If I have a water pipe of certain diameter and length placed outside at minus 40 Celsius, what would be the minimum flow rate that would prevent the water from freezing? I know there's Q = (L*θ)/Rtotal for the calculation of the heat losses, with θ being determined from the water temperature and the environment temperature, so I can presuppose values for these as well. The R of the pipe is also determined by the pipe manufacturer, so that's not a problem either. The question is, how is the flow rate affecting the whole freezing action? Would there be a minimum value for the inlet water temperature? Can this be close to zero and just find the required flow to prevent freezing?

 

Interesting question - I'm afraid I don't know the answer but I'm commenting so I can see it if it comes up.

I guess there must be some kind of relationship, because you sometimes see fast-flowing rivers (and waterfalls!) frozen when it's especially cold, but not when it's just quite cold.

I assume it's a function of flow speed, water volume and temperature...