Good question! In general, this is not correct.Water freezes at 32°F, regardless of whether itis moving. In still water, such as lakes andponds, the top of the water freezes first, andsince ice is less dense that liquid water, itremains on the surface and insulates the rest ofthe water from the cold. The rest of the ponddoesn’t freeze because the temperature of theground below never reaches freezing. Forexample, in Wisconsin (my home state!) the soiltemperature two feet below the surface never goesbelow 32°F, even in heart of winter.
For flowing water to freeze, the surroundingair has to be colder than 32°F, because theflowing water mixes with itself. So, thecolder water on the surface mixes with the warmerwater from the bottom, and the average temperatureis somewhere between the two. Even so, if it getscold enough, the mixing isn’t enough to keep thetop of the river from reaching 32°F, and the riverforms a layer of ice on top. The water flowingbelow, however, is still above 32°F, or it wouldfreeze as well.
However, there are a number ofadditional factors that can influence the freezingprocess. If there are any dissolved salts orother solutes in the stream, the freezing pointwill be lowered. For example, the freezingpoint of sea water is around 28°F. Also, themotion of the water can cause heating. Forexample, water in a waterfall gains kineticenergy as it falls, which is converted into heatand sound energy at the bottom. Therefore, thesurrounding air temperature would have to be lowerto force the water in the waterfall to cool to32°F and freeze.
Finally, the fact that the water is movingmight influence the freezing behavior, but itwould encourage freezing rather than discourageit. For example, if you have a very smooth,clean container of pure water (such as astore-bought bottle—Fiji Water seems to workwell), you can sometimes lower the temperature tobelow the freezing temperature, because there areno places where ice crystals can start to form(called nucleation sites). This process iscalled super cooling. Then, if you shakethe bottle or hit it on the table, you introducesome air bubbles into the water which can nucleateice crystal formation, and the water willspontaneously freeze and become ice. You can trythis at home by buying a bottle of water, andputting it in the freezer for a few hours, thencarefully removing it before hitting it on thetable to nucleate ice formation. In the case ofthe river water, the motion of the water, and thefact that the ground is not a smooth, cleansurface, would prevent the water from everbecoming super cooled.
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