How does one know if running water is enough to avoid frozen pipes?
An opened faucet will already lower the chance of a pipe bursting.
The typical way a pipe bursts is when it is fully shut. Since it is watertight, there is no place for the water to go. When the water freezes and expands, the only way to go is the side of the pipe, so it bursts.
When the faucet is opened, even just a little, it allows the water to drip out. Now, you say, the water is frozen, wouldn't that still burst? The answer is no.
As the water freezes and expands, the kinetic energy exerted by the ice against the pipe actually melts the ice, and just enough will melt and flow out of the faucet. This is how ice skating works. The physical pressure on the ice creates a thin layer of water, which obviously refreezes immediately once the pressure is removed. You can also easily demonstrate this by using a knife on a block of ice. The pressure from the tip of the knife melts the ice, even though it is just as cold.
So with the faucet opened just a little, as the water pipe freeze over, you'll eventually see the ice &quot;leak&quot; out of the faucet. This is the water melting and freezing immediately. Even though the opening of the faucet will eventually freeze over completely, that frozen opening is still substantially weaker than the pipe, and the expanding ice will continue to &quot;leak&quot; out of the faucet and not burst your pipes.