Report No. MAE-363
S. Allen, C. Bastien, G. Bowlin, D. Chianese, E. Cote, L. Dosiek, P. Eddy,
B. Gallagher, S. Ganguly, K. Henderson, B. Kasiske, A. McIntyre, E. McKeever,
J. Schaefer, B. Schwerdt, A. Sharpsten, B. Shepardson, J. Smith, L. Smith,
B. Sutton, S. Sutton, M. Thiel, M. Toh, R. Turner, M. Whelan, F. Wirkus-Carter,
M. Woody, and J.J. Zhang
Mechanical and Aeronautical Engineering Report MAE-363
Mechanical and Aeronautical Engineering Department Report No. MAE-363
(Clarkson University Course Report No. CU-HP303-02-001)
Junior Honors Science Seminar
Clarkson University, Potsdam, NY 13699
Liquid Paths - Sarah Allen
Fountains: Mesmerization and entertainment - Chris Bastien
Untitled - Gary Bowlin
Aesthetic Features of a Water Fountain - Eric Cote
The Mood of the Fountain - Luke Dosiek
Title of the Essay: On Rippling Water - Patrick Eddy
Aesthetic Water Features - Kara Henderson
For a Soothing Rhyme, it's Fountain Time - Brad Kasiske
"Nothing" - Adam McIntyre
"Endorphine Fueled Meditation" - Eric McKeever
Calmness Through Softness - Justen Schaefer
Subtle Fountain - Anna Sharpsten
The Inward Music - Bryan Shepardson
Intellectual or Natural Relaxation? - Jason Smith
Saturated - Brian Sutton
Serenity - Sean Sutton
Tranquility - Mike Thiel
The aesthetic features of a Fengshui fountain - Melissa Toh
The Docks versus the Dam - Matthew Whelan
Essay - Faustin Wirkus-Carter
Untitled - Matthew Woody
Reflections on a Water Fountain - Jun Ji Zhang
"Water Meditation" - Danielle Chianese
A Walk Through Nature - Beth Gallagher
The Story of Me - Srabonti Ganguly
The Seven Senses of Mother Nature - Laura Smith
Thousand Word Picture - Ryan Turner
Here I Find Freedom - Brian Schwerdt
Appendix – Daniel T. Valentine
This document is a collection of material prepared by the students and instructor of the Junior Honors Science Seminar Course, HP303, during the Fall 2002 semester at Clarkson University. The students investigated the art, science and engineering of water fountains by developing a variety of designs. As a principal part of the work by eight groups of students in their efforts to create eight water-fountain designs, the purpose of design was examined. Each of the twenty-eight students listed on the cover prepared a one-page document on the ‘aesthetic’ features of a water fountain. Twenty-eight written works were submitted in the form of an essay, a poem or a piece of music. The essays, poems and music are the main features of this report. In addition, an Appendix by the editor provides a discussion of some of the dynamics associated with water in motion to help those interested in seeking deeper insight.
To initiate the investigation that led to the preparation of the contents of this report, we raised the following questions: What is it that we are trying to accomplish with the design of a water fountain? In other words, what does a water fountain or water feature express? These questions are open-ended, of course, and subject to numerous interpretations. To clarify the questions, we purchased a garden-pond liner and fountain equipment to observe the interaction of water bells emanating from circular-annulus nozzles, the fog created by an ultrasonic mister and the water jet discharged from a piece of circular-plastic pipe. In addition, we considered the following notions and questions: Let us suppose that we want to design an artifact that can put us in a meditative, comfortable and relaxing mood. Let us call this an “aesthetic” state of mind. What is this “aesthetic” mind set or trance of sorts? Let us think about the interacting water bells and the ultrasonic mister that we observed as part of our investigations. Let us recall related experiences we may have had, for example, experiences like those of observing the surf when we were at the seashore, the flames of a fire when we were in front of a warm fireplace, or the rapids created by water flowing over rocks when we were on the banks of a stream. We want to consider and try to express in writing the following: What do you see? What do you hear? What kind of water feature could entertain you for an extended period of time?
The essays are the first thoughts of youth in their own language. It is true that the essays, poems and music were part of an assignment in school. However, the instructor (the editor) emphasized that it was their thoughts and opinions that were of primary interest. Hence, with this as a ground rule, any editing was kept to a minimum for fear of destroying the raw qualities and sincerity of thought. I offer the essays, poems and music as a challenge to the reader to write their own thoughts on the purpose of their own creative activities. What is your purpose for doing art, doing gardening, doing construction, doing science, doing business, or doing engineering, etc.? How important is your purpose to you?
The editor acknowledges the Clarkson Space Grant Program for inspiration and partial support to develop this course.
Hannawa Falls, NY D.T.V.
Round and round goes the bell of the water
And round and round goes the water itself
And that which is the pitch of its motion,
The bell of its dome, the patron of sound.
Variations on a Summer Day---Wallace Stevens
The poem of the mind in the act of finding
What will suffice.
Of Modern Poetry---Wallace Stevens
The concept of a water fountain, what is it? It could be a practical concept such that it is designed to control the moisture of a particular space. It could be designed to aerate a pond to improve the quality of its water. However, I think that we can all agree that this is usually not the primary purpose of water fountains. They are usually designed for aesthetic reasons. It may be desirable or there may be a need to design water fountains for lobbies of buildings, for outdoor plazas or for gardens. The desire or need would be to improve the ‘quality’ of the environment and, hence, to enhance the enjoyment of visitors to such spaces. It is this purpose that is discussed in the essays, poems and music.
The design of water fountains ought
to be like the design of objects of fine art. Hence, to consider the notions of
aesthetics related to water fountains, it is worthwhile to consider other art
objects. Some of Escher’s graphics deal with water ; a good example is his
“Three Worlds”. If words are the medium, then the poem is the art object. Hence, examples of art objects that provide
experiences analogous to what might be provided by optimal design of water
fountains, the poems of Wallace Stevens  are particularly good. Some of his
poems are sufficiently abstract that the experience of reading them provides
thoughtful digressions from more mundane everyday experience. We examined
copies of fine art objects, the poems of Stevens, as well as the pictorial
illustrations of fluid mechanical phenomena published by Van Dyke  in
preparation for writing the essays. Without further digressions, the editor
invites you to enjoy the raw thoughts of youth on a rather difficult topic.
While I have never been to any falls, I have been to the sea, and whether it is the unchecked turmoil of Nature or the tame trickle of a diminutive fountain, most forms of water in motion put me in a contemplative state all by themselves, without lights or additional sounds to highlight their features. There is something incredibly relaxing about the rhythmic yet not - rhythmic sound that falling water beats out in its chaos-driven path, falling down dips into itself, rolling and breaking over itself, swirling and spiraling with itself. In smaller, calmer trickles, the sounds are light and musical, reminiscent of flutes and small bells, or even of birdsong - high-pitched and twittering, wavering as the flow's path. In larger, more massive quantities, the sounds is more akin to static, but it does not have the same incessant, grating buzz that comes through a radio or a television that is broadcasting nothing; the sound of quantities or water falling or great waves breaking has a pulse to it, as though some great heart beats out in the center of it all where no man sails, and drives the rhythm that the waves and falls beat out. The rhythm is just a little faster than the calmed human pulse, feeling as though every beat comes just a little sooner than it should, pressing the soul towards anticipation, inducing a sort of quiet excitement that is heady and seductive even as it soothes. Yes, even such drumbeats as the run-together beatings of a falls against its basin can be described as soothing, for there is always a cool connotation associated with the sound of water, be it white noise or woodwinds - possibly a link between the feel of it passing over the skin or the breeze coming off of it, bearing spray or just the coolness into our faces, onto our clothes and along our skin. This coolness and the tranquilizing rhythm with which it laps up against the extended hand, a submerged torso, in time with its music, lulls and massages both the mind and the body into a transcendental, philosophical, quiet state.
Opening one's eyes to drink in the water reveals its deceptive white glittering as it shimmers down to the pool below, the glassy clearness of it that bears a dark reflection of the world around it, or the blurry, shining curtain it draws across half the world. Contained streams seem almost futuristic and beyond our time in their smooth cohesion and almost glasslike surfaces, while broken trickles and droplets recall the immeasurable past in which rivulets and drops of their kind traced along canopies of leaves, shooting off tips of basins of puddles formed in wells between roots and stones and higher piles of dirt. Sitting quietly, watching and listening to water play - either through a water feature of man's design of Nature's, for it makes not difference - has the ability of making man feel comfortably small, either by drawing him in to the level at which tiny molecules bump together to alter flows, clump together to form drops, fall as drops to terrorize small things such as insects or nourish mice, birds, squirrels; or by making him feel vastly diminutive compared to the awesome power that water possesses, that represents the greatness of the universe and his small part in it, like a tiny drop spraying off of the grand flow of the powers that be. And yet, unlike fire and brimstone, water can introduce this perspective while soothing the recipient, such that he or she does not feel cowed or slighted in any offensive manner, only awed and filled with wonder at the world in which she (or he) suddenly finds him/herself.
Fountains: Mesmerization and Entertainment
As common today as the automobile, fountains can be found almost anywhere. Their characteristics range from monumental to subtle, function to decorative, futuristic to natural. Most fountains are a blend of these features. The fountain proposed by the indoor dynamical group is exactly that. The majority of the time its aim is to produce a calm, relaxing, meditative state of mind, ideal for contemplation. At specified intervals some of its features will change in order to create more entertaining and exciting effects. The goal of the indoor dynamical fountain is to successfully produce both of these atmospheres.
Before a fountain can be created to impart a calm, meditative state of mind, one needs to know what this mental state is. Most people will agree that the ocean tide, or the dancing flames of a fire, or the motion of water in a stream are calming and mesmerizing. They would be harder pressed to say why, and the variety of their answers would be overwhelming. When I hear the sounds of the ocean, specifically the sound of the tide rushing in and out, I notice its steady rhythm. Perhaps it's calming and relaxing because subconsciously it reminds us of the steady, unfailing heartbeat we listened to for the first 9 months of our existence. Similarly the sounds of a stream gurgling and splashing could be related to the sounds heard by an infant inside the womb (blood rushing through the body, sloshing of amniotic fluid, etc.).
The hypnotizing effect of fire is harder to explain. When I see a flame dancing, I see an object moving completely at random, yet remaining visually fluid and graceful. Personally I look for patterns in things, and fire may e mesmerizing because it seems to lack any pattern to its infinite shapes and movements. Similarly the splashing of water droplets and the breakup of waves may be so complex to model that for most people their motion and shapes appear completely random and infinite. Perhaps my desire to find a pattern leads me to this hypnotic state, encompassing my mind entirely in that task, leaving my body completely relaxed for the moment.
The indoor dynamical fountain will also try to entertain people for short periods of time as well. It will do this through laminar jets that create a pattern and appear to chase each other. Controlling water to create clean arcing jets and patters is entertaining because it demonstrates technological achievement. It is also something rather unique because controlling water flow outside of a rigid container is difficult given the properties of water (its malleability and lack of cohesiveness, etc.).
Although it's enormously difficult, if not impossible, to define why something is calming or mesmerizing, it is considerably less difficult to recreate these feelings with a fountain feature. Instinctively people recognize that which is or is not relaxing. They can't say why, only that it is or is not. The same can be said for an entertaining. Given these considerations, the indoor dynamical group hopes to create a fountain that can be both calming and entertaining at different times.
Moments of peace often frame aesthetic scenes. Whether a scenic lake, a dense wood, or even a red sunset over a skyline, artwork is often centered on the presence of peace, immutability, and strength. A fountain often stirs a sense of awe in its audience. Derived from the larger natural waterfalls, fountains recall us to the strength and power of these natural wonders. At the same time on a smaller scale, these wonders can bring us back to a more congenial world. The light sound of water flowing by, as if by a small brook, brings about an inner peace that we would associate with living in the county, care free of our busy lives and packed streets, taking us away to somewhere comfortable.
Another common genre is the idea of capturing the moment. This instills energy in the viewer. The rush of victory, the crush of defeat, and many other forms of instantaneous emotion are captured by this form of art. Perhaps however, a piece might be used to inspire a sense of grace and freedom. Jets seem to represent a more ephemeral view of aesthetics, just a moment and it’s gone, and either to jump again or to lie in wait until some outside stimuli requires its response.
A more abstract work relies on the properties of water in order to convey these ideals, and more commonly it is used to create awe. To wonder and how something was a accomplished, water waves going upstream instead of down, vortices in a otherwise serene surface, or interactions between multiple sheets are great examples of how an abstract work would utilize the properties of water rather than more natural references.
Whether depicting the immutable or the ephemeral, good art instills emotion. Perhaps with a water feature the best thing to depict is either immutability or awe. The pure permanence of water, and its ability to overcome any obstacle in its way (maintaining its flow) or in the sheer awe that surrounds its activities (breakups of cascading sheets, water bells, wave patterns) are two very valid ways to classify a water feature as a work of art.
Aesthetic Features of a Water Fountain
When I see or hear a fountain, I think what comes to mind is the chaotic nature of the water being brought into some sort of harmony. The sound of the water interacting with itself, and the smell of the mist in the air is certainly a relaxing experience. The different types of sounds that a fountain can make, in addition to the various shapes of fountains and their jets, are properties that seem to calm and relax people quite well.
Keeping this in mind, we hope to recreate some of these perplexing aesthetic properties within the atrium of CAMP with our fountain. In addition to just the fountain mechanics, there are other sorts of properties that perplex people, especially those of an engineering discipline. For example, reflecting on how a particular piece of machinery works or functions might mesmerize an engineer. This could vary from anything such as the flowing of electrons through a light bulb, to the various bits in a computer switching from high to low in a rather chaotic, yet controlled, manner.
Building on these thoughts, we hope to construct a fountain that will mesmerize people at CAMP in various ways. We hope that the fountain and fluid mechanics of our water feature will be soothing to the ear and pleasant to the eye. In addition to this however, we hope to construct a fountain with a design appropriate for the CAMP atmosphere, in that people will be able to see through components, and see how they actually work; a transparent solenoid perhaps, or clear piping with a visible pump. This will hopefully create a second property that people – engineers in particular - can be mesmerized by. Engineers will certainly have an appreciation for how such things work. Based on this belief, presenting the mechanical parts for viewing should add an additional element of aesthetic pleasure and enjoyment.
The Mood of the Fountain
In designing our garden feature outside the ERC, the main purpose is to create a place that anyone can go to escape the perils of the plant earth for a few minutes between classes or on the way home. I would like the feature to be an oasis of sorts where a person, after a rough day of work, can come and leave all of his or her ill feelings from the day. It should be cleansing in nature, cleaning the soul of any bad feelings. Its unique sequence of water flow should aid in doing so.
If one were to approach the feature, the first thing they would be drawn to is the large waterfall cascading from the roof of the ERC into our first ground basin. They would see the power of water and the power of gravity as the sheets of water come cascading down the side of the building and chaotically crash into the pool below. Witnessing this natural chaos of the water would mesmerize the visitor who would begin to forget about their problems for a moment.
The visitor would next see the first basin emptying into our ground level basin via the bamboo ladder. This is another example of the power of water and gravity, but it is a much, much calmer effect. As the water bubbles down the ladder, it moves like one fluid entity, not like the random splashes of the waterfall. This babbling brook effect, soothing in its own right, when placed right in front of the violent waterfall, should help to bring our visitor's problems of the day into perspective. By seeing the water calmly draining from the waterfall's basin, the visitor realizes that his or her problems really aren't that big, and they will eventually work out, much like the chaotic "problematic" bottom of the waterfall eventually gets smoothed, or corrected as it poetically babbles down our bamboo ladder.
Feeling much better, our visitor prepares to leave, but not before seeing our simple fountain in the ground basin. This will remind him or her how problems can even be turned into good things, as the water, originally in the turmoil of the waterfall, has been transformed into a controlled flow of beauty and great style in the fountain. Hopefully, our visitor will put this all together, and leave our little alcove with a smile.
Title of the Essay: On Rippling Water
Discrete and appropriate subtitle: goes here
One of the most important features of our water feature should be a pool of water of some sort. A pool of water allows for the creation of wave patterns. Waves interact with each other in intricate patterns that capture the mind.
A wave travels outwards from its starting point in a ripple. A continuous input of water will tend to make a continuous set of ripples. This alone can be entrancing; however there are also the effects that occur when waves interact. A wave hitting a solid boundary reflects off of the boundary. With a continuous set of ripples this alone gets fascinating. The waves meet the continue on in the direction they were traveling as though the other wave didn't exist, however, in the region they meet tons of things happen. If they were both peaks, then the peaks add up to a larger peak. When they are both at a trough, then the trough gets deeper. When continuous ripples interact with each other the pattern is like a diamond moving checkerboard.
Wave fronts tend to be arcs. The curve of the water expands outward from a single point, though often the churning bubbles of the water entering obscure the exact point. This creates a target bulls-eye around the entry point of the water, drawing the eye into it, enticing the mind to observe the bubbling center.
The water bells provided another interesting place to observe a wave. When the surface of the bell was interrupted but not completely pierced, it would leave a wake pattern in the surface of the bell below the intrusion. In an instant of time our minds can barely comprehend the V-shaped wake distributed itself outwards forming the arced pattern observed.
The Aesthetics of a meditative water fountain must incorporate features that entrance. Being entranced involves letting go of the reasoning and watching. The reasoning may come back later, but to meditate one has to let the thoughts go. Once the slate is clean, a complete drawing can be made. This image is pure and clean, and not tainted by everything else that was on the slate before hand. A water feature functions much like a sponge for the brain. Watching the hypnotic dance of the water clears away the other distraction in one’s mind.
Aesthetic Water Features
As I lay back and listen to the waves as they hit the shore, I am relaxed. When I sit in a boat that is anchored to the dock, its rocking motion helps me to unwind. Both of these actions involve the motion of water and help to put me in a relaxed, peaceful state.
Water has such an effect on people. Growing up outside of Niagara Falls, NY, I see time and time again how powerful, flowing water can mesmerize people. No matter what language is spoken at the falls, the common thread is always amazement at how dominating and peaceful the water can be.
As I look at the interacting water bells we saw in class, I am reminded of this tranquil state; it is like water has a soothing identity in itself. Although the water bells interfered with one another, neither bell was broken. The bells had enough water pressure to endure the interference and maintain the original shape of the bells. S the two water bells interacted, the sound they made also had a soothing element. In a way, this interaction shows us that although intrusions can divide and separate, the overall affect is constant; the sound is still gentle and comforting and the sight of the water bells remains unchanged.
I can see how two interacting water bells would put me in a meditative state when incorporated into a larger water feature, it would be on the same magnitude as watching the waves lap against the short. A large water feature, whether or not it has many components or is simple in number of components, has a sort of presence about itself, it has power, beauty and serenity. This type of water feature could entertain me for extended periods of time. With or without all of the bells and whistles, a large water feature has the ability to instill feelings that large monuments are not capable of because they do not incorporate the motion and interactions of water.
For a Soothing Rhyme, it's Fountain Time
There is more to designing a perfect water fountain than the machines themselves, it must also speak to every individual and touch them in a unique way. The flow of the water has the ability to speak and portray feelings and emotions that can't be described on paper. The rhythm of the water must be consistent and fairly calm to instill a sense of peace. Everything must appear to have a smooth edge to it without excessive turbulence to make one feel that the serenity is unchanging and everlasting. Every feature should have enough beauty and rhythm to amaze every onlooker to the point where they never want to leave. It should almost feel surreal, like something that perfect couldn't possibly exist. The water should sound of smoothly flowing water to give an ability to relax. Every person should be able to close his or her eyes and, by sound alone, be able to sit there for a long time completely mesmerized by the fountain's tranquility. This sort of relaxing atmosphere would allow every person who viewed it an opportunity to clear his or her mind and escape from the real world. It should be the types of place people go to when they have too much to deal with in life or when they need a clear mind for spiritual guidance. Every person will view the fountain in his or her own way, but no matter how he or she views it, it should be unanimous that it's a relaxing, tranquil, perfect atmosphere.
When I picture myself sitting in front of our water feature, I picture myself hearing absolutely nothing. "Nothing" is, of course, met with an immediate negative connotation and a negative reaction; these features are supposed to make noise! Here I must assure the reader that I hear nothing not because the feature is broken, or because I am taking liberties in my writing. A listener hearing "nothing" is a great part of my plan for a water feature.
This begs an excellent question: why do I hear nothing? I hear nothing not because there is an absence of sound. Rather, I hear nothing because, in a spot in front of the fountain, I have reached that state of mind whereby all sound blends together and fades away. In these states, distinct sounds like peoples' voices, the rushing water, the wind meandering through the trees, combine into a cacophony of white noise; staring off into the water feature, the listener hears all these things, but at once does not hear them. Thus, we encounter the paradox that water brings.
When away from school, I live very close to Niagara Falls. I have seen the falls on a great many occasions; in elementary school, I saw it several times a year. These visits provide me with a great bank of knowledge to draw memories from. From this bank, I have tried to withdraw the sounds that I heard the water makes as it plummeted on its course over the precipice. I cannot. Enough water to fill thousands of swimming pools passes over the brink in a second, yet I cannot recall it making a single sound. As I stared off into the swift currents, as I watched crests and bubbles tremble on the edge of their very destructions before they were subdued by the torrent as it pressed on and carried them downwards where they met crash and mist, I became at peace. In this peace, I experience the paradox of water: in my peaceful state (my "trance") all sounds run together, and fade away. I do not hear the crash of falling water, nor do I hear the voices of those around me. I hear nothing, and it is brilliant.
We should make a fountain that is fun. We should make a feature that resembles a dog, and another that may resemble myriad other creatures. We must make a fountain that creates in its viewer the meditative state that I describe in the above paragraphs. Clarkson is a busy, bustling place; too often, professors and students hear only the bustle, hear only the noise. These people need a place where they hear nothing at all.
“Endorphine Fueled Meditation”
Moments that seem to be the most stimulating to my mind tend to occur during exercise. I would say that the majority of my thought breakthroughs on any subject or problem, whether academic or social, have occurred during exercise. When I head out on my bike or go for a lonesome run, I tend to push myself just hard enough to get my breathing heavy and constant. Usually after a few minutes of this kind of workout I am deeply "tranced" out. Sometimes I feel that I become a little dangerous to myself, i.e. not paying attention to traffic or the lines on the road. Mostly I just fall into a world of my own thoughts.
I know that exercise probably does not sound like it is relaxing to the reader, but it can be if the right attitude is taken. I do not ride or run with any particular goals or ambitions other then to kill a few hours time, and to see some different scenery. I think seeing scenery from a different perspective plays a large part in the meditation process. It is absolutely amazing how much more I notice riding my bike then I do driving my car. If I ride my bike down a road I can tell you what kind of flowers are around a particular house's mailbox, and if they smell sweet or not. In my car, I am lucky if I can tell you what color the house is and I will only know how it smells if the field out back have just been fertilized.
I think that this change of perspective is what our fountains could do. They should allow the viewer to see the water from and point of view that do not normally see. This different point of perspective may be all that is needed to induce some deep thought or meditation. Almost everyone has seen water on a large scale, i.e. lakes, rivers, and oceans, but I bet few people have closely studied the subtleties of water. I am talking about making water features that highlight the interaction of tiny waves, the wonders of surface tension, or patterns of eddies that form behind a blockage in a flow. These fountains could be very small scale but also very interesting. I think that a fountain could highlight a single one of these phenomena and be entertaining for years.
Calmness Through Softness
Often times, I have sat in nature and been lost in the moment. There is not common theme between where I lose myself. The beach breeds thoughts of distant lands and underwater kingdoms. A campfire lends itself to simple thoughts of reflection of recent actions. A brook or a stream can soothe the mind and cleanse the spirit. The location makes no difference. Replace the sand of the beach for the concrete of a pool in quiet backyard. Substitute the smell of burning cedar for the faceless propane of a fireplace in the den. Shift yourself from the water gently gliding over sticks and leaves and stones, to water trickling down a ceramic pagoda to an artificial koi pond in a Japanese garden in the middle of city ark. All of these places can steal conscious thoughts and replace them with an eerily calm emptiness that sets the mind into motion. Place means little in the ways of causing people to lose themselves into the moment to slip into a conscious or unconscious meditation state. Instead, it is what is seen and what is heard, not where one is.
I think that the way to entertain people through calming them with water is based on the shapes that the water is in. If people are present around water that holds soft shapes, and gentle curves, that causes the most inner peace, even if it is just temporary. I feel that people, when exposed to gentle and soothing surroundings; they will echo that inside of them. This is the same theory that applies to sensory deprivation tubs. When people lie inside of them, with just the gentle, soft rocking and waving of the water, they feel that inside. When a person looks at a small waterfall and notices the gentle parabolic waves (although they may not be totally aware of what they are looking at), they feel the same. When they notice large, soft, arching water bells from a fountain, they are relaxed. People do not get this same feeling from say, the roughness of a water slide at the amusement park or the turbulence on a raging river. It is the smooth lines that people can barely make out from a soft spring rain that results in relaxation.
Along the same lines, soft sounds will help to relax people as well. If we wish to have people sit alongside one of our fountains to relax or meditate, it would be much easier to put people into that state with the babbling of a brook or the gentle splashing of a fountain designed to cut down on splash that will help set people at ease. It is because of this that the raw power of Niagara Falls, or the annoying and erratic dripping of a showerhead that keep people awake and or make them feel alive.
is for these reasons that I think the fountains we design, if we are trying to
help people relax and mesmerize them, or if we are trying to provide something
that they can stare at for hours on end and just think, need to based upon
softness. Soft curves, soft lines, soft
sounds. Sure, we could entertain them for a few minutes with the flashy show of
a jumping water fountain or an intermittent water jet show, but to keep them
really entertained, both with the water feature, and with themselves, softness
and gentleness are what is needed.
I want this fountain to be a place of beauty and calm. Too much of school is running around between ugly building and stressing out about class and homework. Something like this fountain might help put a smile on some faces throughout a normal day. If it does this it will have been a success in my eyes. I don't want some ugly monstrosity. That would defeat the purpose, as people would most likely be impressed or scornful as they passed the water feature. Subtle beauty is what I'm aiming for.
Even though I love both water and fire, I have never been able to just sit and contemplate either. To me they're more of a background setting for something else. For example, there's not much I love more than sitting in front of a fireplace, with a fire going, and reading a good book. Yes, I can read a good book anywhere, but the fire makes it special. This applies in that we can go to school and take any path to and from buildings, but a fountain would make that walk just a little bit extra.
Water is fascinating but, having a very short attention span, something constant and continuous like a water feature could not keep me entranced for hours. It is, however, a wonderful setting. Particularly soothing is the tinkle of water falling a short distance, such as the sounds made by a bamboo ladder, or a small waterfall or spray. Not loud enough to make casual conversation difficult, but loud enough to be heard and enjoyed.
Subtle beauty is the key. The beauty is there, but you only see the intricacies if you look closely. Sound is there, but quietly, to please the subconscious. This leaves room for exploration and inquisitive minds, while still providing beauty for casual glances. That is my favorite type of beauty, something that has depth, but doesn't baffle someone who can't, or won't, look beyond the surface.
The Inward Music
The nature of water in motion is musical. What ties the lowliest brook and the Fountains at Bellagio together are the rhythms, the tempos, the melodies and the harmonies that an observer senses as both are watched. Both cases deserve attention for drastically different reasons, however.
The idea of a brook is not a very clear one - brooks can very greatly in their complexity - but we can consider a brook to be a natural feature of water movement. The idea that it is natural means that it was not created specifically for someone's pleasure, but pleasure can still be derived from it. The repetitive pattern of the water hitting rocks in the middle of the stream set down the bass line for the singing sound of the rushing currents. Sometimes animals such as birds are drawn to the stream and add a harmony of their own. By far however, the most important part of the piece is the song created in the observer's head. This is where the true melody is formed, but it would remain undefined without the presence of the other parts.
On the other hand, the Fountains at Bellagio define much of the symphony for the observer. In this case, the water is explicit in setting out the rhythms and the leading parts and accompaniments for the observer. At this point, the observer is not involved in the piece, but the difference is that the Bellagio fountains use their canvas to tell stories. It is up to the observer to place himself within the piece and interpret what is being said. This is akin to a subtle opera being staged by the water itself.
While I feel that both scenarios achieve the same goal through their different means, I prefer the idea of the dynamical feature from both the designer and observer point of view. As the designer, I want to be able to explicitly suggest the story myself. The dynamical features give me the ability to add intricacy and depth to the music on a level of scale that aren't possible with more "natural" features. And in observance, the contemplative nature of the interaction between dynamical features would be the most interesting part of any water feature design. Therefore, I have my own particular bias towards the dynamical features. However, a water feature is about feeling the music presented to you by the feature and filling in the gaps for you, and that is what we should aim for.
Intellectual or Natural Relaxation?
There are two major designs being considered for our water feature design. Each design approaches the goal of aesthetic value from a different point of view. The goal is the same. Each fountain has the purpose of making the viewer stop and reflect, even if only for a moment. And in this reflection come relaxation, a sort of meditation, and comfort. The following is a brief description of the effects that each of the fountains has and how they differ from each other based on the effects they produce. The end result is a choice between intellectual and natural relaxation effects.
The garden water feature is probably one of the most common types of water fountains. The meditative effects from this style of fountain come from the natural sounds of interaction between the streams, waterfalls, and ponds. The fountain is very natural in appearance and in operation so it coerces the viewer to reflect on their most basic emotions. This reflection can best be described as a meditative state. It is a form of daydreaming, I suppose, in which we tend to focus on the water so intently that all thoughts seem to disappear. It clears the mind and relaxes the body. The benefits of such a fountain can be useful in or around an academic building where the stresses of classes, research, or learning cause our minds to become cluttered with thoughts and emotions.
The dynamical water feature has its aesthetic value in its ability to awe the viewer. This awe is derived from a feeling of curiosity mixed with intrigue. The interaction of water jets, sprays, and sheets that are not naturally occurring features leads the mind to wonder what engineering creates that effect. This gives the fountain an educational aesthetic that can have the same mesmerizing affect as a waterfall in a pond. The natural curiosity of people will draw them to look at the fountain and figure out how it works. This can further be enhanced by designing the fountain with all of the parts, valves, pumps, etc. showing. In being able to see everything that is happening, the viewer actually learns something during the process. There is still a mind clearing effect to the fountain because the viewer stops to think about what is happening, though not to the same extent as with the garden feature. The best description for this effect would be "educational enlightenment." This effect is very befitting of a university building and is amplified by the strong engineering background of Clarkson. That would make this fountain design a better choice for its aesthetic value.
Water has very meditative qualities. From rain falling onto a canvas tent or aluminum roofing, to ocean waves rolling into a beach, the sounds of water has the power to sooth and relax. It has the ability to create a tranquil atmosphere where a person can just unwind. Everybody has experience this at least once in his or her lives.
One experience in my own life to which I can relate, takes place very close in a large stream in Allen Falls. When the dam upstream is opened, there is a spot where you can sit and have a waterfall flow right over you. I remember just sitting there with a few friends and being mesmerized by this simple water feature. What was it that gave this situation the ability to leave one in an "aesthetic" mind set? In this instance, it was a combination of many different affects. The main feature was the ability for me to interact with the waterfalls. Not only that, I was part of the water feature. By placing a let or an arm out, I suddenly was able to create different water qualities. The ability to interact with the water, could entertain someone for hours. Besides the interactive aspect of the waterfalls that I was in, however, there were other mesmerizing values to it. I sat there for around an hour, just watching and observing and relaxing. What was it about the water that allowed me to enjoy this trace-like state for such a long period of time? Maybe it was the sounds of the water landing on the rocks below and running off of the ledge above me. Maybe it was the feel of the cool mist spraying us as we sat underneath everything. Maybe it was watching as the water fell before us, constantly changing paths. I would watch as individual drops would fall in front of us, and never would they land in the exact same spot. Maybe it was the taste and smell of the water in humid air from the mist of the water. It was a combination of all of these. This water feature had appealed to every one of my senses.
In building a water feature that was intended for indoor viewers, it would be difficult to all five senses. However, by paying special attention to the senses that we do have to appeal to the viewer. In order to construct a feature that would be able to entertain for along period, it would need to appeal to the three available senses, hearing, seeing and touching. Sound is a very important aspect to a successful water feature and therefore, should be highly considered during the design stages. A soothing trickling can relax anybody into a meditating state of mind. Sight is the other major sense to which the water feature can appeal. This is why our group has incorporated many colored lights and laminar jets, as well as several "aesthetic" features into our design. Finally, the viewer should be able to interact with the feature on some level. Whether running his hands through a set of waterfalls or water bell, allowing him, to 'get his hands wet," in some laminar jet, we will allow the viewer the ability to become part of the feature.
As a member of the Outdoor Monumental water feature group, we would like to design and construct a fountain that would serve as a monument for the 9/11 tragedy and remind us that the lives that were lost in the disaster. We would also like to create a place where people can sit, watch the moving water and contemplate their thoughts.
As an outdoor enthusiast, I like to "get in tough" with nature when I want to clear my mind or contemplate some deep thoughts. Usually, I'll go hiking and find a quiet place near moving water or on top of a mountain to sit and meditate.
The most memorable experience I can describe occurred during my freshman orientation trip with the Outing Club. Over a period of four days, we climbed several high peaks in the
Adirondack region. The second day into the trip, I was being shown how out of shape I was as I started to lag behind most of the group. A bunch of the guys on the trip decided to drop their packs and hike up a side peak before they conquered Mt. Marcy, the highest point in New York State. Another kid and myself decided to skip this optional hike and get a head start on the real challenge. During the climb upward, I was ale to get about 20 minutes ahead of him by the time
I reached the summit. It was a gorgeous day and not a cloud in the sky. As I sat down at the top, I realized that I was all alone, which was quite unusual on such a nice day. The peak is usually crowded with dozens of hiking wanting to get a tremendous view. Even the mountain stewards, who are stationed at the top of several of the peaks, including Marcy, were not around due to a meeting that day. I was truly alone. The view from the top was indescribable. It makes you realize how insignificant you really are in the world. You can see forever in every direction as you battle against the wind to stand up straight. As you look out, you can see bald eagles struggling for progress, as they fly below eye level. I had a lot on my mind that day, starting college, leaving friends behind, and I was able to meditate for quite some time before the rest of the group showed up. It is an experience that I will never forget and it is the type of atmosphere that a fountain might be able to provide.
Although I don't think that a monumental fountain will be able to provide this exact type of environment, it will provide a place to sit and think in a different way. Moving water has the ability to capture one' mind, just like the view I experience at the top of Mt. Marcy. One could watch the water moving in our fountain for hours and let their mind wander as they sit in a state of contentment. We also hope that our outdoor fountain would be a way to remember the tragedy that occurred at the World Trade Center buildings last year.
The water feature provides several visual and acoustic stimulations. The waterfall is a feature that allows for the observer to not only see it, but it has a distinct sound as well. The rivers provide for the soothing sound of a babbling brook. An observer is therefore able to experience the feature without having to look at. This allows for the water feature to be effective without having to see it. Thus, the feature can accomplish its goal of providing tranquility while people are paying attention to their work or social gatherings.
Visually, the feature transports the onlooker to a place away from academia. The waterfall and rivers allow onlookers to feel isolated from the world around them. For some, this feeling adds to the sense of peacefulness to the feature. The waterfall serves to draw people in, not only with the sound, but with the visual as well. The river also offers itself to help in the soothing of the soul. Personally, I could sit for hours and watch leaves tumble through waves and eddies and other currents found in a river.
The aesthetic features of a Fengshui fountain
The two fountains that really capture my attention are the Fengshui fountain I have at home, and a display fountain in one of the malls at home. The Fengshui fountain I have at home is very similar to the one I have in mind to design. It is a medium-sized fountain that reaches up to half the height of a room, and has a rock base. The water flow is just a simple water feature of water rushing down from the top of the rocks, crashing down to the bottom with a light splash depicting a waterfall. The water fountain at the mall is a very sophisticated water feature whereby jets of water fly by and land in total precision. This fountain is circular in shape, and an example of how it works is this: one jet of water, originating at the center of the fountain would shoot to end of the fountain in an arch and land precisely into the hole of this end. At the crux of its performance, there could be as many as 20 jets of water shooting over one another, but never colliding in a picture of precise grace. I have often stood at this fountain for 10-15 minutes on end just staring at it. Likewise, this has entertained many shoppers and tourists and I have seen many tourists taking a video of it with their video camera.
The fountain I have chosen to design would have the theme of a Fengshui fountain. I have always been deeply intrigued by the Fengshui fountain, which attempts to capture the elements of the Chinese art of geomancy dealing with the influences of good and evil spirits believed to attend the natural features of landscape. To achieve the elements of a true Fengshui fountain, my fountain has to encompass most, if not all of these features: soft lighting to illuminate the flow of water splashing onto rocks, a relaxing, continuous flow of water, and intricate water flow that not only exudes a certain relaxing charm, but also intrigues a person looking at it. I envision it to put me in a meditative, comfortable state by its natural flow of water, splashing softly onto the rocks beneath, a whole picture of calm and peace. Also, soft lighting is crucial and it has to focus appropriately on the rocks and water to illuminate the grace of the fountain.
The combination of enjoyable exterior stimuli with a relaxed physical state can produce not only enhanced mental relaxation, but also physical effects. This weekend, I was at my family's house on Bradley Brook Reservoir in Eaton and I had the opportunity to spend a great deal of time near the water. Over the years, I have grown accustomed to spending up to a half an hour at times just looking out across the lake from the docks. Unfortunately, since the peacefulness gained by enjoying the view has become so much of an automatic response, it was difficult at first to identify specifically the physiological effects of such an experience. As a result, I decided to undertake a personal experiment to contrast two cases of water flow, interrupted flow and steady flow.
In an effort to compare and contrast two water 'flow systems," I spent some time on the dock listening and watching the waves interact with the shoreline and I also walked to the spillway and watched the sheet of water that constantly flows down it. From the docks, I felt that the visual scene contributed more towards producing the state of relaxation than the auditory environment. In fact, I found the sound of the waves to be distracting, which I attributed to the interaction of the docks and the waves approaching at a diagonal direction. The result of the dock interrupting the flow of the waves was an irregular non-rhythmic slapping of the waves on the shoreline rocks. In contrast, when I sat on the edge of the concrete wall of the spillway the auditory experience produced additional physiological effects. Since water was constantly flowing down the spillway in a thin sheet, there was a consistent and regular sound produced, much like that produced by the water bells in class. In addition to obtaining the mental and physical relaxation that I found on the dock, I found that, after sitting there motionless on the concrete for a few minutes, my back, particularly around the spine, was in a state that I can only describe as auditory massage. Although it is difficult to put such a state of relaxation into words, it is important to note that in both situations, at the dock and on the spillway, this state of relaxation was produced by fixed external stimuli. The relatively static image of the lake as well as the consistent and regular flow of the water down the spillway was most effective in promoting relaxation.
Water is an embodiment of the mind. It can be tranquil or raging, furious, calm, soothing, sporadic, extraneous. Any emotion can be reflected or caused by water. Since ancient times the sound of waves has been attributed a measure of tranquility - the seashore has been a place of relaxation. A fountain should be what the sea is: calming, full of wonder, dynamic. It should calm the soul and enlighten the mind. It should provide inspiration and beauty. The art of a fountain should not be noticed, but felt, an unconscious awakening of the soul. The process should not get in the way of the effect. It should provide wonder and awaken thought.
It does not take a specific type of fountain to attain these lofty characteristics. Any one will do. Just so long as it can be seen, heard, felt, and yet not understood. For through a contemplative state of meditation lies the true path to solace and wonder. For some, the mere presence of still water may be enough to elicit this response. Others may require something more to achieve true wonderment, a complex aggregate of colliding laminar flows perhaps.
Thus, a fountain should be artistic in form and dynamic in nature. It should be simple in design, yet hold infinite layers of complexity to provide fuel for human wonder. A fountain should be the creation of the designer’s heart as well as his mind.
With our new fountain, the waterfall off of the roof of the ERC, people will be attracted to the school and to the ERC to see the wonder of our creation. There are not many water features of this nature so it will bring in people to just view the waterfall and enjoy its beauty. On top of the visual effect of the waterfall, it will also have a sort of therapeutic sound as well. People can sit outside of the ERC when it is nice out and do their work while listening to the relaxing sound of the falling water. It will be a larger scale version of the therapeutic fountains that are sold in the stores that are kept in people's houses. The sound of constant water falling and hitting rocks or falling down a bamboo ladder is an extremely relaxing sound. We just have to be careful that we do not have too much water flowing off of the roof so that the noise gets a bit loud and bothersome. With a reasonable amount of water flowing off of the roof, it should in fact be an extremely relaxing sound to listen to as you do your work outside of the ERC. We would also put some fish in a second pool so that we can add to the entertainment factor for our water feature. People will not only look at the wondrous waterfall, they will also watch the fish swim around in the pool.
Reflections on a Water Fountain
Jun Ji Zhang
What is the purpose of our water feature? There is so much pressure in today’s times to make sure that an object has a meaning, to make sure that it serves a purpose, it is a sad fact that one simply can’t enjoy something simply for the joy of enjoying it. But that is in itself a purpose I suppose. In today’s times, it is all the more important to be able to just stop and smell the roses so the saying goes. That is the purpose of our water feature. My original purpose for the garden spring was to make a nice simple place for one to sit and relax. That was it. Nothing more, nothing less. The spring was not to dazzle someone with fluid mechanical phenomenon, that was the role of the monumental fountain, or to impress someone with clever timings of jets and sprays, that was the role of the indoor dynamics fountain, the spring was simply a nice quite place to rest and think.
What I had wanted to create was a place of escape. A place for someone to just get away from it all, be it stress from exams or homework, frustration over friendships or relationships, or simply just for somewhere to go. I wanted a place where I could go, sit down, and not have to worry about who one person is with or what I need to do to prepare for an exam the next day, I wanted a place where I could just sit and think about anything I want, whether it be about the things I don’t want to think about or just reflect on what is going on in my life. What I see is a nice waterfall, full of life and sound and chaos, and yet at the same time, quiet and serene. What I also see is a number of slow streams, along the lines of babbling brooks with a few bridges that ends in a few small ponds. The waterfall is more of a place to stand and think. The streams are instead, a place to walk along, to follow the water to wherever it may flow and provides an environment to walk and talk, even if you are simply taking the long way to classes or something.
That’s all I wanted, a simple quiet and relaxing place to walk along, to sit along, or to just look upon. Nothing fancy, nothing amazing, just peace and quiet. And in today times, a little peace can go a long ways.
Lilting notes fall
From bamboo instruments.
Babbling water flows
From here to there.
A roaring tiger
Leaping through the air
In graceful arcs.
Cool mist rises
To tickle sensitive skin;
Raising bumps on arms
And hair on neck.
A sweet softness caresses
Fingertips, leaving a
The bite of autumn
Teases nostrils into flaring
To catch the scent of
- or maybe, instead,
The rich aroma of
A hot summer is soothed
By the smell of wet.
The warm tang of spring
Tantalizes taste buds,
The hint of thunderstorms
And the acrid tang
By a lighting flash.
Pale blue water
Reflects the sky
Of the same shade.
I do not see the white foam,
I am taken back
Into memories of happy times.
All my senses are aroused,
Nerves afire, but calmed,
By the presence
Of my water feature.
A Walk through Nature
As I walk around I see nature
Enveloping me in its glory
I look up and see the sky
I wonder how
How did it get so peaceful and serene?
I look at the trees beside me
Their branches swaying and leaves fluttering
The birds are drawn to its beauty
Settling themselves in it
Calling it "home"
The pond in front of me
Calls me to look at its magnificence
"Look at my swirling waters
Admire my creatures beneath the lilies and murk"
I am mesmerized by its complexity
As I walk further I see a weeping willow tree
So sad and droopy
I can almost feel its melancholy
I want to hear its story, its tale of misery
And help it become alert again
As I stroll along, I hear a noise
Not a loud sound, but a peaceful calling
I come upon a stream, a clear blue running of water
Stones and twigs line the brook, as if to protect it from the wilderness
While the clear liquid continues its daily routine of flowing
All too soon I have ended my journey
I have come to the end of my trail
But the nature around me has not
It will stand the test of time
The Story of Me
I start off as a trickle, gently from the top of the world,
Making hardly any noise;
But as I grow and learn,
And think and flow into the world,
I become louder, bolder, eager to venture out into the Universe,
Form what they call streams, rivers, rivulets and waterfalls,
And eventually turn into the very essences of life.
At times I move gently, shhhhhhhhshhhhhhhh,
A mere whisper of the sound of eternity,
Other times I seem terrifying, uprooting trees and homes, birds and beasts,
I can build or destroy, sustain or kill; integrate or disintegrate,
Some worship me for this; others make use, while others still deplore me,
And yet all need me, yet all I need is to know every part of me,
To reach out through my arms and limbs and reach the ocean, which is I.
I reflect life and death, Nature and the Universe;
Many try to understand me and fail,
I too try to understand and fail.
All I yearn is travel far and wide,
Touch the sky, fly as snow and rain, hail and wind,
To finally reach me.
And so at the seashore I extend my arms to reach back,
To the land where I was born.
So powerful and yet powerless,
In constant search of myself for all eternity...
The Seven Senses of Mother Nature
Four tiny elementals dance upon a rock
Playing tag and Simon says
As they continue their game the rock becomes....
Fairies with mist for hair and a droplet for a body
Dance and intertwine, pulsing
Creating the ebb and flow
The crash of tiny bodies against
The rock creates a loud symphony -
A mesmerizing chant offered to Mother Nature
The fairies smirk as the pace quickens
They wear smooth the surface
Upon which they trod
They laugh as the moon tries to keep up
Watch the droplets leap and Chant
Fire a much different sort of elemental
Begins its slow ceremonial
With a sharp flash, a tiny flicker
Then appears the drummer
Crack snap crack click
The hunger begins as the babies grow
The dance - hard fast engulfing all
Cleansing purifying -
Giving the surface over to
The Mother's last warm embrace
The adults tire and fall into slumber
Knowing they will again dance their glorious dance
Air spirits fly high above
They weave patterns in the sky
Gliding over the surface and
Rolling across rock
Wearing it thin and smooth
The wind creaks and howls
Inviting the others to play
They smile as the others join in
Ready to continue their game.
The Earth pixies camouflage themselves
Against the rock, they blend in
They watch and wait as the others
Play - they join in
The earth trembles and shakes
With a roar they jump in
Sing sweetly they all combine
C'etait la vie de l'elements
Pour vous le petite choses chant et dance
La mere adore tout le monde
La Vie belle
Viva le Reine
Thousand Word Picture
Words escape the hand and the mind
Fleeing from a tranquility of stillness.
What letters could write thought down?
How do you spell a sensation?
What chance does fleeting speech have
Against the sea of serenity?
The whitecaps crash on the heart;
Tide of tranquility it tries to break.
But like the beach it cannot be broken,
The torrent of water, the regularity of the flow,
Mimics the beating of the heart
And adds to the restfulness.
The moment is frozen in time,
The mind is encased in a bubble impenetrable
Floating on air. Life slows to a point.
There is only a feeling of solitude,
A feeling of being water, sky and moon
And being nothing, no one, nonexistent
As life slows to a point;
Life, so turbulent, laminar now
And a picture could not capture the moment.
A word could not capture the moment.
I cannot capture the moment.
Here I Find Freedom
Lyrics & music
I walk away down to the stream
I'm just frustrated, blowing off steam
I could watch the water dancing all day
It says "jump in, I'll take you away"
Here I find freedom
Here nothing is expected of me
Here I find happiness, peacefulness, bliss
No one but me can ever exist
You say you're sorry for all that you said
I don't respond, you lower your head
What you don't know I'm not really there
The babbling water has taken me somewhere
I can find freedom
Here nothing is expected of me
Here I find happiness, peacefulness, bliss
No one but me can ever exist
Repeat and fade
Here I find freedom
Here nothing is expected of me
Here I find happiness, peacefulness, bliss
No one but me can ever exist
Here I Find Freedom Brian Schwerdt
The principle conclusion is that there are important purposes for the design of water fountains and water features. Such devices are not necessarily of practical importance in the sense of engineered products designed to improve our abilities to do various tasks associated with life in modern society. Fountains are a link between practical artifacts and intellectual pursuits that are afforded to many of us by modern conveniences. In other words, many of us, particularly in the U. S., have the leisure time necessary to admire and to advance cultural artifacts that provide thoughtful contemplation that goes beyond the necessities for mere survival. It may very well be that those of us, who are afforded this luxury to think and to do creative work, may lead relatively long and content lives. Hence, if we are provided the opportunities to create, it is our duty and responsibility to advance the state of our knowledge and our fine art.
The youthful thoughts of the authors of the essays, poems and music are important because they are the thoughts of people with whom the responsibilities and duties associated with the leisure to advance and create reside. Reflecting on the thoughts they have expressed at the outset of their efforts to grow within our society allows us to reflect on the plans we make or have already made for our future activities. Life's work is a process of activities that lead to incremental accomplishments as we grow. It is the effort of process and not, necessarily, any reward that is key to achieving success. This is particularly true when we judge ourselves. It is personal satisfaction that is most important. Friendly competition among peers is good! Particularly when it comes to creative and intellectual pursuits. There is an element of friendly competition revealed in the essays, poems and music. The communication of ideas and procedures within the rules of friendly competition can help to advance self-knowledge effectively. This kind of competition leads to furthering societal knowledge and, hence, must continue.
With the thoughts expressed on the purpose of art and engineering of water fountains, eight groups of students developed eight water fountain designs. The designs ranged from consideration of the needs of Fengshui design, to the requirements for monumental designs of waterfalls off of buildings, to the designs of dynamical water features for indoor spaces, to the design of water gardens, to the designs of sculpture with water in motion that include a model of the World Trade Center and a model of a small dog. The latter object was actually built to demonstrate the application of fluid dynamical phenomena as a medium for sculpture. A picture of this water feature is provided in the Appendix along with a discussion of some of the dynamical features of water in motion that are of interest and are of practical importance to the fluids engineer.
Phenomena of fluid motion in water fountains
The fluid mechanical phenomena associated with water fountains are of practical importance in a number of mechanical systems and production operations in industry. The examples discussed in this appendix are the water bell, the water jet and the ultrasonic mister. All authors had the opportunity to observe qualitatively each of these flows. These features are illustrated in Figure 1. Three of the authors, Sarah Allen, Gary Bowlin and Laura Smith, created this water feature as an example of using water to create sculpture; it is an abstraction of Laura Smith’s pet dog. In the figure, from left to
Figure 1. Water sculpture illustrates use of water bells, water sheets and a water jet.
right, is a water jet (representing the tail of the dog), a water bell (the body of the dog), a water sheet (one of the two ears of the dog) and another water bell (the head of the dog). A submerged ultrasonic mister is used to create the mist that can be seen primarily inside the center water bell and in the left side of the photograph. The shape of the water bell on the right is particularly clear. The water bell is a thin sheet of water that emanates from a circular-annulus nozzle. There is air inside and outside the bell. One question of interest to the fluid mechanic is: Can the shape be predicted from first principles of Newtonian mechanics? G. I. Taylor  published a paper on this problem in which he described such a theory. He found a relatively simple solution of the equations that describe the shape of an axially symmetric sheet of water for cases where the effect of gravity is negligible. The shapes predicted were compared with photographs of water bells he produced in his laboratory. The shapes compared remarkably well. How can we apply the theory to the water-bell problem of interest to us?
According to G. I. Taylor , the shape of an axially symmetric, thin-sheet water bell is described by the following formulas:
df/ds = [ cos f - a + (b sin f)/u ] / ( y – u ) , (1)
u2 = 1 + 2 b x, (2)
a = (r uo Q p)/(8pT2), b = (r Q g)/(4 p uo T).
The parameters in the formulas are defined as follows: The angle of the tangent to the surface of the thin sheet with respect to the x coordinate axis is f. The x coordinate axis is in the vertical direction from the nozzle; it is the axial coordinate. It is in the same direction as gravity, g = 9.81 m/s2. The volume flow rate of water from the annular nozzle is Q in m3/s. The density of water is r =1000 kg/m3. The surface tension T = 0.073 N/m for the air-water interfaces. The y coordinate is the radial coordinate perpendicular to the x-axis; it corresponds to the radial location of the center of the thin sheet of the water bell. The parameter s is the distance measured from the exit of the nozzle in the direction along the sheet. The change in s is related to the change in the x and y coordinates of the water bell as follows:
dx = ds sin f, dy = ds cos f. (3)
All distance coordinates, i.e., x, y, and s, are dimensionless ratios of actual distances divided by the characteristic dimension R = (r Q uo)/(4 p T). The parameter p is the pressure difference across the surface of the bell between the air inside and outside of the bell. The velocity u is the speed of the water inside the water sheet that makes up the bell; it is in the s direction. The parameter uo is the initial speed at the exit of the nozzle at the origin of the water bell at (x,y) = (0,0). Hence, finite values of a correspond to cases with imposed pressure differences across the bell. Finite values of b correspond to cases with gravitational effects are taken into account. Taylor  examined cases where a = b = 0. For the bells in the water sculpture of Figure 1, a = 0 but b is finite. It is the latter class of bells that is of interest herein.
An alternative approach, as compared with the analytical approach applied by Taylor, is applied to solve this system of equations. A relatively simple finite-difference, computational-approximation method is applied. A computer code was written to implement the method in the m-file language of MatLab . Comparisons of computer predictions with the theoretical results reported by Taylor were made to check the computer tool. The comparisons were in excellent agreement. Subsequently, the tool was applied to investigate the effect of gravity on the shape of the bell. The predictions compare reasonably well with the observed water bells. The computational method is described next. Subsequently, examples are discussed.
We approximate the first term in Equation (1) by the following finite-difference form:
df/ds = ph(n+1) – ph(n) / ds,
where f = ph(n+1) at s = s(n+1), and f = ph(n) at s = s(n), and ds = s(n+1) – s(n). This is an approximation of the change in slope, f, between two locations along the sheet, viz., s = s(n) and s = s(n+1). The write hand side of Equation (1) is evaluated at s = s(n). The value of n=1 corresponds to the initial location of s = 0 at x = y = 0. All data are assumed known at s = s(n). From this information the data at s = s(n+1) are computed. The increment ds is selected sufficiently small to get a reasonably good solution. The changes in x and y are computed by similar difference approximations of Equation (3). The m-file procedure is given in detail in Table 1. The table is for the case for b = 2, ds = 0.001, fo = ph(1) = 90 degrees (which implies a horizontal discharge from the annular nozzle) and uo = 1. Executing this example in MatLab leads to the result in Figure 2. The bell shape is consistent with the observations (remember that the x direction is in the vertically downward direction and that the y direction is in the horizontal-radial direction).
The effect of gravity is illustrated in Figure 3. The cases shown are for ph(1) = arcos(0.2) over a range of b = beta values. The b = 0 case corresponds to the cases considered by Taylor, i.e., the case of zero gravity. Finite values of beta illustrate the fact that the water bell is elongated in the direction of gravity. This is consistent with visual comparisons between the photographic data presented by Taylor  and the bells in Figure 1.
Figure 4 illustrates the effect of discharge angle on the water bell for the beta = 2 case considered above. For the case with ph(1) = acos(-0.2), the annular sheet moves upward somewhat before gravity dominates and forces the sheet towards the positive x direction. The central bell in Figure 1 has a slight upward angle at the discharge of the annular nozzle. The shape of the bell supports this observation.
Next, let us consider an actual example. Let us estimate the size of the qualitative features of the water bell in the right hand side of Figure 1. The pump size is a 200-gallon per hour (nominal size) garden-feature pump. Hence, Q = 200 cm3/s. For the properties of water given above, beta = 2, where uo = 1 m/s was used to calculate this parameter. The distance in (x,y) are ratios of the actual distance divided by the characteristic distance R = (r Q uo)/ 4 p T), as defined by Taylor . In the present case R = 22 cm. The shape of this water bell is illustrated in Figure 2. The maximum radius of the bell is approximately 0.5R at a distance of approximately 0.6R below the nozzle discharge. Thus, the actual distances are (xR, yR) = (13 cm, 11 cm). This is the correct order of magnitude of the actual size in Figure 1. Hence, the theory describes the shape of the bells observed reasonably well. In addition, since Taylor already showed that, when the effect of gravity is unimportant, the theory worked quite well in predicting the shape of the bell. Hence, it is not unexpected that it works for the water bells observed in the present investigation. More detailed and precise application of the theory is left to the interested reader. This concludes our technical discussion on the shape of the water bell.
The next problem to be addressed is the shape of a columnar jet of water leaving a well-designed nozzle at a prescribed angle and a specified speed. This problem is equivalent to the problem of determining the trajectory of a projectile (i.e., the "ballistics" problem). Note that the shape of the jet used to model the dog's tail in Figure 1 is somewhat parabolic in shape. The distortions are most likely due to the jagged edge of the opening of the plastic discharge tube. There are other fountains that
TABLE 1. The water bell m-file
% Specified constants:
alpha = 0.0;
beta = 1.0;
% Selection of step size for numerical integration of ODE
% (integration is in the stream-wise direction tangent to
% the sheet):
ds = 0.001;
% Initial conditions at x = 0.
x(1) = 0.0;
y(1) = 0.0;
ph(1) = acos(0.0);
% Approximate solution:
for n = 1:1:2000
u = sqrt(1.0 + 2.0 * beta * x(n));
co = cos(ph(n));
ap = - alpha * y(n);
bb = beta * sin(ph(n)) / u;
dn = y(n) - u;
ph(n+1) = ph(n) + ds * (co + ap + bb)/dn;
x(n+1) = x(n) + ds * cos(ph(n+1));
y(n+1) = y(n) + ds * sin(ph(n+1));
Figure 2. The shape of a thin water bell discharged in the horizontal (y) direction
subject to surface tension and gravity (acting in the x direction) effects.
Figure 3. Illustration of the effects of gravity on the shape of a water bell.
Figure 4. Illustration of the effect of discharge angle on the shape of a water
bell. Solid line is for ph(1) = acos(-0.4). Dashed line is for ph(1) = acos(0.0).
Dashed-dotted line is for ph(1) = acos(0.4).
were examined by various groups of authors that use columnar jets. Thus, in this part of the discussion of technical issues an analysis of a columnar "laminar" jet is discussed.
Although somewhat idealized, the analysis is instructive. There are two main purposes for presenting this discussion. The first is to illustrate how easy it is to obtain solutions to the simultaneous differential equations that can be used to model the trajectory problem. They are evaluated by the same type of computational method used to solve for the shape of the water bell described above. The second purpose is to illustrate the shape of the water jet with and without air resistance included in the analysis.
The following equations for the horizontal and vertical components of the acceleration describe the motion of the water within a columnar jet of water:
du/dt = -k sqrt(u2+v2) u, and dv/dt = - g - k sqrt(u2+v2) v, (4)
u = dx/dt, and v = dy/dt. (5)
The coordinates of the trajectory (i.e., the coordinates that describe the shape of the jet) are (x,y). Equations (4) and (5) are solved by a similar method as we used to solve for the shape of the water bell. The details of the method of solution are fully illustrated in Table 2.
Table 2. MatLab m-file tool for water jet trajectory analysis
% "The Water jet trajectory problem"
% Numerical computation of the trajectory of a water jet
% discharged at an angle theta with an outflow speed of Vs.
% They are:
% theta = discharge angle in degrees.
% Vs = discharge speed.
% Equations of motion:
% Note that u = dx/dt. v = dy/dt. Note that gravity, g, is in the -y
% direction. The location of the nozzle is x = y = 0. The air
% resistance at the outside surface of the jet is specified
% by the resistance coefficient k. It is assumed to be a constant.
% The air resistance is assumed to be proportional to the speed of
% the jet squared. It is assumed to act in the opposite direction of
% the direction of motion of the water in the jet.
% The components of acceleration are thus:
% du/dt = - k sqrt(u^2 + v^2) * u.
% dv/dt = - g - k sqrt(u^2 + v^2) * v.
% INPUT DATA
% Specified constants:
k = 0.0;
g = 9.81;
dt = 0.0001;
% Prescribed initial condition:
% theta = 40.;
% vs = 100.;
theta = input(' Angle of the nozzle: ')
the = theta * pi/180.;
Vs = input(' Discharge speed: ')
u(1) = Vs * cos(the);
v(1) = Vs * sin(the);
% Location of the nozzle exit:
x(1) = 0.;
y(1) = 0.;
% Approximate solution of the water-jet trajectory:
u(n+1) = u(n) - dt * (k * sqrt(u(n)^2+v(n)^2) * u(n));
v(n+1) = v(n) - dt * (k * sqrt(u(n)^2+v(n)^2) * v(n) + g);
x(n+1) = x(n) + u(n) * dt;
y(n+1) = y(n) + v(n) * dt;
if y(n+1) < 0
slope = (y(n+1) - y(n))/(x(n+1) - x(n));
b = y(n) - slope * x(n);
xhit = - b/slope;
fprintf(' The location the jet hits the ground = %5.1f \n', xhit)
if y(n+1) < 0; break; end
% Graphical presentation of the results:
if y(n+1) > 0
Two examples were computed and are compared in Figure 5. The jet is launched at an angle of 45 degrees with an exit speed of 1 m/s. The two cases are without friction (k = 0) and with friction (k = 0.5). Friction is air resistance. The frictionless trajectory is parabolic as expected. The effect of friction is to foreshorten the trajectory a bit. Further computations are left as an exercise for the interested reader. The method described in Table 2 provides an example of a tool that is useful to compute and draw columnar jets when contemplating the design of water features.
Figure 5. Illustration of a water-jet trajectory with nozzle angle of 45
degrees and discharge speed of one meter per second.
Finally, a comment and citations of technical literature are provided next to help those interested in developing an understanding of the fog or mist created by the "Ultrasonic Mister" illustrated in Figure 1. The phenomenon that produces the jet of water that breaks up into a mist when the jet encounters the air is know as acoustic streaming. It is a phenomenon described by Lighthill . For an appropriately selected frequency of sound (or ultrasound) the jet breaks up into a mist. A relatively sophisticated version of the fogger was designed by Bar-Cohen . For further details on this and related phenomena the reader may wish to consult recent reviews by Riley  and by Glezer and Amitay . The more recent papers are cited to provide an entrance into the technical literature on acoustic streaming. They are also cited to introduce the reader to the Annual Review of Fluid Mechanics. This series of publications are particularly useful for those of us who are interested in research, in technical insight and in technical analysis.
 Escher, M. C., et al (1989): Escher on Escher: Exploring the Infinite, Harry N. Abrams Publisher.
 Stevens, Wallace (1972): The Palm at the End of the Mind: Selected Poems and a Play, edited by Holly Stevens, Vintage Books.
 Van Dyke, Milton (1982): An Album of fluid motion by, Parabolic Press.
 Taylor, G. I. (1959): The dynamics of thin sheets of fluid I. Water bells, Proc. Roy. Soc., A, vol. CCLIII, pp. 289-95.
 Etter, D., et al (2002): Introduction to MatLab 6, Prentice Hall.
 Lighthill, J. (1978): Acoustic streaming, Journal of Sound and Vibration, vol. 61, pp. 391-418.
 Bar-Cohen, Y. (2002): Ultrasonically Induced Fountains and Fogs, NASA TECH BRIEF (excerpted from the JPL New Technology Report NPO-21064), vol. 26, no. 9, pp. i-ii, 1-5.
 Riley, N. (2001): Steady Streaming, Annual Review of Fluid Mechanics, vol. 33, pp. 43-65.
 Glezer, A., and Amitay, M. (2002): Synthetic Jets, Annual Review of Fluid Mechanics, vol. 34, pp. 503-29.