This is an article I have been writing bit by bit since October. The point of the article is to improve and consolidate the Streams, Effective distance, additives and other articles into one big one. Admittedly, most of the article was written last Saturday, but it's not complete yet despite it's massive length! This article is already longer than the 5000 word Aquabatalicus, and it will not be getting any shorter.
I will be posting this article in installments because I hope to get feedback on certain parts. For this article to be as effective as I would like, feedback is necessary to fine tune each part.
(a note: subscripts don't appear correctly here at the moment)
Water nozzle and stream physics
This text is the replacement for the old "Streams" article I wrote in 2004. Since that time, we have learned a substantial bit more about how to make water guns perform better, and I have neglected to keep my article current. This article serves to describe all known performance enhancements that can be done to water gun designs, with a stress put on the water nozzle and the stream because that is where most of the improvement can be made.
Water nozzle knowledge is fairly scarce, but much has been learned. Several years ago, water nozzle physics were almost considered magic, with Larami being the magicians. This is no longer the case as hundreds of people build their own water guns every year. We no longer turn to Hasbro for performance, we get it ourselves, even better than the best they fed us. This information also still will apply to regular factory-made water guns because the physics does not change from brand to brand, including homemade water guns.
I will not throw around the term "revolutionary" in this guide because whether or not this would be revolutionary is determined by acceptance, not the author. If these methods are to be revolutionary, hype would be unnecessary. I fear that most of these concepts are too advanced to many of my readers, stifling most of any said "revolution." My best efforts will be made to simplify these concepts, but the reader must realize that they themselves are the ones learning and they have to take the initiative if they are interested.
Note to the readers: In this guide, I will use the term distance as opposed to range and the term shot duration as opposed to shot time. Range has an actual statistical meaning and distance would be better used. Shot duration also better describes the statistic. Please note these differences from the typical notation.
Why improve nozzle and water gun design?
What's the point of water nozzle improvements? Performance increase is the main goal. With an improved water gun design, your water gun will shoot a farther distance at the same power.
A greater efficiency is obtained through more intelligent design. No longer are people just building a water gun and hoping that it performs well - they are designing to know that it will perform well.
Some people have congratulated me on writing guides such as this one. The greatest satisfaction I get from this article is knowing that I help people make better water guns. I don't charge money for this information or tell you to go take a class on fluid mechanics. I get right down to the point. Not everyone is smart enough to handle a college level course and you don't have to take one to know how to do most design improvements.
Fluid mechanics background information
Before you can proceed further in this guide, you must be comfortable with basic fluid mechanics terms. If you do not fully understand there terms, you simply will not be able to understand anything else described in this guide! You aren't saving yourself time by skipping this important section, you are wasting it! I will present these terms in plain English, mostly because I don't know them any other way myself.
I assume that one who is reading this guide has a basic understanding of how a water gun operates and the parts of a water gun. If you do not have that knowledge, I would recommend the HowStuffWorks article on the subject as it is written very well and has easy to understand animations. Alternatively, disassemble a Super Soaker water gun and figure out how it works from there. In the future I likely will be writing my own guide on how a water gun functions, but that project is not high on my list of priorities because of the excellent resources already available.
Pressure is essentially how much force is being used to eject the stream from the nozzle. The pressure source is the pressure chamber. There are many different types of pressure chambers, such as rubber CPS systems and air-pressure systems. Each system has it's advantages and disadvantages that I will not cover in this guide. When I refer to power or pressure in this guide, I am speaking of the force used, almost analogous to horsepower in cars. A pressure drop-off is attributed to most air pressure systems excluding constant air pressure. CPS systems such as rubber CPS, constant air pressure, and spring powered water guns have a much more constant performance. The drop-off or lack of drop-off can be seen in a water gun's output curve, which will be covered later in this guide.
Viscosity is the tendency for a fluid to stick together. Certain fluids, such as glycerin, have a higher viscosity than water. Viscosity varies by temperature, but as a general rule viscosity improves slightly as a fluid gets colder.
The size of the orifice is essentially the size of the part commonly called the nozzle. The size of the orifice determines much of how a nozzle will perform. For water to exit a smaller hole, it must accelerate. For that reason, smaller nozzles typically have a greater velocity than larger nozzles at the same power. Orifice size determines many things, such as output and stream velocity. Smaller nozzle orifices will have a greater velocity and lower output, while larger nozzle orifices will have a lower velocity and higher output.
Drag on the stream is caused by the stream hitting the air. Depending on the stream cohesion (a combination of the viscosity of the stream and how well the stream is formed), stream velocity (determined by the nozzle orifice size and pressure) and the size of the stream, stream break-up will occur a distance from the nozzle. Stream break-up can be described best as the stream breaking into many smaller droplets of water by the drag on the stream. These droplets will fall to the ground prematurely because the stream's velocity was reduced by drag as well. Shoot any water gun and you will see that by the end of the stream, the stream breaks into smaller droplets that hit the ground. Almost never will a cylindrical stream shaped as it exited the nozzle hit the ground due to steam break-up, unless of course the stream only traveled inches.
Flow is said to be laminar when it has a tendency to follow a linear (i.e. straight) path. Laminar flow is affected less by drag because it does not flow randomly. The opposite of laminar flow is turbulent flow. Turbulent flow is less linear and more random. Turbulent flow is measured in Reynolds numbers. Typically a Reynolds number of less than 2000 indicates laminar flow.
The shot angle can greatly affect the distance of a water gun. Due to projectile physics, the range of any projectile including a water stream will be greatest at a 45 degree angle. An angle greater or less than 45 degrees will result in less distance. A higher angle (up to 90 degrees) will give the stream more height, while a lower angle (as low as -90 degrees or 270 degrees) will reduce the height of the stream.
Internal diameter can be best described as the smallest diameter the water must pass through as it travels from the pressure chamber to the nozzle. Internal diameters of all other portions of the water gun are not important because the water will not flow from the pressure chamber to the nozzle in those parts. A larger internal diameter allows for more flow but also allows for more turbulence - internal diameter is a double-ended sword.
Units and variables used in water gun physics
Typically, a mixture of both metric and the English system of measurement is used in water gun physics. The reasons for such a mixture is simple - water guns are used worldwide and people always seem to use the units most familiar with themselves.
Distance (or range) is nearly always measured in feet. Meters are much less common in practice. This choice may be due to the fact that a meter is approximately three times longer than a foot and you will receive a more precise measurement using feet. If meters are used, please use decimals as well to record a more precise measurement. The variable d is used to describe total distance.
Output is how much water exists the nozzle orifice per second. Output is measured in three systems, two of which are essentially the same. I prefer units of mL/s (mL per second) because it provides the most accuracy. The English unit of ounces per second is also commonly used. The traditional system (in units "X") used in water gun physics was used by Larami in the CPS water guns, based upon the output of a Super Soaker XP 70. It is generally accepted that the output of an XP 70 is one ounce per second, or 30mL per second. The conversion between ounces per second and X is very simple - 5X output equals 5 ounces per second. The variable o is used to describe average output over a interval, while oo is used to describe initial output. Instantaneous output would be written as ot, where t is time in seconds.
Shot duration (shot time) is measured only in seconds. Shot duration is defined as the time the water gun is emitting output. The simple explanation would be how long the shot lasts. The variable tf is used to describe shot duration. tf stands for time final, which simply the final instant output was being made. Time final essentially occurs when o = 0.
Capacity of a certain part of the water gun is measured in many units, depending on how appropriate they are. Metric units are the ones I use most often, though some will use the English system of gallons and ounces. Being a smaller container, pressure chamber capacity is measured in mL. Water reservoir capacity is measured in L. The variable vf is used to describe the total pressure chamber capacity when full. vf stands for volume when full.
Pressure is how tightly packed the gas molecules powering the water gun are. CPS systems, with exception to constant air pressure, do not use pressure to operate and will not have a pressure value. Pressure is nearly exclusively measured in PSI (pounds per square inch), though some others prefer bar and atmospheres which are approximately equal. Pressure drops proportionally to the output, and thus output curves are appropriate enough to also be used as rough pressure curves. Pressure is defined by the variable po which is the initial pressure. Pressure at any moment can be given as pt, where t is any moment in time. Final pressure, pf, is always 0.
Velocity is how fast and in what direction the stream is moving. Velocity is an uncommon, but essentially useless statistics. Basic physics can find a position function, and the velocity function can be found rather quickly from that. When used, the variable for velocity is v which also can have subscripts much like output and pressure. Velocity of the water in the position function is different than the velocity of the water exiting the nozzle, and thus there are two velocity functions in reality. The second, even less common, velocity function should be proportional to the output curve.
Nozzle orifice diameter is defined as the diameter of the nozzle, and is a very important number. The nozzle orifice diameter determines many things about how the stream will react, namely the stream velocity, output, and distance. Nozzle orifice diameter is nearly exclusively measured in fractions of an inch, though some people (such as Big Bee from Buzz Bee Toys) do use the metric mm measurement. This statistic is mainly used for homemade water guns, and thus you will use the drill bit size of your nozzle as it's nozzle orifice diameter.
Nozzle orifice diameter is described in the variable n, but you can use subscripts to differentiate between different nozzles if your water gun has the capability to use more than one (i.e. n1, n2, etc.). The square of the nozzle diameter n^2 is much more useful to us, and I will describe why in the section below.
Water gun statistics
To measure your current performance, you must measure the statistics of your water gun. The only way to know that you have an improved water gun is to measure it's performance to see it's performance increase.
Output, pressure, and velocity all come in two forms - average and instantaneous. Average is the common average of the statistic over the shot time or indicated interval. Instantaneous on the other hand is the statistic as a specific time. Instantaneous statistics require Calculus knowledge to use. If you are not familiar with the basics of derivative Calculus, then you likely will not be able to use instantaneous statistics, though you should be perfectly fine interpreting graphs of output, pressure, or velocity. Instantaneous output will be discussed later in this guide.
Capacity is the easiest statistic to measure. To measure reservoir capacity, fill your water reservoir completely and then pour it back out to measure the volume. To measure pressure chamber capacity or pressurized reservoir capacity, charge your water gun fully and discharge into a container to measure.
Shot duration is also another easy statistic to measure. Fully charge your water gun and fire it, starting a timer simultaneously with your firing. Stop the timer when water is no longer being shot out (o = 0). You also can approximate shot duration with an output curve to find mathematically where o =0, but that will be covered in a later section of this guide.
Distance is a very easy statistic to measure, but a tricky one when it comes to accuracy. Many people want this number to appear as high as possible, after all, the higher the distance the better! Do not become part of that crowd. You want accuracy in your measurements. Nearly always a drop of water that shoots several feet from the puddle at the shot. Do not measure to the last drop of water. Measure to the end puddle where most of the water shot is focused - that is your "effective distance." Tape measures and other similar devices are also a necessity when it comes to measuring distance. You can not simply approximate distance, you must get distance correct.
Output can not be directly measured. The average output over the interval from t = 0 to t = tf can (or in layman's terms, the average output over the shot duration) be found by dividing the pressure chamber capacity by the shot duration. Note that the units for output are mL/s, and note that you are dividing the capacity (taken in mL) by the time (in seconds). That is how the unit system works.
Pressure will be harder to measure depending on your water gun's design. If you install a pressure guage on your water gun you will have an easy time measuring pressure. Special nozzle attachments are possible as well if you want to measure pressure without having a permanent pressure guage attachment on your water gun. Remember that pressure is proportional to output - given a constant nozzle orifice size, as output decreases, so does pressure.
Average velocity over the shot duration can be found by dividing the distance by the time it takes for the water to reach that distance. Note again the units here - ft./s - which describe the process being done to get the measurement. Instantaneous velocity could be also be found by making a function to model the stream's motion and then by taking the derivative of the function with respect to time, but that would be too complicated for those who are not familiar with Calculus.
The next installment will come once I finish up the nozzle size table.