A general rule of thumb is that water seeks comparable levels. That is why there is no such thing as an infinite siphon or a reverse siphon. So, is it a rule of thumb that a gravity fed fountain will not achieve a height higher than the reservoir that feeds it? JMG.
No, it isn't a rule at all. Make the fountain spicket extremely small in diameter and the reservoir really large (in width and length, low in height). The Venturri effect will easily give the water enough velocity to clear the reservoir.
What's the Venturri effect? Intuitively, I don't think a gravity fed fountain could exceed the height of the reservoir (unless the reservoir is under extra pressure, of course)... Let me do some maths...
Spoilsport, I will look into the Venturri effect. However, water pressure depends on depth, not shape. So, water pressure feeding the nozzle depends on depth of water in the reservoir: more depth, more feed pressure. Temperature of the reservoir water changes the density of the water and that changes the depth the reservoir water has to be to operate the nozzle. Water pressure exiting the nozzle depends on the nozzle design. Some low pressure fire hose nozzles operate at a feed pressure of 50 psi. A reservoir has to be pretty deep to feed 50 psi to that low pressure nozzle. Are you fairly certain a gravity fed fountain can, by the Venturri effect, achieve a height exceeding the height of the reservoir that feeds it? There must be losses in the transfer of water from the nozzle to the reservoir to prevent the system from being impossible by my prior proof that all perpetual motion devices cannot produce more energy than they contain. Surely the edges of the stream of water might marginally evaporate so that the transfer is not 100% and the transfer is not a perpetual motion mechanism. Losses from evaporation would be the fuel of the system that would need to be added to the reservoir to keep the system functioning: the nozzle has an operating feed pressure that will not be met if the reservoir water level is below a particular value. Hmm. I will look into the Venturri effect. Marks Standard Handbook for Mechanical Engineers shows Venturi meters but not "Venturri effect." What text did you find "Venturri effect"? JMG.
Venturri effect is the effect that happens when fluid is pushed through an increasingly smaller pipe. To keep the flux equal on each end the fluid must accelerate as it pass through. In other words, the pipe starts out wide and goes towards an increasingly smaller size until it reaches the nozel. I think it was a high school physics textbook actually, but I could be wrong. I could also be wrong about the name or even the effect could not exist. Who knows, memories get mixed up sometimes. Obviously flux has to be equal on both ends of the pipe when it is full of water and the only way I can think that this would happen is by the effect I described, which is exactly the way I remember it from the textbook. I just found this link too: http://itll.colorado.edu/modules/templates/dsp_body.cfm?action=indphenomenon&phenomenon=118
One last thing. I think I am wrong about this now that I consider it could create a perpetual motion machine, but who knows?
You must have meant Venturi effect. Venturi effect is used to increase velocity and decrease pressure of fluid flow. The height of the reservoir has to be higher than the height of the nozzle to have any flow at all. How low of a height are you forecasting will work with a Venturi nozzle to achieve circular fluid flow by a gravity fed fountain that feeds the reservoir powering the fountain? JMG.
I guess you hadn't read my new comments yet, but it occurred to me that the it would allow a circular flow, which is clearly impossible.
Water hammer devices allow for pumping water up stream but there are losses of water which prevents the water hammer device from being a perpetual motion device. A fountain squirts water upstream but not likely higher than is necessary to provide constant operating pressure for the fountain. There are nozzles that adjust to variable pressure to maintain a stream of water at various input pressures. Hmmm, I still doubt the potential for a venturi effect to allow water to flow out of a basin's bottom into a basin's top. JMG.
The Venturi effect is why some brass/plastic twist hose nozzles can squirt over a house and others of different designs cannot at the same input water pressure. However, a house is not as high as the column of water to produce the input pressure of county water. Suppose you want to have an input pressure of 50 psi, the column of source water has to be over 90' high. Is there a 50 psi nozzle that can shoot a stream of water 100' high at an angle to refill the column of water? Probably not. JMG.
If a perfect liquid under constant pressure P is forced out an opening of area A, is there a formula for the velocity of the ejected liquid?
There should be, ask Spoilsport. However, if a low pressure 50psi fire hose nozzle can shoot water to a point on a building 116 feet above the height of the nozzle, then the Venturi effect allows circular motion of fluid minus evaporation losses. JMG.
Yeah, I definitely doubt it too, although it would be pretty freaking awesome. I really want to try and expirement with this. Maybe once work slows down I'll find the time mess around with physical items.
The worlds highest gravity fountain does not squirt higher than the source of its feedwater. All of the world's lesser gravity fountains do not squirt higher than the source of their feedwater. Using firehose nozzles as a basis, data does not give answers to prove or disprove my corrollary that a nozzle does not exist which will allow water to fountain into the basin that feeds the fountain. Nozzle design matters: some nozzles reach farther than others with the same psi and gallons per minute (gpm). Data from Elkhart Brass shows some 50psi nozzles that can, at a height of 4 feet and an angle of 32 degrees in still air conditions, reach a point on the ground that is 200 feet from the nozzle. That does not answer the question if the nozzle can shoot a target 116 feet above the nozzle. That angle might have to be steeper than 45 degrees. Wind can stop the system altogether by preventing the water from entering the basin. JMG.
I think a fire hose might be a different case... Do fire hose pumps produce constant flow, constant pressure, or something else?
Usually a fire hose is connected to a fire hydrant. Without a fire hydrant, water is pumped from a reservoir such as a water tank. In the case of a fire hydrant, pressure depends on the number of hoses and the number of hydrants in use at one time. In the case of pumped water from a reservoir, pressure can be constant while supply drops with use. If there is a fire department whose 50psi nozzle can eject water to reach a target 116 feet above the nozzle, then one can make a perpetual motion machine that violates my general rule that no such machine can exist. If there is a 50psi nozzle that can eject water significantly higher than 116 feet, water can be made to flow uphill. JMG.
Nozzles from Elkhart Brass perform based on the water pressure entering the nozzle. To measure that pressure, a gauge is placed between the nozzle and the hose. When I refer to a 50 psi nozzle, I mean a nozzle fed with 50 pounds-per-square-inch water pressure. Some nozzles designed to operate at a higher water pressure will not reach very far at 50 psi. The effective reach, farthest distance water touches ground, depends on water pressure and the flowrate. Pressure and flowrate are directly proportional to effective reach. An increase in pressure increases effective reach. Also, an increase in flowrate increases effective reach. To see the effect of pressure on effective reach, get a paper or plastic jug. Fill it with water. Leave the lid off. Puncture the sides at different heigts. The lowest punctures have the highest effective reach because water pressure increases with depth. This example may be found on the internet as a lesson plan for school children. To see the effect of flowrate and effective reach, buy a cheap spray bottle from a garden supply store. Those multipurpose bottles can either emit a steady stream or a mist. Mist does not go as far as a steady stream. Mist permits less flow than steady stream. A hairstylist might mist a persons hair while another person might use the steady stream setting to squirt a cat off a couch from across the room. JMG
Oh, because mist evaporates, a misting nozzle can put water higher than a reservoir but the mist will not do work unless it is condensed. That is why micro nozzles cannot make perpetual fountains. JMG.
