The path of most resistance

[Mike Buckley]

Thanks to the path of most resistance, the least amount of water is flowing over the high point of the waterfall. A detail from Skogafoss in Iceland.

Captured with a shutter speed of 1/1250. Notice that individual droplets of water located immediately at the top are stopped in their action. Yet the further the water gets from the top, the more the drops are combined. If the image showed water even closer to the bottom it would appear in sheets of water. That's not to say that the action isn't stopped, as I think it is. So, I don't understand the physics of falling water enough to explain why the draped sheets of water only appear further away from the top of the falls. Anyone?

C&C encouraged, as always.

[Bobobird]

THAT is what a waterfall looks like. I was beginning to think that all waterfall shots were silky and harmless.

[glenng]

Bobobird I totally agree with you it gives the feeling of the power of the water love it.

[Coinneachmhor]

Yet again a stunning image Mike - the drama and power you have portrayed is immense. Personally I love the graduation of the water as it falls.

[darknight]

lovely image mike, seems to covey great power.
and as for the water droplets, think of a running/dripping tap, each droplet as it falls accelerates away from the the top and away, so each new drop is actually slower than the one accelerating away, now friction does tend to slow them after a while, so in a waterfall causes them to crash together and merge, so creating a larger slower force

[ajohnw]

It probably something to do with gravity, waters resistance to flow and air resistance. All things fall at 9.8m / sec ^2 so after I sec they travel at 9.8m/sec, at 2 sec 19.6m/sec (44mph). Or some feature in the rock wall the water is falling over. As per this one which bugs me as I could see shape in all of the water before I calibrated my monitor. Be interested to know how others see it. Now there is scarcely any shape where the water hits a rock by the wall. The dark areas are still as intended.



-

[darknight]

hmm, ok, not strictly true, all objects fall at the same, the speed of gravity on earth which is 9.81 m/s^2. hence an elephant will fall at the same rate as a bowling ball but not velocity. newtons 2nd law.
an aerodynamic object will reach the ground quicker than the bowling ball because of the least resistance to the friction. the air friction is the key, if you used the above in a vacuum allowing equal resistance then the aerodynamic object and bowling ball will fall at the same rate

[ajohnw]

hmm, ok, not strictly true, all objects fall at the same, the speed of gravity on earth which is 9.81 m/s^2. hence an elephant will fall at the same rate as a bowling ball but not velocity. newtons 2nd law.
an aerodynamic object will reach the ground quicker than the bowling ball because of the least resistance to the friction. the air friction is the key, if you used the above in a vacuum allowing equal resistance then the aerodynamic object and bowling ball will fall at the same rate

That's what I was implying but suspect that waters resistance to flow resistance has a strong effect as well.

-

[MrB]

Most of the effect you see in a photo of a simple waterfall, like the one in Post #1 (where the water just falls over the edge and drops through the air), is probably due to motion blur rather than the drops combining as they fall.

As others have explained, the effect of gravity is to accelerate the drops. The further they fall the faster they go, until they reach their "terminal velocity" - a constant speed at which the forces of gravity (speeding them up) and air resistance (slowing them down) are balanced, by which point they will be spread out, as Mark has described, but they will not crash together.

An example:- Somewhere near the top, a drop might be falling at 5 feet/second, so during your shutter time of 1/1250s, it will travel 1/250 of a foot - almost negligible movement in your photo. Lower down a drop might have reached 50 ft/s, so during the shutter time it will travel 1/25 of a foot - almost half an inch, which would make a white streak in your photo. And so on - those white streaks will appear longer further down the fall. It is those white streaks of all the countless falling drops merging in your photo that create the appearance of a sheet of water.

The effect is more complicated in a waterfall such as the one shown in Post #6, because some of the water drops onto rocks on the way down. This sends droplets in all directions which do then collide with other drops, compounding the effect of the motion blur.

Philip

[Mike Buckley]

Thanks to everyone for both the kudos and the explanations!

If I understand everyone correctly, it seems that my original premise that I was using a fast enough shutter speed to stop the action all the way down a waterfall is actually incorrect. Right? If that's so how fast does the shutter speed have to be to stop the water all of the way down? (Not that I dislike the sheets of water. I'm just trying to get a handle on this.)

The reason I ask is that the image shown below is shot at 1/2000. I did that because I thought that would stop the action all the way down and wanted to see what that would look like. As you can see, there are still the sheets of water and they begin to appear reasonably near the top of the waterfall. (Sorry for posting this image a second time in as many days, but I want to make viewing it convenient for you.)

[dubaiphil]

Well when anything is falling under the influence of gravity, it accelerates to a terminal velocity which may be as great as 9.81m/sec. This depends on the object's resistance through the air, and the air pressure itself.

Now if a falling object is liquid, then its structure and shape will change as it accelerates and is subjected to air resistance. So your little round droplets at the top will elongate nearer the bottom as they pick up speed.

So even if the droplets weren't hit by other droplets on the way down and you had a fast enough shutter speed, the droplets would look different depending on how far they had fallen.

I think!

[Mike Buckley]

Now if a falling object is liquid, then its structure and shape will change as it accelerates and is subjected to air resistance. So your little round droplets at the top will elongate nearer the bottom as they pick up speed.

If the air resistance is exactly the same throughout the length of the waterfall, there would be no sheets because all water droplets would fall at the same increasing rate of speed. Correct? If so, is it reasonable to conclude that the sheets of water are caused by different air resistance encountered on the way down that cause the various droplets of water to accelerate at different rates of speed?

As all of you can surely tell by now, I'm not a scientist.

[GrahamH]

Bear in mind the droplet size is NOT constant. Initially the water is single body and as there is less energy in movement in any direction, surface tension easily keeps it together as a single body. As it passes over the edge of the falls the acceleration increases, more energy and more space to spread out means that there is an increased tendency towards droplet formation.
As velocity increases, there is more buffeting by the surrounding air and the large drops have a tendency to break apart. henec, the lower down the waterfall, the smaller the droplet size. Air movement can more easily move these droplets around and hance form sheets of DROPLETS. The droplets have relatively little tendency to form together as surface tension tends to keep the droplets discrete. So, there is SOME growth, but a greater tendency to breaking apart.
Check out a cloud. They are white due to the number of small droplets. As the cloud stops growing, the small droplets tend to collide and grow (very little energy between them so less tendency to break apart again). Larger droplets means a darker cloud.

Botto of waterfall tnds to be lighter than the top, demonstrating a smaller droplet size.
Graham

[Mike Buckley]

Very helpful, Graham. I didn't realize that the droplet size changes throughout its travel to the bottom of the waterfall. Others had explained that using different words that didn't penetrate my pea-size brain.

[FrankMi]

If I am following the logic, the water is more in the size and shape of distinct water drops as it starts to fall and break into smaller and smaller drops as they accellerate through the air to become very much like the mist we see at the bottom of a tall waterfall.

If this is correct, then a higher shutter speed isn't going to make the mist-sized dropplets near the bottom of the falls look any more distinct.

[MrB]

I find it difficult to accept that drops of water break apart as they fall. The highest water fall is rain falling from a cloud - by this logic the rain drops would never reach the ground, all we would get at ground level would be fine mist which is obviously not the case.

The misty spray from a high water fall must be due to drops breaking up by collision - either with each other due to air currents or gusts of wind knocking them together, or with the rocky surfaces on the way down, or with the water in the plunge pool when tiny droplets rebound (as photographers try to capture) or air bubbles trapped with each drop burst as they float up to the water surface.

Philip

[FrankMi]

Hi Phillip, I didn't mean to infer that this occured with falling rain but was rather specific to the scenario encountered at a waterfall where the sheer volume of water, air currents and rocks were contributing factors. Sorry if I wasn't clear with my observation.

[MrB]

Nothing to apologise for, Frank - I think we are all trying to get our heads around this phenomenon! I suspect that, in a straight waterfall (i.e. one that drops without hitting rocks on the way), the vast majority of water drops would remain as distinct drops, just like raindrops, all the way down. However, you have probably hinted at an answer to the question in the second part of your Post #15 - even with the correct fast shutter speed to arrest their movement near the bottom of the fall, they wouldn't be visible because of the mist created by those that have broken up for whatever reason.

Cheers.
Philip

[FrankMi]

To clarify my post a bit further, most of the water coming off the top of Mike's waterfall isn't in the form of 'drops' but rather a fairly solid stream, dynamically fluid and an ever-changing shape as it may be.

[ajohnw]

Personally I think the rainbow is down to mist caused by the falling water hitting the water below. As I see it - It starts of with what may loosely be laminar flow and turbulence increases for a variety of reasons. The water is flowing in another type of fluid - air. That and near by rock surfaces, the wind and probably even the Coriolis effect will cause turbulence and turbulence causes more turbulence. The other aspect is that irregularities in the top where there may be laminar flow will cause variations in velocity = more turbulence when they mix and probably in most cases the main cause of it.

I googled "waterfall fluid dynamics" out of curiosity. Some are trying to model it but most point out it's an impossible problem. A mathematician might describe it chaotic. A bit like the weather. A small change can have a major effect.

-