Does falling water chill due to losing gravitational energy?

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December 24th, 2014 at 6:44:32 AM permalink
Wizard
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While looking at a waterfall in New Zealand somebody said that that water temperature goes down after falling down the waterfall because it loses potential gravitational energy. Is this true?
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December 24th, 2014 at 9:42:36 AM permalink
AZDuffman
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Quote: Wizard
While looking at a waterfall in New Zealand somebody said that that water temperature goes down after falling down the waterfall because it loses potential gravitational energy. Is this true?


A quick google search yielded this.

I would have guessed it would be warmer as the friction from the fall would generate heat to warm it, however I am more of an expert at Irish-engineering than physics.
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December 24th, 2014 at 10:17:07 AM permalink
Pacomartin
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Quote: AZDuffman
I would have guessed it would be warmer as the friction from the fall would generate heat to warm it, however I am more of an expert at Irish-engineering than physics.


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December 24th, 2014 at 10:34:43 AM permalink
Face
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Quote: Wizard

This is rather unrelated, but while looking at a waterfall in New Zealand somebody said that that water temperature goes down after falling down the waterfall because it loses potential gravitational energy. Is this true?


On the surface, the thought seems laughable. Of course, almost all of my thermodynamics studies came in the form of one, long conversation with WoV member Doc, so I'm certainly not an expert. But it seems a simple enough problem.

PGE is a ridiculously simple formula. It's something like mass X height. It's just the energy it took to put something up high. As far as I know, PGE can only "turn into" one thing - kinetic energy. Release the "something" and the potential turns into kinetic and it moves. That's it, as far as I can tell.

Now, if you want to get really specific, yes, thermo comes into play. The water falling of course falls against itself on a molecular level, and it also rips passed the O2, N2, and other molecules that make up our atmosphere. This creates friction, and all friction creates heat, so there would be some level of warming. However, water falling tends to spread, increasing its surface area. And water, what does it do when exposed to air? It evaporates. And the more surface you can expose, the quicker it evaporates.

Evaporation is an endothermic phase change, that is, it requires absorption of heat to make it happen. So just as a draft on your wet arm absorbs heat to evaporate and cools down, so to would air passing over the fall (or the fall passing through air) cause the water to cool as it evaporates.

That's what my self-taught physics says, anyway. The cooling is completely plausible, but it's evaporation that's the cause. I welcome any challenges to my claim =)
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December 24th, 2014 at 10:36:42 AM permalink
Ayecarumba
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Quote: AZDuffman
A quick google search yielded this.

I would have guessed it would be warmer as the friction from the fall would generate heat to warm it, however I am more of an expert at Irish-engineering than physics.


My initial reaction would be the water cooling due to increased evaporation as the water surface spreads over the falls, shedding heat carrying mist. Could it also be that the water decompresses over the falls? Maybe that is a twist on the gravity potential since the pressure of the water is caused by gravity. I seem to recall that the water pressure at the bottom is why the top of a lake will freeze solid before the bottom.

Edit: Slow typing... Short version: What Face said.
December 24th, 2014 at 11:15:17 AM permalink
Face
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Quote: Ayecarumba

My initial reaction would be the water cooling due to increased evaporation as the water surface spreads over the falls, shedding heat carrying mist. Could it also be that the water decompresses over the falls? Maybe that is a twist on the gravity potential since the pressure of the water is caused by gravity. I seem to recall that the water pressure at the bottom is why the top of a lake will freeze solid before the bottom.


Sorry for the derail, but I can't help myself =p

Water can't "decompress" as water cannot be compressed to begin with. Liquid water is its most dense phase. Anyone who's drowned an internal combustion engine learns this the hard way. Water goes in, pistons compress, water can't compress, spectacular failure as pistons and valves all explode under the pressure. Some of us have had to learn this lesson more than once, believe it or not =p

Re the freezing, I think it's a few things at play. Water freezes on the surface always because that's where the energy transfer occurs the fastest. Any change in the earthen floor is going to be a very long and drawn out process, whereas the air above changes drastically in just a normal day to night cycle. It's 50*F+ here right now. Air is 50, land is 50, water is 50. When Canada gives a wave and says "hi", that air is gonna drop to 20 within a few hours. The earth will take days to do the same. So the body of water will cool fastest, and freeze first, where it is contacting the cold - the air, on top.

But pressure does play in at some point. Since liquid water is its densest form, it must expand to freeze. Water on the surface has an easy go; it just expands, pushing nothing out of its way. Water on the bottom doesn't have it so easy. At 10', it has a full atmosphere worth of weight to move, and that continues in a mostly linear fashion. 20' = 2 atmos, 30' = 3 atmos. But after this, I get lost. Squeezing stuff causes the release of heat, which you would think would assist in freezing. But the weird jumble of phases that water possesses breaks down my logic and I can't understand it well.

If I had a baton, I'd be passing it right... about...
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December 24th, 2014 at 1:06:17 PM permalink
odiousgambit
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Quote: Face
Squeezing stuff causes the release of heat


I think in the case of water, incompressibility means it releases no heat
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December 24th, 2014 at 4:55:37 PM permalink
Wizard
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Quote: Ayecarumba
My initial reaction would be the water cooling due to increased evaporation as the water surface spreads over the falls, shedding heat carrying mist. Could it also be that the water decompresses over the falls?


Evaporation was brought up many times in this discussion but we tried to specifically discount it as a cause of the cooling but more of a result of other factors. For example, I think we could all agree that the falling water tends to disperse and then rub against more air molecules, causing it to heat up and partially evaporate.

This may also be the result of the gravity theory. In other words, does falling cause the water to release gravitational energy, perhaps in the form of some evaporation, causing the remaining liquid water to cool?

In other words, does gravity have anything to do with it, other that causing the water to fall over the side to begin with?
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December 24th, 2014 at 6:18:27 PM permalink
ChesterDog
Member since: Oct 24, 2012
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Quote: Wizard
...In other words, does falling cause the water to release gravitational energy...


Gravitational energy (mgh) is transformed into kinetic energy (mv^2 /2). Here is the classic demonstration of the conversion of gravitational potential energy into kinetic energy.

The equation for conservation of potential and mechanic energy is: m g h1 + m v1 ^ 2 / 2 = m g h2 + m v2 ^ 2 / 2, where g is the acceleration due to gravity or about 9.8 meters/second^2.

Let H be the height of the top of the falls so h1 = H, and h2 = 0. Suppose the water speed at the top is 0 and the speed at the bottom is V. So: mgH = mV^2 / 2.

And then suppose the water at the bottom of the falls comes approximately to rest due to dissipation of the kinetic energy, which means that the kinetic energy must turn into another form of energy--internal energy of the water. The equation for that is mgH = m c (T2 - T1), where c is the specific heat of the water (about 4.2 x 10^3 joule / (kilogram * degree Celsius),) where 1 joule = 1 kilogram * meter^2 / second^2. Therefore, neglecting evaporation T2 - T1 = g H / c . Or T2 - T1 = (0.0023 degrees Celsius) * H.

To take evaporation into account we would have to know what fraction, f, of the water evaporates. Then we would solve this equation for T2 - T1: m g H = m c (T2 - T1) + f m K, where I'm using K to stand for the "enthalpy of vaporization" of water, which is about 2.44 x 10^6 joules / kg at 25 degrees Celsius.
December 24th, 2014 at 7:03:52 PM permalink
Wizard
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Quote: ChesterDog
Gravitational energy (mgh) is transformed into kinetic energy...


Okay, I think we can all buy that. When water falls over the waterfall it makes a lot of noise and causes spray when it hits the bottom. I would call that gravitational energy converting to kinetic energy.

Let me rephrase the question this way. If there were a waterfall in a vacuum, to tease out the effect of air friction, would the water cool down half way down?

p.s. Welcome to the forum! Hope you'll stick around.
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