Wednesday, February 25, 2009

Fountain Basics

This post is a response to Jim.  Jim has several 0.125" diameter hoses that he cut with a clean edge, and supplied with pressure from a garden hose.  His fountains shoot up to their apex, then break up into a gloppy mess, just like mine used to, but for a different reason.

There are three, well, no, six things you need to make a laminar stream work:
  1. Accelerate the water to high speed without producing a lower-speed boundary layer.  After the water exits the nozzle, internal shear will accelerate the boundary layer back up to the speed of the jet, and the shear will then be redistributed through the jet as turbulence, which will then lead to breakup.  I know of two ways to minimize the boundary layer:
    • Large diameter tube ending in a flat plate with a small diameter hole.  This design minimizes the distance over which the water is both at high speed and in contact with the wall.  There will be a boundary layer, but it'll be really thin.  The downside is that you end up with plumbing behind the jet which is really bulky compared to the jet.
    • Form the jet first, then use a circular knife to cut the boundary layer off the main flow before the boundary re-accelerates.  This is how firehose nozzles work.  They take the water stripped off and reintroduce it to the stream with a venturi.  This nozzle is less bulky but needs a bigger pressure drop and is more difficult to make.
    • I found that water beads up on my 316 stainless nozzle more than on my PVC pipe.  It's possible that the 316 doesn't drag on the water quite as much as PVC would have, although I can't confirm that.
  2. Remove all vorticity from the water.
    • The problem is that angular momentum is conserved, and angular momentum is (mass)*(tangential velocity)*(radius).  When you constrict a flow from 6" diameter to 0.5" diameter, the velocity increases by a factor of 12x, which means the centripetal force increases by 12^3 = 1728x (that's right, v^2/r).  If my 6 inch flow starts out at 3 RPM (20 seconds to turn once, barely turning), then the half-inch jet will be rotating at an average of 432 RPM, and the centripetal force at the surface will be 13 m/s^2, which is more than 1 G.  Since 1 G will rip drops of water off the underside of a wet object when the water is much less than a half inch thick, it's no surprise that this rotation will rip apart a half-inch diameter stream.
    • A long, narrow nozzle should take out vorticity through friction with the nozzle walls.  The same friction will lead to lots of turbulence.  I have no idea why this turbulence is not a problem for the firehose nozzle.  I did some experiments with a watering can that we have which features a nozzle about 12" long and 1/3" diameter, and found that the stream would travel about 3 feet before it broke up.
    • If you do the large-diameter, hole-with-flat-plate nozzle, then you have to remove the vorticity some other way.  I did it with layers of twin-wall polycarbonate, cut on a table saw, epoxied into place.  In this YouTube video, they do it with soda straws.  I've read that the minimum length needs to be 12x diameter.  My flow straighteners are 1 foot long, and have channels 7mm across, so the ratio is 43:1.  Probably overkill.
  3. Eliminate even minute variations in your water flow.
    • You'd think a hose bib would give you smooth water flow, but it doesn't.  I know because my fountains shot blobs of water with direct pressure from a hose bib, but worked fine once I put an LC filter between the hose and the fountain.  The YouTube video mentions the same problem in passing, but doesn't say how to fix it.  Directly connecting my pump led to blobs, the LC fixed them too.  (My hose bib has 200 feet of 1/2" copper pipe leading to it, so I'm astonished that any flow variations were getting through.  My best explanation is that the copper pipe is elastic, and the resulting distributed capacitance combined with the pipe inductance is forming a transmission line.)
    • The filter is simple: you have a run of smallish diameter pipe (that's your inductor, 20 feet of 4x your jet diameter should do), and a Tee fitting going to a vertical pipe into which the water can expand momentarily (your capacitor).  My expansion pipe rises higher than my fountain jets, and is open to the air, so that it acts as a pressure regulator as well.  I found that the water from my pump in my 2" PVC pipe would flutter irregularly perhaps 1/4" up and down.  You can also do it with a closed pipe that traps air above it, if you can figure out how to ensure there is air up there.  So long as you don't introduce bubbles into the stream, the closed pipe should work better because it has a smaller column of water between the pressure source (air) and the flow.  That column acts like an inductor which would tend to isolate the capacitor and limit its high-frequency response.
    • If the source of variation is turbulence in the fountain, then you'd want the capacitor close to the fountain, and the inductor between that and the supply (hose).  If the source of variation is the supply, then you'd want the capacitor at the supply, followed by the inductor going to the fountain.  When filtering power into sensitive analog electronics, we use "pi" networks, which are just a capacitor at both ends of an inductor, basically because the noise could be coming from both places and we are hedging our bets.
  4. Get rid of all air bubbles.  Even tiny bubbles cause major flow disruptions.  I have my pumps below grade, so that the water pressure at their intakes should be either above air pressure or very close to it.  This should eliminate air leaks past the O ring on the strainer basket cover, which I think was a source of bubbles in my last pool.  The strainer baskets always seem to have a little air pocket at the top.
  5. Don't go straight up.  I may have screwed this one up.  My jet angle is just 12 degrees off vertical (here are my calculations), so that the jets slow from 19.7 feet/second at the nozzle to 4.1 feet/second at the apex.  The extra flight time and variation in velocity give the flow more opportunity to glob up.
  6. Filter the water.  I may have screwed this one up as well.  I wanted to have low power pumps (700 watts total) push a lot of water (200 gallons/minute), which means very low pressure head (10 feet or 4.3 psi).  No filter that I know how to buy has ports larger than 2 inches, so any standard filter would have a very high pressure drop.  So instead I have 7mm holes in my flow straightener, and .590" holes for my nozzles, and I'm hoping to catch anything even nearly that size in the strainer baskets of the pumps.  I also have the ability to backwash my flow straighteners using filtered water from the main pool pump, which can crank up to 3.5 horsepower if needed.
Okay, so Jim, here's your problem: those presumably short hose segments are making a big boundary layer in your jet, so when it slows down near the apex there is plenty of time and turbulence to glob up.  The problem is worse because the jets are just 1/8" diameter, so the boundary layer may be the entire diameter of the jet.  You need to pick a different, bigger nozzle.  I can recommend the flat plate nozzle, and the YouTube video above shows you how to do it cheaply.  You are also going to need to smooth out the water supply from the hose, and the LC filter described above should do that at low cost.

Good luck, and please let me know how it goes!  If you can, post pictures of the flow at 1/1000 second exposure or faster (full sunlight with any camera will work great).

Other links:
  • Pretty good Google Answer on the subject
  • Badly formatted webpage, no pictures, but same idea here.  They actually worked on chopping the stream on and off.