latent heat loss of water in pipe
Latent heat is 80 kcal per Kg in all cases, and ends with a pipe frozen solid.

Total heat is 85 kcal per kg in all cases. Now, if the water is actually flowing, you have some other factors that you haven't told us about, (lenght, wind, etc.) as well as not telling us if the water is flowing or not. In general, uninsulated water pipes below freezing are not a great idea unless there is constant flow of warm water, and you don't mind losing the heat.