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'[OT] Homebrew fountain help'
2006\02\28@225430 by

I'd like to make some fountains for my home, and I'm wondering
if anyone has any input.

In particular, I'm wondering about an equation describing the
behavior of a stream of water emerging from a hole in a
reservoir.  Google search terms are proving elusive.  It seems to
me that the equation should be pretty simple, based on depth
of water and size of hole.  The result should be a half-parabola.

Anyone have any ideas?

Mike H.

'[OT] Homebrew fountain help'
2006\03\01@051550 by

Hi Mike,
I'm non sure if this may be useful for your question
(however, many methods for water measurements are explained)

http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/

regards
Marco

---------- Initial Header -----------

>From      : piclist-bouncesmit.edu
To          : "Microcontroller discussion list - Public." piclistmit.edu
Cc          :
Date      : Tue, 28 Feb 2006 21:54:29 -0600
Subject : [OT] Homebrew fountain help

{Quote hidden}

> --
I'm affraid you must talk with an experimented gardener instead of
searching for formulas, but it is your choice. The clue looks to me in
dimension right the pump debit and the water loss by infiltration and
evaporation.

success,
Vasile

On 3/1/06, Mike Hord <mike.hordgmail.com> wrote:
{Quote hidden}

> -
Mike Hord wrote:

> I'd like to make some fountains for my home, and I'm wondering if anyone
> has any input.
>
> In particular, I'm wondering about an equation describing the behavior
> of a stream of water emerging from a hole in a reservoir.  Google search
> terms are proving elusive.  It seems to me that the equation should be
> pretty simple, based on depth of water and size of hole.  The result
> should be a half-parabola.

It seems to me that you have a pressure (the depth of water above the hole)
and a resistance (basically a function of the diameter of the hole, I
assume). That would determine the speed at the hole. The rest is
(simplified) vector arithmetic with gravity: The speed component at the
hole will remain constant (approximately), and the speed component caused
by gravity will increase according to the known formula.

Not sure where you'd find the resistance of a hole (or a short pipe). I
have a handbook here with some diagrams (for longer pipes, which could
possibly be extrapolated), but that won't help you much :)  But probably
someone else can give you a tip -- or this helps you already to google for
something.

Gerhard

Mike Hord wrote:
> In particular, I'm wondering about an equation describing the
> behavior of a stream of water emerging from a hole in a
> reservoir.  Google search terms are proving elusive.  It seems to
> me that the equation should be pretty simple, based on depth
> of water and size of hole.  The result should be a half-parabola.

Once you have the velocity of the water as it leaves the hole, plain old
highschool physics will give you the parabola.  The speed of the water would
be a function of the pressure and probably the diameter at small diameters.
I don't know how to compute that, but a few simple experiments should be
able to provide the answer relatively quickly.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
AHHHHHH!  Fluid dynamics!  Run away!  Run away!

I suspect you will have some difficulty finding simple equations to
describe this.  Scientists are interested in much more rigorous
models, and fountain designers would rather set up a set of
experiments and gather empirical data.

I've always wanted to make a laminar flow fountain.  It looks like a
glass rod in a parabola:
www.wetdesign.com/elements/laminar/index.html
http://www.wetdesign.com has a bunch of other interesting ideas for
fountains and fountain heads.  They have a lot of patents as well, so
it's worthwhile looking through those.  Chances are if you call them
with your question they may give you some help.  The patent has
expired, patent number  4,795,092.  It may be that the later patents
on control machanisms have also run out.

It's going to be awhile before I move that project off the back burner...

-Adam

On 2/28/06, Mike Hord <mike.hordgmail.com> wrote:
{Quote hidden}

> -
Again, I'll collapse many replies into one:

On 3/1/06, Marco Genovesi <marco.genovesilibero.it> wrote:
>
> Hi Mike,
> I'm non sure if this may be useful for your question
> (however, many methods for water measurements are explained)
>
> http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/

Yes, actually, it was VERY helpful.  Apparently, water escaping
from a hole in a reservoir under a given head h will travel with
velocity equal to an object dropped from height h.  Hole size is
NOT a parameter!

Olin pointed out:
> Once you have the velocity of the water as it leaves the hole, plain old
> highschool physics will give you the parabola.  The speed of the water would
> be a function of the pressure and probably the diameter at small diameters.

It seems not.  I will experiment, some, but I don't know if it's worth it.
A brief experiment last night suggests that any head height above maybe 1/2"
starts to require a very large basin indeed to catch the water.

Adam suggested a website:
http://www.wetdesign.com

Which seems pretty good.  I'll check it out for further info.

Thanks for everyone that responded.  Now I'll impart a little bit of
info to those
reading this topic with bated breath:  using an ultrasonic mister with flat
tonic water yields a mist that glows under a blacklight (or so I've heard).

Mike H.

At 07:46 AM 3/1/2006 -0500, you wrote:
>Mike Hord wrote:
> > In particular, I'm wondering about an equation describing the
> > behavior of a stream of water emerging from a hole in a
> > reservoir.  Google search terms are proving elusive.  It seems to
> > me that the equation should be pretty simple, based on depth
> > of water and size of hole.  The result should be a half-parabola.
>
>Once you have the velocity of the water as it leaves the hole, plain old
>highschool physics will give you the parabola.  The speed of the water would
>be a function of the pressure and probably the diameter at small diameters.
>I don't know how to compute that, but a few simple experiments should be
>able to provide the answer relatively quickly.

There's a square-root law between the pressure across an orifice and
the flow rate. Since it's subsonic, Bernoulli's equation for incompressible
flow will probably be close enough (in reality the flow will be a somewhat less
for real fluids such as water by 10-40%, and there are tables published
for correction).

The maximum height an ideal fluid jet goes to is calculated here from
Bernoulli's equation:
highered.mcgraw-hill.com/sites/dl/free/0072454261/132215/cen54261_ch12_web.pdf
In particular, see page 17.

>Best regards,

Spehro Pefhany --"it's the network..."            "The Journey is the reward"
speffinterlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

Mike Hord wrote:
> Olin pointed out:
>> Once you have the velocity of the water as it leaves the hole, plain
>> old highschool physics will give you the parabola.  The speed of the
>> water would be a function of the pressure and probably the diameter at
>> small diameters.
>
> It seems not.  I will experiment, some, but I don't know if it's worth
> it. A brief experiment last night suggests that any head height above
> maybe 1/2" starts to require a very large basin indeed to catch the
> water.

I don't understand how that point relates to what I said.  What part of it
are you saying seems to be incorrect?

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
Pookie was reading this thread over my shoulder and she thinks she has the
answer.  When we play the game of throwing the ball on the house and she
catches it,  she seems to know just how far from the house the ball is going
to land..  And now she tells her secret.

She learned that the higher on the roof the ball lands and starts it roll,
the faster it is going when it hits the gutter cover and comes straight off
the roof.  So she thinks you could simulate the water falling a distance
than converting that down speed to a across speed by rolling a marble down a
ramp from the height of the water column, rolling across a small part of the
table to get it to go horizontal, and look at it's path.

But then, Pookie is just a dog.

Bill
with Pookie's insight

{Original Message removed}
Mike Hord wrote:

> Apparently, water escaping from a hole in a reservoir under a given head
> h will travel with velocity equal to an object dropped from height h.
> Hole size is NOT a parameter!

Only as long as all the premises of the Bernoulli equation are valid. When
you get to small holes, the hole size (that is, the flow resistance) does
become a parameter. Think of it this way: in macro physics, there are
usually no discontinuities. With a hole size of 0, the flow speed is 0. So
as you approach hole size 0, the flow speed approaches 0, too.

Gerhard

On Tue, 28 Feb 2006, Mike Hord wrote:

> I'd like to make some fountains for my home, and I'm wondering
> if anyone has any input.
>
> In particular, I'm wondering about an equation describing the
> behavior of a stream of water emerging from a hole in a
> reservoir.  Google search terms are proving elusive.  It seems to
> me that the equation should be pretty simple, based on depth
> of water and size of hole.  The result should be a half-parabola.
>
> Anyone have any ideas?

It depends a lot on the discharge speed. At low speed you get a piece of
a parabola, at higher speeds the air brakes the water seriously and you
get something else. Also look up vena contracta and the Bernoulli
equation, and Reynolds numbers. If the diameter at the vena contracta is
too low wrt. the speed of the flow you get pulverisation instead of a
jet. This can be fixed by using a proper nozzle which produces the vena
contracta under control (of the nozzle walls). The Reynolds number
predicts the type of behavior (based on speed, density and the
dimensions of the jet). The short version of this is, that there is no
such thing as a long range, low volume jet. At least not with normal
liquids (like water).

Peter

On Wed, 1 Mar 2006, Mike Hord wrote:

> Thanks for everyone that responded.  Now I'll impart a little bit of
> info to those reading this topic with bated breath:  using an
> ultrasonic mister with flat tonic water yields a mist that glows under
> a blacklight (or so I've heard).

I would suggest an experiment with a plastic spray bottle before
commiting to this. Getting mist is much harder than getting an
unbroken jet, and that is harder than getting a broken up
jet.

Peter
> >> Once you have the velocity of the water as it leaves the hole, plain
> >> old highschool physics will give you the parabola.  The speed of the
> >> water would be a function of the pressure and probably the diameter at
> >> small diameters.
> >
> > It seems not.  I will experiment, some, but I don't know if it's worth
> > it. A brief experiment last night suggests that any head height above
> > maybe 1/2" starts to require a very large basin indeed to catch the
> > water.
>
> I don't understand how that point relates to what I said.  What part of it
> are you saying seems to be incorrect?

Only that hole size is unrelated to the stream path, which is
counterintuitive.

Mike H.

Mike Hord wrote:
>>>> Once you have the velocity of the water as it leaves the hole,
>>>> plain old highschool physics will give you the parabola.  The
>>>> speed of the water would be a function of the pressure and
>>>> probably the diameter at small diameters.
>>>
>>> It seems not. ...
>>
>> What part of it are you saying seems to be incorrect?
>
> Only that hole size is unrelated to the stream path, which is
> counterintuitive.

You should read what I wrote.  I didn't say the water speed (which
eventually affects the path, but speed is the real question here) was
unrelated to hole size.  I believe the hole diameter is largely irrelevant
when large, and the speed is a function of pressure then.  But at small hole
sizes some effects that can be ignored at large hole sizes start to become
significant.  Look at cappillary action as an example.  For small holes
where surface tension is significant over the area of the hole, there will
be a certain minimum pressue just to cause any flow.  You can easily verify
this yourself with a drinking straw.  Put an end into water, then lift it
above the water.  Some water will remain stuck at the end of narrow straws
completely blocking the straw.  This doesn't work on larger diameter straws.
There are also edge effects of viscous friction.  Small diameters have a
larger portion of the area that is subject to these edge effects, making
them important for small diameters but ignorable for large ones.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

> Once you have the velocity of the water as it leaves the hole, plain
> old highschool physics will give you the parabola.

I don't think you GET the velocity.  Hydrodynamics probably gives
you speed, but since direction is determined by non-rigid fluids
pushing non-rigid fluids in randomish directions as it exits the
orifice, you don't know the exact direction that your stream (or
even parts of your stream) is traveling, and (as noted) the impact
point varies a lot.  Producing one of those Disney-style hopping
water pulse things is apparently a lot harder than you'd think,
sorta like the difference between flashlight beams and laser beams.

BillW

On Wed, 1 Mar 2006, Mike Hord wrote:

>> I don't understand how that point relates to what I said.  What part of it
>> are you saying seems to be incorrect?
>
> Only that hole size is unrelated to the stream path, which is
> counterintuitive.

The hole size is *very* related to the stream path. If you read my
previous posting then you should know that a small hole with high
pressure (=head height) will yield a fast stream that will break up and
be strongly braked by air, thus not rising to the expected height.

Peter
Peter wrote regarding 'Re: [OT] Homebrew fountain help' on Thu, Mar 02 at 13:31:
> The hole size is *very* related to the stream path. If you read my
> previous posting then you should know that a small hole with high
> pressure (=head height) will yield a fast stream that will break up and
> be strongly braked by air, thus not rising to the expected height.

So, how does one maintain a coherent, relatively small stream?  I'm
specifically thinking about those water "sculpture" things that you
see at theme parks and other outdoor venues, where there are various
combinations of synchronized streams of water at various times.  Do
they rifle the nozzle to keep the stream together, or it entirely
based on matching the pressure to the orifice size?  Maybe something
to do with the length of the orifice?

--Danny, wondering why they didn't cover useful things like this in
his "fluids" physics course :)
I saw something on television once about this..
Apparently they packed the nozzle with a bunch of
drinking straws, or something very similar, to help
the water remain cohesive for longer squirts.

This was for a wider stream, perhaps 3-5 inches across.

This was just the last step in a more complex
preparation, I'm sure.

Of course, everything you see on TV must be true!

> {Original Message removed}
On 3/3/06, Danny Sauer <piclistdannysauer.com> wrote:

> So, how does one maintain a coherent, relatively small stream?  I'm
> specifically thinking about those water "sculpture" things that you
> see at theme parks and other outdoor venues, where there are various
> combinations of synchronized streams of water at various times.  Do
> they rifle the nozzle to keep the stream together, or it entirely
> based on matching the pressure to the orifice size?  Maybe something
> to do with the length of the orifice?

Apparently (at least on some of the fountain type devices I have
looked out) keeping air out of the stream seems to greatly help in
holding it together. To this aim I have seen devices that rather than
pump directly out the spout pump into a surge tank (or something like
it) and then have the outlet to the spout come under the 'air' line. I
presume this would also lessen the variations in pressure that could
contribute to the stream breaking up. At least the jets I was looking
at seemed to all have nice smooth nozzles..

Antony.

I remember something along the lines of having to remove static from
the watrer flow also. If it is allowed to charge the water , then the
like charges cause the water stream to break up quicker. Placing a
mesh near the exit point to dissipate the charge can help.

RP

On 03/03/06, Antony Wuth <foobiegmail.com> wrote:
{Quote hidden}

> -
> > Only that hole size is unrelated to the stream path, which is
> > counterintuitive.
>
> The hole size is *very* related to the stream path. If you read my
> previous posting then you should know that a small hole with high
> pressure (=head height) will yield a fast stream that will break up and
> be strongly braked by air, thus not rising to the expected height.

But we aren't talking about rising to anything, merely the distance
a stream of water emerging from a hole in a reservoir will attain.
That, as Olin rightly pointed out, is largely defined by velocity,
or at least, the ideal (maximum) distance is.  And, as the document
the first respondent posted points out, velocity of a stream of water
leaving a reservoir is related to head height, but not hole size.

Of course, in this real-world, non-ideal system, the water is going
to slow down as it moves through the air and so the further it is
allowed to fall, the less the final shape will resemble the predicted
parabola, until the stream is eventually falling in a straight line.

Which makes me wonder:  could I use charged rods or plates to
cause the stream to bend?  THAT would be interesting.

Mike H.

Mike Hord wrote:
> Which makes me wonder:  could I use charged rods or plates to
> cause the stream to bend?  THAT would be interesting.

Yes you can.  But if you figure out the voltages required you'll see that
would be a rather dangerous fountain to be near.  Hmm, tens of thousands of
volts, water splashing around, open for access to people.  I think UL
certification is rather a long shot.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
On 3/2/06, Olin Lathrop <olin_piclistembedinc.com> wrote:
> Mike Hord wrote:
> > Which makes me wonder:  could I use charged rods or plates to
> > cause the stream to bend?  THAT would be interesting.
>
> Yes you can.  But if you figure out the voltages required you'll see that
> would be a rather dangerous fountain to be near.  Hmm, tens of thousands of
> volts, water splashing around, open for access to people.  I think UL
> certification is rather a long shot.

And knowing my friends, it'd be a bad thing to have in my home.

Perhaps I could enclose the whole thing in some kind of protective case.
Or maybe I could just scrap it as being more trouble than it's worth.

Mike H.

On Thu, 2 Mar 2006, Danny Sauer wrote:

> So, how does one maintain a coherent, relatively small stream?  I'm
> specifically thinking about those water "sculpture" things that you
> see at theme parks and other outdoor venues, where there are various
> combinations of synchronized streams of water at various times.  Do
> they rifle the nozzle to keep the stream together, or it entirely
> based on matching the pressure to the orifice size?  Maybe something
> to do with the length of the orifice?

Nozzles where the shape and consistency of the jet is very important
(like those used for turbines) use a variable geometry nozzle together
with variable discharge (valve) to set up the jet. Some firefighting
gear also uses such principles. The variable nozzle is normally of the
needle type (there is a needle shaped plunger inside the profiled hole -
think giant size needle valve).

Since the jet depends on a lot of variables it is probably best to make
some experiments by fitting a number of straight nozzles to a garden
hose fitted with a manometer and see the 'real life' figures that can be
obtained. Discharge can be metered by timing the filling of a bucket. Or
get one of the 'needle valve' type plastic nozzles on sale in the
gardening department and experiment. The reason this is not taught in
high school physics is likely the fact that the relevant math is too
deep.

Hydraulics texts cover nozzle design (but not free-flying jets). For a
free flying jet of liquid the Reynolds number for the jet shape in air
(i.e. its airspeed) and the turbulence of both air and jet determine
where the jet breaks up.

This is an interesting paper:

http://www.wjta.org/Book%201/1_4a_Sterling_and_Abbott.pdf

Note to what lengths they go to insulate the nozzle from vibration. Also
NO rifling is used. The nozzle must be very smooth.

Peter

> I saw something on television once about this..
> Apparently they packed the nozzle with a bunch of
> drinking straws, or something very similar, to help
> the water remain cohesive for longer squirts.
>
> This was for a wider stream, perhaps 3-5 inches across.
>
> This was just the last step in a more complex
> preparation, I'm sure.
>
> Of course, everything you see on TV must be true!

Absolutely. If filmed from the same angle with the same lights and under
the same conditions, it might even be repeatable... ;-)

Peter
> I saw something on television once about this..
> Apparently they packed the nozzle with a bunch of
> drinking straws, or something very similar, to help
> the water remain cohesive for longer squirts.

Well, they do essentially that for wind tunnels, where the wind source
is coming from a ~ 2ft tube, and its all acoustically isolated, but
anyhow.. the straws *do* work to "straighten" out the flow..

> This was just the last step in a more complex
> preparation, I'm sure.

Yep.. I forgot what some of the other things they did were.

--
andrew

On 3/2/06, Danny Sauer <piclistdannysauer.com> wrote:
> So, how does one maintain a coherent, relatively small stream?  I'm
> specifically thinking about those water "sculpture" things that you
> see at theme parks and other outdoor venues, where there are various
> combinations of synchronized streams of water at various times.  Do
> they rifle the nozzle to keep the stream together, or it entirely
> based on matching the pressure to the orifice size?  Maybe something
> to do with the length of the orifice?

These fountain nozzles cause the water to go into laminar flow -
similar to what happens in an ideal wind tunnel (ie, no turbulence).
You'll occasionally see laminar flow out of a faucet - when it hits
the sink or water there is little or no splashing and it's very quiet,
sometimes causing standing waves in the water surface.

The person who figured out how to do that on demand, under pressure,
and through large distances went on to the company Wet Design.
They're the people that did the moderately famous fountain in front of
the Belagio: http://www.wetdesign.com/elements/laminar/index.html

The patent has expired, patent number  4,795,092.
http://www.freepatentsonline.com/4795092.html
(free login required)

Take a short length of pipe, say 6" diameter, 9" long.  Cut enough 3"
straws to fill the middle third of the pipe.  Put screen material in
front and behind the straws and afix to the inside of the pipe.

On the outlet of the pipe, afix a stiff plastic pane with a hole in
the center.  The hole should be the desired size of the water jet
(1/2" for instance) and should be beveled so that the sharp edge
(smaller side) is toward the interior of the pipe, and the larger side
facing outward.  It's this knife edge that forms the actual stream,
and any imperfections in it will show on the stream.

The inlet of the water is on the bottom third of the pipe, on the side
of the pipe, pointing in tangentially such that the water swirls
around the pipe in a circular fashion before going through the straws.
The bottom of the pipe is simply capped off.

The patent shows all of this. Figuring out the right volume/pressure
of the water to get a good stream is not indicated.

The next tricky part is starting and stopping the stream so you end up
with the "glass rod" look rather than a turbulent start and dribbling
stop.  Their method uses another strem of water or compressed air in a
fan spray just above the outlet of the fountain.  When this spray is
on, it knocks the fountain stream to a diverter back into a drain.
When this spray is off, the fountain exits normally.  This high
pressure spray can be readily and quickly switched on and off.  This
is easily heard at these exhibits.

There are some parts the patent describes which I did not include
(some extra packing material, a nozzle guard, etc) so refer to the
patent, but this is the basic idea.

Some individuals seem to have found success at homebrewing it:
www.hiddenmickeys.org/Imagineering/LeapFrog.html
Alas, no pictures.  I didn't understand his description until I viewed
the patent, perhaps you'll have the same experience with my
description.

If I ever get around to building one, I'll be putting up instructions
and pictures...

-Adam

On Tue, 7 Mar 2006, M. Adam Davis wrote:

> Some individuals seem to have found success at homebrewing it:
> www.hiddenmickeys.org/Imagineering/LeapFrog.html
> Alas, no pictures.  I didn't understand his description until I viewed
> the patent, perhaps you'll have the same experience with my
> description.
>
> If I ever get around to building one, I'll be putting up instructions
> and pictures...

I am willing to bet a small sum of money that you will have good luck
with a plastic garden faucet (handheld 'gun' type with variable nozzle
of the needle valve kind). Just take a good look at a cutaway view of a
Pelton turbine jet and shape the plastic implement to be as similar in
proportions as possible.

Peter
It would surprise me greatly if someone could obtain turbulence free
(laminar flow) water jets from such an arrangement.  If I get around
to it, I'll try it out.

-Adam

On 3/8/06, Peter <plpactcom.co.il> wrote:
> I am willing to bet a small sum of money that you will have good luck
> with a plastic garden faucet (handheld 'gun' type with variable nozzle
> of the needle valve kind). Just take a good look at a cutaway view of a
> Pelton turbine jet and shape the plastic implement to be as similar in
> proportions as possible.

Ok, I finally found some more material references wrt nozzle geometry
wrt. jet length:

http://engr.smu.edu/rcam/research/waterjet/Par4.html

This seems to indicate that going beyond 200 jet diameters is not
good, and 100 jet diameters is safe (for the jet shape).

For 100:1 these figures result (roughly) (the equivalent Re is 1000 in
air for the 3 mm nozzle and deteriorates fast with increasing speeds):

nozzle  jet l.  jet speed        pump        pressure
dia.    mm      m/sec                l/min        bar (less nozzle loss)
--------------------------------------------------------------
3      300     2.4             4.0     0.03
6      600     3.4            22.0     0.06
12      1200    4.8           130.3     0.09

The low speeds indicate that even a small wind will interfere with
operation.

Peter

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