# At what temperature does flowing water start to freeze?

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?

• 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. Commented Jun 16, 2023 at 15:24
• Wow! But still the density is bigger than 0C ice. Commented Jun 16, 2023 at 15:36
• Have you looked into the stagnation temperature? Moving water contains kinetic energy that warms it if the water stops, acting against freezing. Commented Jun 16, 2023 at 16:04
• 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? Commented Jun 17, 2023 at 10:53

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.