Is there a pressure gradient along the nozzle? Is the exit pressure higher than the entry pressure? Would such a gradient exist in a gravity-fed system?
Nozzle design can consider the Bernoulli equation. Using the Bernoulli equation and having the center of the nozzle the same height as the center of the inlet pipe, the equation simplifies. If the mouth of the nozzle is smaller than the butt of the nozzle, water flows faster out of the nozzle than it did flowing into the nozzle. With that understanding and the Bernoulli equation, a nozzle reduces pressure and increases velocity; or, increases pressure and reduces velocity. Such facts of construction work no matter what supplies the water pressure. Am off to town. JMG.
Let me provide some equations. Consider a symmetrical conical nozzle. Let its diameter that connects to the hose be D. Let its diameter that does not connect to the hose be d. Let V_1 be the velocity of water entering the nozzle and let V_2 be the velocity of water exiting the nozzle. V_2 = ((D/d)^2)V_1 Let P_1 be the pressure entering the nozzle and P_2 be the pressure exiting the nozzle. Let p be the density of the water flowing through the nozzle. P_2 = P_1 + p((V_1)^2)(1 - (D/d)^4) With those pressure and velocity relations one can state the Venturi effect. However, I have previously considered it is impossible for there to be a nozzle such that the ejected water will exceed the height of a column of water providing pressure P_1 to feed the nozzle. If you can find such a nozzle, you can make water flow uphill. Once up a high hill, water can fall and generate power. Such a system generates more power than is necessary to replace water lost to evaporation. Such a system, although not perfect, produces more energy than is put into it. Such a nozzle cannot exist. Oh, the higher one goes, the less water weighs, the higher the column of water to produce the desired P_1. In addition, water density varies with temperature. Any change in density changes the height of a column of water to produce the desired P_1. JMG.
The Greeks have it! Well all you people are being mislead. It can be done and has been done. Raising water up a tube /PVC pipe to a height higher than the source using air pressure had been done by the Greeks some 1700 years ago. Look up Heron of Alexandria and you will find this has all been done. email me if would like a graphic of the process. michael.mulvey@roadrunner.com
Thanks Water guy, but the original post specified "gravity fed fountain". We know that you can raise water higher than the source if you use a pump driven by another source of energy.
