecules attract one another so the water doesn't "want' to turn into a spray.

2) Other molecules are moving away downward and upward so there is space opening up toward the center. The molecules "have to" move in there to prevent spray.

In other words, it's minimal energy. It would take energy to spread out or compress the stream any more than it is. But that is sort of tautological.

 

[arashmh]

Two forces combine to cause this effect. First, there is an attractive force between water molecules due to hydrogen bonds. Then we have gravity of course. As the water exiting the tap begins to accelerate due to gravity, it pulls on the water behind it through the intermolecular forces. Imagine you have two balls attached by a piece of rope. Set the balls as far apart on the ground as the rope will allow and then go and pull the middle of the rope in perpendicular direction to the rope. What happens? The balls don't move parallel to your pull, they move inward until the contact each other! A similar effect is happening here.

Dear Drakkith
Thanks for your interesting example. I assume that in this analogy, the rope plays the role of gravity force , right ? why should we just pull the middle rope while gravity acts on all molecules? If we pull every rope upward , all balls will displace horizontally for a little and then they all move parallel to my pull .. isn't it the case ?

 

[arashmh]

Aha, I haven't answered your question. How does a single molecule know? It has to do with

1) water molecules attract one another so the water doesn't "want' to turn into a spray.

2) Other molecules are moving away downward and upward so there is space opening up toward the center. The molecules "have to" move in there to prevent spray.

In other words, it's minimal energy. It would take energy to spread out or compress the stream any more than it is. But that is sort of tautological.

Thats a good point, can u explain how preventing from being a spray bring the energy to its minimal level ?

 

[Drakkith]

Dear Drakkith
Thanks for your interesting example. I assume that in this analogy, the rope plays the role of gravity force , right ? why should we just pull the middle rope while gravity acts on all molecules? If we pull every rope upward , all balls will displace horizontally for a little and then they all move parallel to my pull .. isn't it the case ?

No, the rope acts like the intermolecular force. Your pulling acts like gravity.

 

[PatrickPowers]

Thats a good point, can u explain how preventing from being a spray bring the energy to its minimal level ?

The molecules attract one another. That means it would take work/energy to move the molecules apart to make a spray. Anything that takes work/energy by definition takes the water out of its minimal energy state, so you can expect that to not happen spontaneously.

 

[arashmh]

No, the rope acts like the intermolecular force. Your pulling acts like gravity.

I c , by the rope i meant the pulling of the rope. now , in your analogy we pull the central rope only or all ropes ?

 

[arashmh]

The molecules attract one another. That means it would take work/energy to move the molecules apart to make a spray. Anything that takes work/energy by definition takes the water out of its minimal energy state, so you can expect that to not happen spontaneously.

uhu, can we formulate the problem to c when the stream finally divides into multiple streams and sprays?

 

[klimatos]

uhu Klimatus! that's it! I'm looking for the force that causes the molecules to move inward ![/QUOTE]

Exactly. And that force is the pressure differential brought about by the water moving with respect to the surrounding air.

This Bernoulli Effect is often ignored or overlooked. A force that can pluck a forty-pound sheet of plywood out of the bed of a pickup truck, can lift a fully-loaded 747 into the skies, and can suck two passing ships together so strongly that considerable steering effort is required to avoid a collision will find constricting a column of tap water to be mere child's play.

 

[arashmh]

uhu Klimatus! that's it! I'm looking for the force that causes the molecules to move inward !

Exactly. And that force is the pressure differential brought about by the water moving with respect to the surrounding air.

This Bernoulli Effect is often ignored or overlooked. A force that can pluck a forty-pound sheet of plywood out of the bed of a pickup truck, can lift a fully-loaded 747 into the skies, and can suck two passing ships together so strongly that considerable steering effort is required to avoid a collision will find constricting a column of tap water to be mere child's play.[/QUOTE]

can we formulate the problem to c when the stream finally divides into multiple streams and sprays?

 

[cjl]

uhu Klimatus! that's it! I'm looking for the force that causes the molecules to move inward !

Exactly. And that force is the pressure differential brought about by the water moving with respect to the surrounding air.

This Bernoulli Effect is often ignored or overlooked. A force that can pluck a forty-pound sheet of plywood out of the bed of a pickup truck, can lift a fully-loaded 747 into the skies, and can suck two passing ships together so strongly that considerable steering effort is required to avoid a collision will find constricting a column of tap water to be mere child's play.

Except that it isn't relevant in this case for the reason that I've already explained. Twice.

The bernoulli effect works just fine, but in this particular case, there is no change in static pressure as the water falls. Thus, there is no pressure force to constrict the flow.

 

[russ_watters]

Agreed: gravitational head is converted to velocity pressure. Static pressure remains constant at zero (gauge pressure)...

...and reducing atmospheric pressure will have virtually no effect on the shape of the cone. An actual vacuum makes life tough, as the water would boil as it falls, but I suspect for a while it would remain similar.

 

[arashmh]

Agreed: gravitational head is converted to velocity pressure. Static pressure remains constant at zero (gauge pressure)...

...and reducing atmospheric pressure will have virtually no effect on the shape of the cone. An actual vacuum makes life tough, as the water would boil as it falls, but I suspect for a while it would remain similar.

so , up to now, the summary is this : the conic form of the water stream has nothing to do with the air surrounding it , so bernulli goes out of the consideration.

we know that a force pulls the molecules toward the center . if it's not the pressure of air surrounding it , the only remaining choice is the adhesion force between molecules, right ? now assume that in a fictionary case no molecule is pulled toward center and the water stream continues to flow like a perfect column in rectangular shape . put aside the continuity , what will be wrong then in "molecular" level ? do we have violated something in this case ?

 

[cjl]

The problem is that for that to be true, either the density of the flow would have to decrease or the velocity of the flow would have to be constant. Otherwise, more water would be flowing past a given point near the bottom of the column than near the top, which is clearly not possible.

 

[klimatos]

can we formulate the problem to c when the stream finally divides into multiple streams and sprays?

All real-world laminar flows contain irregularities. As the water velocity increases, these irregularities amplify to become turbulence. In falling water, these turbulent flows tend to break the stream apart. Eventually, you get spray.

The forces that turn laminar flows into spray are internal to the flow--not usually external, although external forces can add to the turbulence.