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# Waterfall laminar flow to mist

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## Waterfall laminar flow to mist

(OP)
I was wondering if anyonw knew a formula for the situation when you have free falling water, such as a waterfall to indicate the point where sheet flow becomes droplets?

I know it is a function of flow depth and velocity, but was hoping for some sort of formula to enusre it does not happen.

I am designing a number of free overflow weirs and the landscape architect has requested a "water curtain" effect.

some help would be greatly appreciated.

### RE: Waterfall laminar flow to mist

(OP)
I thought I would reply to my own request rather than re- entering it. Hopefully there is some one who can help me on this issue.

I was thinking it was something to do with Q=VA as the velocity of the water increases with gravity the area has to reduce. But, at what point does the area become small enough that the flow stops being laminar.

Any pointers on an approach to this or where some information might be available would be appreciated.

### RE: Waterfall laminar flow to mist

In my general chem class in high school, this was touched upon.  (I say this not to belittle the subject, but merely to illustrate that this is the extent of my knowledge.)  We were taught that water streams break up mid-air due to electrostatic repulsion, static it picks up from friction in the air.  The static is so much that if pouring gasoline from the correct height, it can ignite.  This was the analogy my professor used.  To test this theory, you may try deionized water vs. tap water and salt water, letting it flow from a through a hole of the same diameter and measuring the distance before droplets form.  Deionized water is a poor electrical conductor.  This may a decent starting point.  Also, I assume this would go into place inside a ventillation chamber and air flows are likely to be turbulent as well.  This would likely disturb the sheeting of water.  Hope it helps.

### RE: Waterfall laminar flow to mist

The lower the Re number for you application the better your water will hold together.  As far as a formula for forming droplets, I have not come across any, but there would have to be some type of analytical numbers out there since I have seen so many waterfalls with sheeting flow that work so well.  My guess is thats its some type of trial and error on the artists part making the water fall and they probably don't share much.

BobPE

### RE: Waterfall laminar flow to mist

You are partially correct.  I have not seen an actual formula, but that's not to say one cannot be developed.  There are three issues to deal with, and any formula would have to inegrate them accordingly.  The first involves the velocity of the water at the point of discharge at the weir structure, the second relates to the total flow if the water and the third involves the distance of free fall of the water relative to the increasing velocity and the corresponding forces acting on the cohesive, or binding, limit of the water as a freefalling body.  For example, misting will occur faster from water discharging from a pipe with a pre-existing velocity than that of a level reservior.

KRS Services
www.krs-services.com

### RE: Waterfall laminar flow to mist

KRServices:

I would disagre, I have seen artistic fountains that have controlled streams of water that launch from pipes in laminar flow that do no mist at all over extremely large distances.

BobPE

### RE: Waterfall laminar flow to mist

Laminar flows from a jetted tube or pipe starts with and ends with the near same velocity and certainly the friction in air is less than in a pipe. Therefore, the flow will remain laminar. However, in a free fall situation, v increases, water gets stretched thin exposing more surface to fricional forces. So you have friction and v increasing; it will go turbulent.

### RE: Waterfall laminar flow to mist

Is it true that d also increases and become very large in free fall which makes the reynolds number large and tending toward turbulent flow?

### RE: Waterfall laminar flow to mist

Overfalls are directly related to the critical depth of the upstream channel. Calculations for the depth, velocities, and overfall lengths are based on the energy equation and the Froude number (not Reynolds--this is an open channel).
The depth at the overfall should by 0.715*Yc (Yc being the critical depth of the channel).  The length from the overfall that the water will flow is approximately computed by the following equation:

L = 4.30*z*(Yc/z)^0.09

(with z being the difference in the ground elevation of the fall. This can be found in any weir or spillway chapter of a book.)

The length calculation should give you the location of the fall's landing.

### RE: Waterfall laminar flow to mist

Bayou:

Everything in fluids that we look at as engineers is related to the Re number, including open channel flow.  The Froude number is a measure how well the fluid is moving through a gravity system.  The critical depth is a measure of where the fluid in gravity flow will go sub or supercritical. I would think you are right in your thinking that having the fluid exit the system in subcritical flow before it travels may be a way to reduce turbulance, but i am not sure. I think the question was how will the flow respond after it flows as a waterfall which is not channel flow.  Re is for gravity and pressure systems so don't be confused, as d = diameter can be substituted for d = depth and can be applied to the free falling water sheet.

BobPE

### RE: Waterfall laminar flow to mist

BobPE,
Like many of these forums, the topic being addressed strays from the original question.  The original inquiry asked about free overflow weirs and a water curtain.  This is an open channel situation. Therefore the Froude number is more fitting within the Energy Equation.

Also, I meant to describe the state of the water passing through critical depth upstream of the weir (about 3*Yc).
That is if it was originally in sub-critical, which is most likely since the question is about landscaping. At the bottom of the fall, of course it is going to have turbulence.

The equation presented would give the distance away from the weir that the water will travel. This will give an approximate location of the location of the water wall from the fall.

### RE: Waterfall laminar flow to mist

I would research fountains and water curtains on http://www.google.com

There I found many interesting sites, such as -

http://www.atlanticfountains.com/architectural.htm
http://www.fountains-direct.co.uk/display.htm

I would contact the manufactures and get info about their items.  You can pump a manufacturer's rep for a lot of good info.

I would consider speaking to the architect about ordering an "off the shelf" unit, especially if I never designed one before or paying  for a special fountain consultant.

It sounds like the architect has great ideas and not enough budget.  I would hate to be the goat if the requested water curtain effect did not occur or unforseen problems occured.  Just understanding the underlying physical laws is not enough.  Engineering is emperics and this is a rather specialized item.

Clifford H Laubstein
FL Certified PE #58662

### RE: Waterfall laminar flow to mist

Why don't you build a physical model and test the results?

Start with a level pool upstream and shallow depth over the weir for best results.  Use plywood or plexiglass for the weir.  Build it a foot wide and to true vertical scale.  Experiment with sharp edged versus broad crested weirs.  Vary the height to determine the effect of fall distance.

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