Why is your hot water pressure low but your cold water pressure is fine after installing new water hetar?

Your cold water comes directly from the main line without hitting resistance. Your hot water travels through your water heater which may decrease the pressure. Is this a new problem or has it always been like this? If it is a new problem you may be getting build-up in the lines near the water heater or even in the water heater.

Hot water also tends to have more deposits in the piping. If you have galvanized piping, you could have a lot of corrosion in the pipes. Hot water heaters do get scaling build up. It might be worth having it checked out, a broken hot water heater can be pretty messy!

The answer may differ according to where you live. In the UK the cold water comes from the main which is kept at a moderately high pressure, for example by a water tower. Any leaks are then "outwards" with less chance of inward contamination. The hot water in a house is generally provided from a tank in the house attic, which auto-refills when water is drawn off, stoppnig when full by a floating arm which cuts off the supply to it. This tank at relatively low height provides lower pressure water to the house boiler.