Well you will have to determine why it is leaking. It is just a loose fitting? try tightening it up with a wrench Is there a crack? Is the pipe white PVC (plastic) or copper or even gray metal? If it is any of these you will need to cut it out and replace that section. You might want to consider hiring a plumber.
Cold water pipes would be the sweaty ones.
It doesn't mend the pipe. The pipe will still have a leak. However, you can use liquid nitrogen to freeze the water in a pipe and create a 'freeze block' which will prevent more liquid from getting to the leak. Once the freeze block is in place, it is much easier to repair the pipe leak.
it's prob the same thing that is wrong with mine. Your hot water pipe is either frozen or it is split...
That depends upon the length and diameter of the pipe connecting to the hot water tank. Also, the greater the distance, the more hot/cold mixing will occur, resulting in even greater water loss. Most copper household plumbing pipe is 1/2" in diameter, and hot water pipes may range from 10' to 80', depending on angles and turns in the plumbing. An 80' pipe will hold about 2 gallons of water. This is water that was heated in the water heater, but upon setting in the pipe gave up all, or most, of its heat to its surroundings.
Depends on the size of the heater Commerical etc
Hot water pipe rust first as compared to the cold water pipe for the same chemical composition of the water.
Cold water pipe.
Copper can rust
Because hot water is still in the pipes from when you turned on the hot water, and when you turned on the cold faucet it had to let out the hot water first. This means you have a single-pipe sink. Double-pipe sinks have a pipe for hot and a pipe for cold and it blends them as it turns on.
Water in pipe freezes, expands, and cracks pipe.
Electrical grounded to the cold water pipe, usually before the first fitting once it is through the foundation..
If you are referring to a regular building, the cold water feed pipe goes directly to all cold faucets, toilets and hot water tank. The purpose seems obvious.
The extreme cold freezes the water and makes it expand in the pipe. When the pipe expands with the water, the pipe will then burst in the extreme coldness.
Vent, return circulation
If it runs continually, as you say, then it can only be the inlet water pipe or fitting, leaking.