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We know that flowing water remains liquid even in the below-zero temperatures (a good example is rivers in arctic regions). Of course water doesn't remain liquid forever if temperature goes down constantly. Also, I know water freezes from surface. But that's for stationary waters like lakes. Not for flowing waters like a dam output which is so fast.

I think it depends on a sort of things, like the speed of molecules, the viscosity of water, etc.

Can we formulate it to find the answer? Perhaps with such a formula we can find the freezing temperature of other flowing liquids as well.

And a minor question: How does the density of flowing water behave in below-zero temperatures?

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    $\begingroup$ The density of supercooled water decreases with increasing supercooling (near the freezing point), going from 0.9999 g/ml at 0C to 0.9775 g/ml at -34C. $\endgroup$
    – Jon Custer
    Commented Jun 16, 2023 at 15:24
  • $\begingroup$ Wow! But still the density is bigger than 0C ice. $\endgroup$
    – Snack Exchange
    Commented Jun 16, 2023 at 15:36
  • $\begingroup$ Have you looked into the stagnation temperature? Moving water contains kinetic energy that warms it if the water stops, acting against freezing. $\endgroup$
    – Chemomechanics
    Commented Jun 16, 2023 at 16:04
  • $\begingroup$ Would you be satisfied by discussing the problem of water at temperature T>0C entering and flowing through a pipe, with the pipe wall maintained at T<0C? $\endgroup$
    – Chet Miller
    Commented Jun 17, 2023 at 10:53

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The flowing does not change the freezing point of water, but it can change how difficult it is for the water to actually reach that temperature.

If the air temperature is at, say, $–5 \rm °C$, the ground will usually be several degrees warmer (as it has a heat sink downward). So in a river, water touching the riverbed will not be cold enough to freeze. Water at the surface, in contact with the air, may begin to freeze, but as soon as it does, the microscopic ice particles are immediately mixed in with the rest of the warmer water. This constant churning keeps the water well-mixed and unable to freeze in bulk. Even when the surface of a river does freeze, the lower layers remain flowing, as they now have an insulating ice layer from the cold air. With low enough temperatures in the air and ground, though, rivers can indeed freeze all the way down.

In addition, ocean water had dissolved salt, which does decrease the freezing point. And even freshwater has any number of dissolved salts and minerals which can have a similar effect.

In short, there is no simple physical formula involving the flow velocity that will predict when rivers or flowing water will freeze. There are a lot of factors. I am sure you can find empirical equations created by geologists or hydraulogists to estimate this for actual rivers and streams.

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  • $\begingroup$ Thank you. Please edit your answer. That's Hydrologist $\endgroup$
    – Snack Exchange
    Commented Jul 4 at 2:37

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