Maximizing a Nozzle's Stream Velocity

[isoaker_com]

So, force is what matters right? That's what I'm reading. And that's what I was saying before.

What I'm trying to say is that whether someone says force or pressure being the cause of movement is irrelevant so long as they are using the terms in their proper context. Pressure applied to an area results in the acting force. Pressure creates force. Force creates pressure.

I am not arguing that pressure or force is the main determining factor. I am saying they are interchangable (well, after factoring in area).

pressure = Force / area

In a water gun, saying force is what drives the stream forward is correct. Saying pressure in the PC creates the force is also correct. You can say pressure pushes the stream since pressure on the water column is what yields the force behind the stream. If there is no increased pressure, there would be no force to push out a stream. If a stream has no force (well, it wouldn't be a stream), there wasn't any pressure in the PC. You cannot apply a force onto an object without applying a pressure onto it. As soon as force meets an object on a given area, you have pressure at that point.

I have no issue with the statement that force moves streams. What I have a problem with is trying to separate pressure from force. Pressure is not the sole determining factor behind force. Pressure times area are the determining factors behind force.



Edit: force, alone, doesn't determine flow rate, either. Need to factor in mass of the stream being moved. Equations relating force to accelerating a given mass can, as done in my previous post, be converted such that it is written in terms of pressure instead of force.

[Ben]

I think you're reading me wrong. I am not "trying to separate pressure from force." In fact, I'm pretty much the first (and still, the only) person to use the force of pressure equation in water guns... I definitely know that pressures can create a force. All I have been saying all along is that the force is the main determining factor in water gun performance and it correlates very well with water gun performance, while pressure does not.

The facts stand that force and pressure are not interchangable when concerning a water gun's performance. Surely, you could do all you want with the force of pressure equation, but that doesn't mean that pressure correlates with water gun performance. The only correlation I have seen in real life and in what I have read is between the force applied and water output/range. You can have low pressure and achieve very high range by having high force. Force and pressure are different, but related.

Certainly, higher pressures mean higher force. I have said that many times in this argument because some people seem to be reading me incorrectly. But low pressure is not bad.

Edit: force, alone, doesn't determine flow rate, either. Need to factor in mass of the stream being moved. Equations relating force to accelerating a given mass can, as done in my previous post, be converted such that it is written in terms of pressure instead of force.

Well, this is something joanna has asked me and I gave her the answer. Now I only wish if anyone would read my posts... the equations use dV as opposed to the entire volume. That is a small cross section essentially and not the entire volume. I also quoted a forum thread where a fluids engineer stated that if the force applied is much greater than the mass, the mass is negligible.

[isoaker_com]

All I have been saying all along is that the force is the main determining factor in water gun performance and it correlates very well with water gun performance, while pressure does not.

The facts stand that force and pressure are not interchangable when concerning a water gun's performance. Surely, you could do all you want with the force of pressure equation, but that doesn't mean that pressure correlates with water gun performance. The only correlation I have seen in real life and in what I have read is between the force applied and water output/range. You can have low pressure and achieve very high range by having high force. Force and pressure are different, but related.

*sigh* You can apply all the force you want onto 1mL of water and steram performance would end up being rather lousy. Take an air pressure PC, fill it to 20psi and fire and you get an 'ok' stream. Fill it to 40psi and you'd get a better stream. Now, one may say, well, the pressure in CPS systems is lower than that in air pressure systems, yet CPS systems work better and I'd agree. It's not a pressure measurement alone, but a pressure over area measurement which determines force. In the same system, however, if you increase the pressure, you increase the force.

Certainly, higher pressures mean higher force. I have said that many times in this argument because some people seem to be reading me incorrectly. But low pressure is not bad.

Again, true. The nice thing about force is that you can compare them directly between different soakers. Pressure, alone, on the other hand, cannot be compared directly between soakers since the area the pressure is acting on differs. If one ends up talking about pressure acting on the same amount of area, comparing either pressure or force numbers will work.

As for assuming a large force being greater than mass to make mass negligible, that only works at particlarly high forces and not with ones used for pushing out water streams from stock or homemade water guns. If you're building a soaker to launch a microlitre of water, I suppose it'd work, but if you're pushing a few hundred mL, forget it.

[joannaardway]

I can no longer be really arsed to argue over something petty like this, especially when both sides are immovable on their opinion.
In the end, force or pressure doesn't matter - the water gun works whatever.

My solid opinion on the matter is this (I'll say it here, because I'm not sure I've explained it properly elsewhere):

Force does play a part in the accleration of the water from the water gun. However, I cannot see this being the force in the chamber for various reasons, including that force cannot be carried when the fluid changes shape.

As far as I am concerned, the force involved comes from the nozzle. I damn well know you said that the nozzle doesn't exert a force, but if it doesn't - explain water gun recoil.
Under the conservation of momentum laws, the water gun recoils because of the force exerted along the line of the stream's acceleration (equal and opposite reaction)
A water gun doesn't recoil up if it's chamber is vertical (other than through mass displacement). It still recoils backwards -which is what a force at the nozzle means.

Momentum is so fundamental that no-one can argue against it, not even me.

Force derived from pressure and the chamber area doesn't make sense. Derived from nozzle area and pressure, it can. As nozzle area is variable, I therefore go by the rule of thumb that pressure is responsible.

Back to your beloved dual valve soaker experiment:
Water is inexpansible. The dual valve soaker will not work because there is nothing to expand into the space it has left (be this air or LRT). Remove the air from the equation, and sure, it won't work. A gas can flow in those circumstances because it can expand of it's own accord. Water can't.

Flow will NEVER occur without something to enter the space left by the fluid. There are no examples you can possibly give to deny this fact.
Even my uncle (who is a fully qualified and highly experienced engineer, and has an incredible reputation) cannot give even one example.

As we have no substance to fill the space left (as water cannot vapourise to exceed the pressure of the atmosphere, at least at RTP), no flow will occur. Even your force argument wouldn't work if the air couldn't expand.

That is the full response to your dual valve soaker point, and I don't really think that I'm sidestepping the point.

[isoaker_com]

@joannaardway: sorry for having the argument sound petty, but things make a lot of sense when, in a given situation, one accepts that you need to swap a lot between talk of forces and pressures.

Let's just talk of an XP70-type soaker (or typical APH design with a single pressure chamber mounted vertically). Pump in water into the PC while the nozzle is closed and the air ends up compressed in the PC. This increases the air pressure in the PC which, as gases do, exerts force vectors in all directions. However, only the vectors that push against the water will be the ones to affect flow as the rest are neutralized by the contained. The pressure exerted by the compressed gas thus applies pressure to the water. Liquids, like gases, end up distributing force vectors in all directions. This means that the continuous pressurized volume of liquid from the PC all the way to the nozzle valve is pressurized. When the nozzle is opened, the force vector from the water pointed towards the nozzle is what is driving the stream forward. One could also just as well as that the pressure of the water in the direction of the nozzle pushes the water out the nozzle. Throw in momentum and such and you've got your recoil. Without the pressure in the PC, there would be no pressure or force at the nozzle. Change the nozzle area, but keep pressure contant, and you change the total force out of the nozzle. Keep the same nozzle and change pressure, you change the force.

As for vertical versus horizontal recoil, there is actually a slight change upwards, but that force vector is compensated in part by gravity and the weight of the rest of the soaker while the horizontal direction is only compensated by the user holding the soaker. If you wish to test that, you'd need to build a blaster that fired directly downwards from its PC, but centered so that you don't mistake off-balance for increased upwards recoil.

Actually, scrap that test. Just take a CPS-type blaster, aim it vertically downwards, and see how much 'vertical' recoil is felt and it should feel a lot less motion than horizontal recoil. This is harder to do with air pressure soakers since the water in the typical PC is also affected by gravity. For an air-pressure system to behave similarly, one would need to add in a divider to split the air from the water to keep the water from change shape as the blaster is re-oriented.


Hope that makes sense.

[joannaardway]

Petty is probably too strong a word - but in proportion to how much it really matters, the force vs. pressure debate has seen a vast amount of input and discussion.

Without a force at the nozzle, the recoil wouldn't exist at all, thus proving that the nozzle (or at least the run up to it) must be providing a force.

I don't agree with chamber force. That doesn't make sense to me. Nozzle force/pressure is still my explanation of choice.

[isoaker_com]

But where is the force/pressure at the nozzle coming from?

I fear I will only continue to fail to explain things so I'm giving up. I'll leave this thread with this diagram to consider.

http://www.isoaker.com/Assets/Images...e_diagrams.jpg

The questions are:
What is the pressure at the question marks in the diagram?
Where is the pressure coming from?
Is force at the nozzles in parts 2 and 3 different?
What about part 4?
Do all the diagrams have the same pressure? What about force at the nozzle?
(resulting overall flow is also affected by stream lamination and resistance along tubing, but is irrelevant when discussing the pressure/force of the emerging stream when a nozzle is first opened)

I don't desire any answers as I have currently given up trying to explain since I'm presently out of ways to rephrase my thoughts. This thread has gotten overly confusing since arguments are swapping around scenarios too much. Change the context and things may look different when they really are not. At the same time, some things can only be properly compared when other things are kept constant. Changing other parameters changes relationships between terms, but underlying relationships remain.

Pressure is defined as force divided by area.

If you have any force acting on any area, you have pressure on that area. Things either get pressurized or move out of the way to release the build-up of pressure and re-equilibrate. The pressure at the nozzle is directly related to the force available at the nozzle so long as the area being pressurized is taken into account. It is often easier to talk about force since one does not need to worry about the area term, but that does not make talking about pressure in a specific context incorrect, either.

[Silence]

Hmm...could I request no more replies until I edit in the rest of my post? No offense to any of you guys, great content, but I'm trying to catch up with my replies...thanks!

Nearly there...

EDIT: Here we go. This is just Ben's long post I didn't really reply to. I'll get to the others as well...

A day or two ago, I found a system that disproves your CPS theory: spherical bladders, like balloons.

Alright...guess I should construct a response now. I've mixed and matched the quotes from different sections so that I don't have to repeat things.

We can all agree that force is what accelerates the water. However, as I've said before, just considering the value for force disregards the mass of the water being accelerated, and thus the resultant acceleration. More force is better than less force, but more force on more water is not better than less force on less water.

Earlier, I explained how the mass, and thus the volume, and thus the area do matter in stream velocity. When you compound the force and the area you get pressure. You seem to have missed this point somewhere.

Originally Posted by Ben

This goes back to your faulty thought that the force is reduced somehow by any change in diameter. That is incorrect and I don't feel I should tell you it any longer.

Originally Posted by Ben

You seem to be reverting to the arguments you made in the LR thread about how the force is reduced at the nozzle... not true... and you know it.

Guess how Pascal's principle explains change in force for hydraulic systems? Through change in surface area/diameter. My logic is not faulty, and I'll repeat, my test proved that through the conservation of momentum.

Originally Posted by Ben

And, on a wider diameter, yes, the water definitely is accelerated less. However, that does not mean the flow is not the same or at least comparable. The velocity should be slower anyway to get the same flow from a larger diameter. So, pressure is proportional to the acceleration. An applied force evens out for the most part for this reason, however, as I speculated before, I do not think the relationship between volume and mass is completely even or I believe there is something else we are missing.

Originally Posted by Ben

Okay, you again are not understanding what I am saying. I definitely know that pressure is created. But you seem to think the pressure, not the spring that is pushing, is pushing the water out. That's wrong.

And I didn't say that the 2 inch piston would perform better than the 4 inch one because of pressure. I did once say that higher pressures would be an indicator that one water gun will perform better at the same force. What I mainly was saying was that more water to move per distance is harder to move. 4 inch chambers have more volume per distance.

Originally Posted by Ben

They're [SuperCannon II and a system in which a 4” piston pushes a 2” piston with a rod] achieve similar performances. They'll be within a certain range, as always.

And your logic in the second paragraph is faulty because pressure doesn't move anything. Pressure does not accelerate anything. Pressure can make things expand, but it doesn't in the case of water at our pressures.

"So, pressure is proportional to acceleration" - My point exactly. Pressure is thus proportional to stream velocity if there's a given amount of time, and the argument outlined in my first post is correct.

"An applied force evens out for the most part for this reason, however, as I speculated before, I do not think the relationship between volume and mass is completely even or I believe there is something else we are missing." - I'm starting to laugh at your logic. As you speculated before? And there must be something we're missing? You can change your opinion to fit the facts, but you can't change the facts to suit your opinion. It sounds like you're just searching for a reason now. (Also, the relation between volume and mass is even enough. If water is incompressible for our purposes, as you’ve put it before, then the density is constant, and the relationship between volume and mass is constant.)

"The velocity should be slower anyway to get the same flow from a larger diameter." - That's why it's perfectly logical for Cv to be part of my method for calculating flow and stream velocity.

Take the original equations:
Q = Cv * sqrt(Pgauge)
v = Q / An
And substitute:
v = sqrt(Pg) * (Cv / An)

Velocity is proportional to the entire system's Cv divided by the nozzle's area. We don't even need to speak in terms of flow. Up to a certain point, increasing nozzle size increases the stream velocity because Cv/A is better for large nozzles (due to the area to circumference ratio). However, past a certain point, the total Cv is pretty much limited by something else in the water gun, and the (Cv/An) value drops as you increase nozzle size.

Wow, that went off on a tangent... Now, the second quote...

...is one of the most ludicrous statements ever. Let’s take a look at what “volume per distance” is the same as “area.” 3 units of length (volume) divided by 1 unit of length (distance) is 2 units of length (area).

So you’re saying more area requires more force to move the water. Force divided by area equals pressure.

The force is definitely what pushes the water out. The pressure tells you how much force there is for a certain amount of water – thus it can tell you the acceleration and velocity. I don’t know how many times we need to repeat this.

Third example: The new system would push a quarter of the mass. It would have four times the acceleration. There’s no way you can justify similar performance – you yourself have finally said the volume/mass is also what matters.

Originally Posted by Ben

I don't get what you're saying in the last paragraph either. If force accelerates the water, then how does pressure tell you how much force is accelerating a volume of water? As far as I'm concerned what you first said proves the force theory because the entire volume of water is moving. That's flow. We're accelerating the entire system, not a small part of it. Then again, you may not understand the concept of an integral.

Originally Posted by Ben

Perhaps I should have explained differently. What I meant was that any pressure created was not powering the system and that it was nearly instantaneously equalized. I do not think you will disagree with that statement. Nopressure differential between the outside and inside.

No, I don't understand the concept of an integral...sounds like it's the anti-derivative though. How does that relate to this case? Thanks.

If you're pushing the piston of a Waterzooka at a constant velocity, there is no acceleration. However, you're still applying force. I'm wondering why this is the case - must be because of drag or something.

Jo and iSoaker have explained how pressure tells you the amount of force accelerating the volume of water. Pressure is force/area. It tells you the force being used to accelerate a volume of water.

Regarding the equalization in a piston pumper: As you’ve said, when you apply force, you create pressure. There is certainly a pressure differential. Once again, while it’s force that pushes the water, the pressure tells you the velocity.

Originally Posted by Ben

Propaganda? Who said that? I said marketing. And I never said they use the correct physics in their patents. I simply said they are more likely to use the correct physics due to their (supposed) qualifications. Look at the later Buzz Bee Toys ones if you want some better physics ones.

The pressure should be fairly constant. Then again, I only have tested pressure over the entire fill with air pressure. Water may work differently.

You sound desperate. You’re completely changing tact here! You clearly argued that the Super Soaker patents were some of the best around for information and qualifications. You even pointed me towards this patent itself! I’m not falling for this.

Pressure should be the same for gases and liquids - as Jo put in one of the recent posts, all fluids act similarly. The only difference is that water does not compress easily, but air does.

Originally Posted by Ben

This is what you say when you know the data doesn't support what you say.

Originally Posted by Ben

I'm not talking about inside of the chamber. I was talking about the difference between inside and outside. And this is another case of where I think you are arguing for the sake of argument, stating nothing worthwhile.

First quote: No, I’ve actually responded to all of your comments adequately. However, if you wish to continue bringing up points that don’t even build an argument, then this argument will go nowhere. Just because I realize that doesn’t mean I think I’ve lost.

Second quote: Ironically, jumping ship after finding the argument is weak what you’re doing right now. Allow me to track that particular discussion back a bit:

Originally Posted by Ben

Can you explain the entire "pressure gradient" thing to me? I am not finding that term used in the links you have posted (unless I'm missing something). Air pressure water guns do not have a pressure gradient anyway, unless this is related to time. The pressure is constant throughout the system unless things such as valves change it.

Originally Posted by Silence

I referred to "a pressure gradient between the internals and the atmosphere is not what creates the force in the chamber." Essentially, the difference in pressure between the nozzle inlet and the aperture.

However, you're right in that there's no actual gradient within the water gun. That's why a pressure difference itself can't create the force acting on the piston.

Originally Posted by Ben

There's no "gradient" unless you count the water decompressing as it leaves the nozzle. And do you want me to quote the millions of pages saying that pressure differentials create force? I could scan in my fluid mechanics book again and even the latest version of University Physics on this one (and if you don't know University Physics is what most colleges use for the basic physics courses).

Originally Posted by Silence

Pressure differentials create net force. Pressure alone creates total force. Equalized pressure in a chamber creates zero net force, because there's equal total force but in opposite vectors.

There's a gradient between the internals and the atmosphere, but no gradient inside the chamber.

Originally Posted by Ben

I'm not talking about inside of the chamber. I was talking about the difference between inside and outside. And this is another case of where I think you are arguing for the sake of argument, stating nothing worthwhile.

You seemed to have been fine with the argument until then. Anyway, you might not have been talking about the inside of the chamber, but then where do your force figures for SuperCannon II come from? That 1250 pounds (1270 to be exact – I did the calculations, so I know where the numbers come from) of force is exerted by the air on the piston. Needless to say, the piston is equalized, so the water exerts 1250 pounds on the piston too. If you’re only considering net force, then consider those 1250 pounds worthless.

Furthermore, your statement, “And do you want me to quote the millions of pages saying that pressure differentials create force?” is what looks like you were arguing just for the sake of it. The earlier posts of mine that I’ve quoted involve net force and total force being thrown around carelessly. Which worked until you felt the need to show the difference, and then insult me after I clarified.

Originally Posted by Ben

Beating a dead force?

There's a qualifier. According to you, low pressure is universally bad. I know that more pressure is better, but their qualifier indicates there's more to the picture than pressure alone.

This is very different than my repeating that force is not a property of matter because you repeatedly make mistakes assuming that force is a property of matter. I know more pressure is benefitial. But, there is a qualifier, and that definitely indicates that there is more to the picture.

Once again, you’re trying to deflect the brunt of the argument and distract people from reading the message. The patent claims that range and pressure are proportional, if not directly so (wind resistance). The qualifier “generally” accounts for the Cv, if you must have me explicitly state facts that you know.

Originally Posted by Ben

Look, he's adding up forces to get the net force. One force is the force of the pressure differential between the inside and the outside. Turns out the outside has higher pressure, so he has to calculate the force pushing upward. Not hard. I don't know how many times I have to say it.

Originally Posted by Ben

Nowhere in the page does it say that they're looking for when there is no pressure difference. They're finding the net force applied to the water to see how it flows. I don't what you are arguing here...

When the pressure differential is zero, the net force is zero. It does not matter how much area you have; zero force divided by any area is zero pressure. I don’t know how many times I have to say it. His method only works because he’s calculating for zero. If he had to do anything remotely relevant to calculating flow (and it was you who claimed my examples weren’t relevant to water guns; look at this), he could not use force to do so. Yes, he could state that there is flow; yes, he can state in which direction it is (positive/negative force divided by positive area equals positive/negative pressure); but he cannot find the flow.

Originally Posted by Ben

And if number of mentions were important to the validity of any theory, yours would lose huge where it matters. 9 pages out of over 680. No pages in the PDF book I quoted at the end. In fact, that entire PDF was based mostly onforce.

Originally Posted by Ben

If you were concerned about the actual physics, you wouldn't argue what you are arguing. I have seen no actual use of the equation you say controlsflow in the manner you use it in aside from people on the internet who don't know how to use it. I try to find highly authoritative sources so you don't just shrug them off. And I have found great sources that state exactly what I have been saying. You can not find a single .edu or .gov website that support what you say.

Originally Posted by Ben

The SS 300 was an approximation based upon where I thought it should be. The CPS 2000 was what I was told once. The CPS 2500 is the samepressure as the CPS 1000, which was somewhat of an assumption, but I think the pressure is at most 25 PSI and I wouldn't consider something off by 2 PSI to be wrong.

“That PDF was based mostly on force” - Was it now? Quote an example. Show me a relation between pressure and force.

My theory works in practice. As I showed you, it perfectly models the figures for the advertisement of the nozzles. It also make perfect scientific and logical sense. You just don’t want to dump the belief that you have clung onto and that others have believed.
“Aside from people on the internet who don't know how to use it” – Well that’s easy to say . Once again, you’re shrugging off my arguments and sources.

I have not seen the Cv equation used either. However, to summarize what I have shown:
- a patent detailing the relation between range and pressure, and implying Cv – a .gov site!
- a list of nozzle specifications that the Cv equation perfectly models
- a PDF at a site for industrial engineers
- various forum threads in which people relate pressure to flow – on a physics forum!
- all those calculators – on .edu sites, too!
- there are five more points or something, I’ll look back for them all if necessary.

There’s other stuff too. All explanations of the experiment with the cup full of water with holes in it – the bottom hole’s stream has the most velocity due to pressure, which is also why the range drops off.

You have yet to show me a single equation relating force and flow/velocity. A single one! You’ve just assumed they’re related after seeing a few examples, notably SuperCannon II. Further analysis proves the force theory to be wrong.

Regarding your “highly authoritative” .edu and .gov sources, I’ve already rebutted those arguments. The “Ask a Scientist” scenario only works since they’re looking for zero force/pressure/flow; the guy wouldn’t have a clue as to how to find the flow if he was restricted to using the force model. (By the way, that’s enough of claiming I’m disputing with NASA; this is just some guy who helps out at the site.)

You’ve referred to all those fancy-schmancy fluid dynamics courses and the Navier-Stokes equations. However, walk me through an equation that connects flow and force – it’s all Greek to me. I’ve quoted the Wikipedia summary of the Navier-Stokes equations, that said you could derive a pressure-flow relationship, but I guess you just wrote that off too...I guess you must not read my posts.

And then the pressures…it “was what I was told once?” It “was somewhat of an assumption?” If I were you, I’d be going on about a lack of credibility and 9 pages out of 680 and blah blah blah. However, I’ll just not use those figures and drop this area of the debate.

Originally Posted by Ben

A true statistical study would average several shots. The maximum is not an accurate view of how the water gun performs on average. Take any basic statistics class. And 50 - 55 was a estimation of the range. It is not the range of several values. That is why I averaged it.

If you want to bias your results, I certainly could do the same. But, I don't have to because my physics are correct. I have seen it in real life, I have seen it on paper. I have absolutely no doubts because I've done it all before.

The maximum is definitely a good view of how well a piston pumper can perform. If this was a water cannon firing at the same pressure and at the same angle every time, then yes, it would be worth it to show the average. But a drop of five feet in a pumper is more likely from a different amount of force applied than from wind/quantum fluctuations/etc.

I was also considering the fact that we received completely different stats for each water gun – probably since they weren’t meant to be compared like this. But we received one figure, precise to the foot – 57 feet – for the Waterzooka LR. For the narrow Waterzooka, we receive a figure precise only to five feet (52.5) and another figure that is precise to who knows what (60).

Let’s say we only use the value of 57 for the LR and 60/52.5 for the narrow Waterzooka. Which of the latter numbers do we use? Should we assume the LR had a better nozzle with little stream and spray difference (justifying the 4.5 extra feet of range)? Should we assume we got the spray figure? Or the puddle figure? Don’t take my assumptions out of context to claim I’m biased.

Originally Posted by Ben

Sure. But you should realize that what you just said is in opposition to much of what you said before. You claim that Supercannon II performs so well because it has very high potential forflow. You claim SuperCAP performs so well because it has a very high potential for flow, despite the fact that it only shoots 2 feet less than Supercannon II and has about half the flow.

I still think the SS 300 is designed to have a high flow coefficient. You claim that it’s narrow near the nozzle – but all water guns are narrowest at the nozzle. The manufacturers gave it a ball valve so that it would have high flow, although they might have limited that flow elsewhere.

If you think I’m being contradictory, that’s because there are two factors to consider: pressure and flow. A gun with high pressure and low flow might perform similarly to a gun with low pressure and medium flow. I might say low flow justifies the SS 300’s range relative to SuperCannon II; and I might say high flow justifies its range compared to the CPS 1000.

Originally Posted by Ben

The Cv value (the coefficient of velocity) represents how much flow velocity is lost when a flow passes through a valve. The velocity lost is proportional to the square root of the pressure. Multiplying the two gives the lost flow. That is how you use it.

Then why does it not use delta velocity (or acceleration, if you will)? Because the flow is constant throughout the valve. You can’t have 50 m/s at the inlet and 40 m/s at the outlet because 10 m/s were lost. (Disregarding changes in diameter.)

Originally Posted by Ben

I never said that the pressure chamber can't be the source. That's putting words in my mouth that I never said. I said that the equation is not used to calculateflow created by a pressure.

I never said you said that. Let me quote from two posts before:

Originally Posted by Ben

I'm saying the equation is great to use to calculate flow lost through a nozzle. I am not saying it is used in a situation like a pressure chamber to calculate how the water flows. Those statements are different and are not contradictory. And you knew this (or at least I hope, because the difference is fairly obvious).

Originally Posted by Silence

The situations are very similar. In both, you have a constant flow coefficient, and you find flow for a certain pressure. Simple as that.

Just because the source of the flow is not a pressure chamber in the PDF doesn't mean a pressure chamber can't be the source.

Originally Posted by Ben

I never said that the pressure chamber can't be the source. That's putting words in my mouth that I never said. I said that the equation is not used to calculateflow created by a pressure.

All you’ve done really is skipped my actual message. Calculating flow through a valve and calculating flow through a water gun are similar. A water gun is a valve – perhaps it’s stretching the definition, but it’s got an inlet and an outlet. If it suits you, ignore the PC and consider the valve to stretch from the bottom of the PC to the nozzle.

Originally Posted by Ben

I don't know all of the factors that are removed, but I do know that some of them are cross sectional area, all of the stuff about turbulence and vorticity, among other things. I don't know exactly what it drops because I am not an expect in the equation, but I do know that as a coefficient, it does drop something at the very least.

Yet the flow coefficient still serves its purpose. In my first post, I suggested increasing tubing size and perhaps using linear flow – likely the most important factor(s) in determining Cv. If you would rather use a model that has five different things to calculate, then be my guest. But for our purposes, the flow coefficient suffices.

Also, I daresay the flow coefficient actually does account for all those factors – not individually though. Changing the cross sectional area will affect Cv. Changing the turbulence will affect Cv. Changing the vorticity will affect the Cv. However, it’s going to be hard to calculate the Cv unless you use CFD or something.

Originally Posted by Ben

And no, saying that you can't rearrange this is completely different than reorganizing the force equation. This one is a simplified equation meant for one purpose. It's like using an equation I derived for the moment of inertia for a certain shape for a completely different shape (if you understand moment of inertia).

I’m still inclined to disagree. Rearranging the Cv equation is just like rearranging any other equation. You just don’t want to believe it.

Once again, consider the entire water gun to be a valve. It has a pressure on one side and a greater pressure on another side. You can calculate flow through the water gun just like you can calculate flow through a valve.

Your shape and moment of inertia analogy is better suited to the use of one valve’s Cv when you should be using another valve’s Cv.

Originally Posted by Ben

What applies a force are the molecules that don't turn fast enough. Certainly, some do bump into the wall and create a force, but it's not as much as you make it out to be. There would be a lot of lost flow if it decreased it as much as you make it out to be.

What do you mean, "concentrate into the thinner tube." Again, the only thing I can think of is that you assume that the water is carrying aforce. That is of course wrong. There is nothing in the water but flow and pressure.

And your tests don't show anything. There's no way that a water stream would push anything near how much force is applied simply due to water gun physics. That's like me saying when I throw a baseball, it'll hit as hard as I threw it. There are a lot of things that affect how muchforce is imparted. Much of that has to do with the fact that we're shooting a stream. The stream breaks up on impact and not all of it is hitting a scale at once. It mainly comes down to the weight of the water. Other things, such as drag, also affect impartedforce. Those tests do not show that "force is reduced at the nozzle" as you like to say.

Originally Posted by Ben

And your tests are inconclusive as I stated several times.

The conservation of momentum says that force will be needed to change the velocity (direction, in this case) of the molecules. The reason a fluid under pressure can exert force in all directions is that the vectors cancel out and the net force is zero.

By “concentrate,” I was describing your claim that all the force applied in to the large piston is used to accelerate the small stream. The problem is that the force is applied to the face of the reducer.

I understand that air resistance would reduce the velocity of the stream. But I did my tests at point blank – once again, less than two inches away. Also, even with air resistance, the stream that applied the most force to the scale would have had the most initial momentum anyway. That much is obvious.

I have no choice but to accept your gravitational force arguments until the weekend or whenever I can do the tests again. I think we can both agree that most of the force was from the water impacting upon the scale, but if you insist, I will do the same test but with the scale vertical and the gun horizontal. I’ll guarantee the results will be the same.

Everybody else has accepted my results. You have simply blinded yourself to it.

Originally Posted by Ben

Again, you doubt the accuracy of my data when it doesn't support your theory. I think you know as well as I do that the main factor inflow coefficients is cross sectional area.

And the force model works perfectly with Supercannon II and SuperCAP. It appears that again you again are not paying attention to what I say or are forgetful. Both initially have similarflow, but SuperCAP has pipe turns increasing turbulence, slightly smaller diameter tubing reducing flow (but there still is well more than enough potential for flow), and a much worse nozzle (ejecting a turbulent stream). Consequently, it shoots slightly less far at the same pressure. And I have explained this to you before.

Then why can’t similar logic be used with the pressure model to explain their ranges? Both have equivalent pressures, both have equivalent forces in the chambers. Yet you reject my explanation in which I talk about Cv in the same manner, yet using the Cv equation.

Originally Posted by Ben

It [A tube with both ball valves closed] will have pressure. I've done stuff like that before with Nerf guns. You yourself say that water carries a pressure. Isolating it does not remove that pressure. Try this out for yourself. I have no doubts about what you'll see.

Originally Posted by Ben

There is flow. But, by your argument and your Cv equation, the flow should be THE SAME as if it were not isolated. Which is it?

I changed my mind. There is pressure, and there is flow for a fraction of a second – too little to be measured or even experienced with small PVC systems at low pressures. Because the flow stops nearly instantly, the total water displaced is not noticeable.

Originally Posted by Ben

You never said slightly. I wasn't quoting. I was just saying that by your argument, a water gun with notably higher pressure will peform more than slightly better than one with the same force but lower pressure.

Remember the use of the square root. Also, remember the relationship between velocity and range. Those two factors more than easily account for what I said.

Originally Posted by Ben

Now you're changing your argument again back to the "force is reduced because it is per unit area" thing you had going before.

And your example is one using huge differences. What about two pipes that have the same volume, and same pressure? One is one inch in diameter and one is four inches. Which will perform better?

They’ll perform similarly. The 4” water gun has four times the volume, but requires four times the amount of air (actually depends on the length) and four times the force. If there’s any difference, the 4” cannon will perform better due to a better (Cv/A) ratio, although in practice, it would take longer to open the valve...

Originally Posted by Ben

Don't see the connection between flow and force? Do you pay attention to anything? Flow is movement. Force accelerates objects, or changes movement. Force can create movement. And have you read the extremely blunt PDF link I gave you? It explicitely states that force creates a flow.

Originally Posted by Ben

I won't go over your head. And if you quoted that because somehow it gave creedence to your theory, realize that just because something is proportional to another does not mean that that one thing controls everything about the other.

Originally Posted by Ben

I'm getting a little confused reading some of your new responses. You took your time posting and I think you were seriously considering much of what I said. Which equation is it? Navier-Stokes or the Cv one? One usesforce, while the other uses pressure. You have not said that Navier-Stokes is wrong. But, you argue that in Navier-Stokes it actually is going to use pressure, essentially. However, that is wrong. Why would they use force if they were just going to calculate the pressure created by it?

Originally Posted by Ben

Again, just because some things are proportional does not mean that that is the only variable that controls it. That is a huge error. And is that the best quote you can find? How is that more important than a blunt statement thatforce pushes water?

No, I mean I want to see an equation that relates flow and force. I know you create flow when you apply force. But what says that 500 pounds on a 3” piston is more powerful than 200 pounds on a 1” piston? Give me a formula that accepts force and calculates for flow or velocity or whatever.

I quoted Wikipedia as saying that derivations from Navier-Stokes related pressure to flow. If you think it says something else, quote the formulas and explain (since I won’t comprehend them). Also, I never said pressure is the only variable that controls flow; indeed, you’ll notice that Cv is part of my original equation.

Of course force pushes the water. But nothing lets you calculate a value of flow from a value of force (unless you use area).

Originally Posted by Ben

Do you even know physics? Force, momentum, velocity, acceleration, and movement are all directly related. A force can and does tell you how much something else will be accelerated from Newton's second law, which can calculate the velocity it moves at and from there theflow . Navier-Stokes is from what I know the central equations of fluid dynamics and has everything you need to calculate the velocity offlow.

That and if more mass is involved, the system simply will accelerate slower, following Newton's second law. With more mass involves comes wider chambers, where a lower velocity is needed to achieve the sameflow. So, technically the flows should be comparable. I do think there is some small difference over a large range of diameters however.

Though, I suppose you'll say anything to deny that force matters when creating flow.

Originally Posted by Ben

Newton's second law DOES account for the mass SilentGuy. Stop ignoring what it actually says. There's less acceleration, but for wider diameters it does not need as much velocity to achieve the sameflow . It's just like the Q = V * A equations you posted before. You can differentiate it to find the relationship between dQ and acceleration (small a). There's less acceleration, but theflow should still be comparable.

I know how everything is related. I’ve already explained how force does not account for area. As you have said, what matters is the force per (volume per distance), which is force per area, or pressure.

Even if the large chamber may be capable of more flow, it all comes down to how the flow is limited by the flow coefficient. You yourself have admitted that flow coefficient limits the flow, but does not create it; that’s what’s happening here. The rearranged Cv equation tells you the maximum flow possible with certain pressures and Cvs. In practice, the wider chambers will only have marginally more flow because the total Cv is barely larger.

You cannot just increase the chamber size for a certain pressure to increase flow. The Cv is going to be reduced by the barrel tubing anyway. You have to increase the barrel tubing size and the pressure, not the chamber tubing size and the force.

Originally Posted by Ben

SilentGuy, I don't know why you keep arguing that pressure determines how a water gun performs. I know for a fact that it does not. I continually pull up highly authoritative sources that say thatforce creates flow, but you continually deny it matters or put some spin on it that "the force is reduced per unit area, so pressure matters." No, it isn't.

It's perfectly fine to be wrong SilentGuy. Believe me, you're just wasting your time arguing with me over this. The more I research it, the more sure I am of theforce model. I can keep bringing up points in contention with what you post and you can keep ignoring them or putting some spin on them about "how theforce is reduced" as you continually have. At this point, I believe nothing is being accomplished by my arguing with you and I will not respond to whatever you bring up. It seems that you are more concerned with justifying something than with changing your view.

My diagram, my stream tests, and Pascal’s principle have shown that force is reduced per unit area. You’re treating my argument like an old wives’ tale.

Regarding frustration with this discussion, I’m feeling the same way. It seems like you’ve been ignoring all comments regarding force per volume, etc.


The whole mixing and matching turned out to be a mess...before I lost the first post, I had gone through as I got to each point and grouped everything. Darn.

[joannaardway]

Originally Posted by isoaker_com

But where is the force/pressure at the nozzle coming from?

I think it's something to do with the Bernoulli principle, where flow, pressure and stream speed are all linked (I believe the rule is that the product is constant?)

Now, you didn't want the questions answered, but I'll give my opinion anyway.

The questions are:
What is the pressure at the question marks in the diagram? In all cases, water can be considered to be isobaric, so the pressure will be 100 psi in all cases, assuming you are refering to the pressure of the water within the system. (Except 3c and 4b, where it's 200 psi and 50 psi respectively)
Where is the pressure coming from? Water pressure, with expansion permitted by an expansive medium.
Is force at the nozzles in parts 2 and 3 different? No (other than through small friction losses). Adding the additional pipe won't affect the force or pressure.
What about part 4? Different, because of the different pressures driving it - the fluid shape changes.
Do all the diagrams have the same pressure? What about force at the nozzle? The first answer of mine more or less explains this. Assuming all nozzles are of equal size, the force is proportional to the pressure.

[Ben]

*sigh* You can apply all the force you want onto 1mL of water and steram performance would end up being rather lousy. Take an air pressure PC, fill it to 20psi and fire and you get an 'ok' stream. Fill it to 40psi and you'd get a better stream. Now, one may say, well, the pressure in CPS systems is lower than that in air pressure systems, yet CPS systems work better and I'd agree. It's not a pressure measurement alone, but a pressure over area measurement which determines force. In the same system, however, if you increase the pressure, you increase the force.

Okay, again, you're stating things I already know. I know that more pressure can mean more force. Please stop telling me that. I know that the models are based upon ideal scenarios. And I know that pressure over area means force. What are you trying to say to me? I know everything you're telling me. I'm really unsure what you are trying to argue.

As for assuming a large force being greater than mass to make mass negligible, that only works at particlarly high forces and not with ones used for pushing out water streams from stock or homemade water guns. If you're building a soaker to launch a microlitre of water, I suppose it'd work, but if you're pushing a few hundred mL, forget it.

I think you're forgetting that most water gun pressure chambers do not exceed one liter in volume. That is 2.2 pounds. The force applied from most air pressure water guns is probably 80 - 100 pounds. That is MANY times more and is exactly why they said it was negligible. Now, I suppose that a water gun like Supercannon II, with 8 pounds of water and over 1000 pounds of force have a higher ratio, but the other ratio isn't bad either. Extremely high forces aren't necessary. In fact, if it was only 20 pounds of force, that'd still be much larger.

Force does play a part in the accleration of the water from the water gun. However, I cannot see this being the force in the chamber for various reasons, including that force cannot be carried when the fluid changes shape.

Umm, momentum is carried by a fluid. Momentum is the integral of force with respect to time. That's how Navier-Stokes works. Force isn't carried. Momentum is however. I don't see how this is a major problem with you.

As far as I am concerned, the force involved comes from the nozzle. I damn well know you said that the nozzle doesn't exert a force, but if it doesn't - explain water gun recoil.
Under the conservation of momentum laws, the water gun recoils because of the force exerted along the line of the stream's acceleration (equal and opposite reaction)
A water gun doesn't recoil up if it's chamber is vertical (other than through mass displacement). It still recoils backwards -which is what a force at the nozzle means.

The recoil comes from the ejection of water. For every action there is an equal and opposite reaction. Basic physics. Because the water is leaving the nozzle, an equal force is applied back. The direction of the nozzle matters because it determines the direction of the water ejected. Not very difficult to understand. And you seem to know it...

One error you seem to make however is the thought that the water has to accelerate through a nozzle for recoil to occur. Umm, that's not true. Ejecting anything creates a force in the direction of ejection. If there was no nozzle to accelerate the water, there still would be recoil. Ever seen a hose jump when turned on? Make something that moves water into another chamber without a nozzle. There still is recoil, but it comes from the movement.

With this being said, when shooting SuperCAP, the backpack actually jumps during a shot. Interesting actually. It comes down to the direction (the vector) mass is moving combined with other force vectors. iSoaker is correct.

Also, I'm quite sure that the nozzle itself provides resistance (a force definitely) in the direction opposite to the flow. But, it's not that resistance that creates recoil either. It's the momement of water.

And why do you care about "force at the nozzle?" What are you trying to prove with this? It seems irrelevant to me.

Water is inexpansible. The dual valve soaker will not work because there is nothing to expand into the space it has left (be this air or LRT). Remove the air from the equation, and sure, it won't work. A gas can flow in those circumstances because it can expand of it's own accord. Water can't.

Flow will NEVER occur without something to enter the space left by the fluid. There are no examples you can possibly give to deny this fact.
Even my uncle (who is a fully qualified and highly experienced engineer, and has an incredible reputation) cannot give even one example.

As we have no substance to fill the space left (as water cannot vapourise to exceed the pressure of the atmosphere, at least at RTP), no flow will occur. Even your force argument wouldn't work if the air couldn't expand.

Cool. This is much like what I have been saying all along. But it doesn't follow your model. What happened to the entire pressure differential thing? Because by your model, there should be flow. Why don't you just dump the model and follow reality?

A day or two ago, I found a system that disproves your CPS theory: spherical bladders, like balloons.

This disproves my theory how? I don't see what the problem is. There's still only one part that doesn't have the other parts cancelled out. Watch a spherical CPS bladder discharge. The end moves in.

We can all agree that force is what accelerates the water. However, as I've said before, just considering the value for force disregards the mass of the water being accelerated, and thus the resultant acceleration. More force is better than less force, but more force on more water is not better than less force on less water.

Earlier, I explained how the mass, and thus the volume, and thus the area do matter in stream velocity. When you compound the force and the area you get pressure. You seem to have missed this point somewhere.

I've already posted several links that state that dV (a cross section of the volume) is what is used in the Navier-Stokes equations. Therefore, the mass matters less than you may think. Even so, as I explained previously, more often than not the force is many times higher than the weight of the water. So, the mass of the water is a non-issue. It essentially is negligible. You're arguing without thinking! You seem to have missed this point somewhere.

Guess how Pascal's principle explains change in force for hydraulic systems? Through change in surface area/diameter. My logic is not faulty, and I'll repeat, my test proved that through the conservation of momentum.

Again, tell me more things I know. The difference here is that the piston is actually reapplying the force. That's how Pascal's principle works.

And I refuse to argue you further on this issue. A force is a PUSH, PULL, OR LIFT. Where's the push, pull, or lift? The piston is necessary to create the push.

Also, if you really wanted to do a more accurate test with "conservation of momentum," fire water guns with a force gauge to measure the recoil force. Seems to be an easier test.

I'm starting to laugh at your logic. As you speculated before? And there must be something we're missing? You can change your opinion to fit the facts, but you can't change the facts to suit your opinion. It sounds like you're just searching for a reason now. (Also, the relation between volume and mass is even enough. If water is incompressible for our purposes, as you’ve put it before, then the density is constant, and the relationship between volume and mass is constant.)

I am getting really annoyed that you fail to read my explanations to this issue you keep hammering. As far as I can tell, you have not read that once.

I speculated previously (in my head, not online, that's still speculation) that mass does matter to a certain extent. And dV indicates that. dV is a small cross section of the total volume. A larger volume will have a larger small cross section. I even posted links about this to prove it... please read them.

So you’re saying more area requires more force to move the water. Force divided by area equals pressure.

The force is definitely what pushes the water out. The pressure tells you how much force there is for a certain amount of water – thus it can tell you the acceleration and velocity. I don’t know how many times we need to repeat this.

Third example: The new system would push a quarter of the mass. It would have four times the acceleration. There’s no way you can justify similar performance – you yourself have finally said the volume/mass is also what matters.

Again, you've missed several key points I made in my posts. If you continue to do this, I will simply not respond any longer aside from a request to read my posts. I spend half my posts telling you to read my previous posts.

To mention another thing you seem to have avoided (perhaps intentionally), to achieve the same flow with a wider pipe, less velocity is necessary. Therefore, less acceleration is necessary. Therefore, a wider pipe should have comparable flow with less acceleration. Not hard to understand.

No, I don't understand the concept of an integral...sounds like it's the anti-derivative though. How does that relate to this case? Thanks.

And integral is an anti-derivative essentially. Does that help? If you needed a different explanation, let me know.

If you're pushing the piston of a Waterzooka at a constant velocity, there is no acceleration. However, you're still applying force. I'm wondering why this is the case - must be because of drag or something.

Umm, you need to learn basic physics. I am surprised I have to explain this. Without things such as drag and the resistance to flow, the piston would continue to move due to momentum. With those in play, the piston would stop without the constant applied force. The force is keeping the water moving.

Jo and iSoaker have explained how pressure tells you the amount of force accelerating the volume of water. Pressure is force/area. It tells you the force being used to accelerate a volume of water.

The total volume of water is what matters. Each individual molecule certainly is controlled by the pressure. Each individual molecule gets closer to each other and the forces of electric charge are actually causing the force. What matters overall (and all the physics I have pointed out show this) is the force. Why do you continue to ignore Navier-Stokes and everything I have posted that says flow is determined by force? And if you do not quote and answer this in your next post, I will simply ask you to read my posts again.

Regarding the equalization in a piston pumper: As you’ve said, when you apply force, you create pressure. There is certainly a pressure differential. Once again, while it’s force that pushes the water, the pressure tells you the velocity.

I know an applied force creates a pressure. However, the entire fluid most definitely is not under a pressure. Thereforce, there is no differential. That's what I have been saying all along.

You sound desperate. You’re completely changing tact here! You clearly argued that the Super Soaker patents were some of the best around for information and qualifications. You even pointed me towards this patent itself! I’m not falling for this.

Pressure should be the same for gases and liquids - as Jo put in one of the recent posts, all fluids act similarly. The only difference is that water does not compress easily, but air does.

Desperate? I consider your continued and intentional ignoring the Navier-Stokes equations desperate. Yet, I do not call you out for it, until now.

And I did not say they were wrong. They never once said that pressure is the deciding factor in flow. They said more pressure is benefitial. I say that too. But they carefully put a qualifier on there. There obviously are other factors. Why do you interpret what they wrote differently?

You seemed to have been fine with the argument until then. Anyway, you might not have been talking about the inside of the chamber, but then where do your force figures for SuperCannon II come from? That 1250 pounds (1270 to be exact – I did the calculations, so I know where the numbers come from) of force is exerted by the air on the piston. Needless to say, the piston is equalized, so the water exerts 1250 pounds on the piston too. If you’re only considering net force, then consider those 1250 pounds worthless.

The 1250 was rounded to the nearest 50. I like square numbers. And actually, (2^2)*pi*100 equals 1256.54 pounds of force. I don't know what you're doing to get that wrong.

Umm, you're the one who's ignoring net force. I said net force before you ever did. I don't know what you're saying here.

Certainly, the water applies force back. But, it does not apply 1250 pounds of force back. I would doubt that the water and pipes apply more than 50% of the force back. The entire force model is a simplification based upon what we know. The force definitely is reduced due to the water, but it is not completely reduced.

Furthermore, your statement, “And do you want me to quote the millions of pages saying that pressure differentials create force?” is what looks like you were arguing just for the sake of it. The earlier posts of mine that I’ve quoted involve net force and total force being thrown around carelessly. Which worked until you felt the need to show the difference, and then insult me after I clarified.

Look, I like bringing up evidence when needed. That's not arguing for the sake of argument. And I have the upmost respect for you and there was no insult intended.

Once again, you’re trying to deflect the brunt of the argument and distract people from reading the message. The patent claims that range and pressure are proportional, if not directly so (wind resistance). The qualifier “generally” accounts for the Cv, if you must have me explicitly state facts that you know.

Cool. Then why does the SS 300's perform well with a Cv that stinks and low pressure? High force is the only explanation. Why you continue to play this down isn't up to debate either: you are intentionally avoiding it.

And proportional does not mean that pressure is the only value in there. Generally certainly accounts for ability to flow, along with turbulence, as well as the force applied.

And why doesn't anyone use the Cv equations to calculate flow created? To reiterate something I posted before, nothing you have posted says that the equation is used to calculate flow. And I have taken a good look. It's useful to see how much flow is lost through valves. That is in fact why it was made. I'll go onto your beloved Physics Forums and ask about this myself if you want me to.

When the pressure differential is zero, the net force is zero. It does not matter how much area you have; zero force divided by any area is zero pressure. I don’t know how many times I have to say it. His method only works because he’s calculating for zero. If he had to do anything remotely relevant to calculating flow (and it was you who claimed my examples weren’t relevant to water guns; look at this), he could not use force to do so. Yes, he could state that there is flow; yes, he can state i