Why do you think it is a "drain pipe" -- can you see what it is connected to, and where it goes?
If it is a drain pipe, that would generally not have anything to do with city water pressure IMO, unless it IS connected to the water heater's PRV, as TGT suggested. At the top of your water heater, can you see the PRV? If so, turn off the city water, open a faucet inside to relieve the water pressure, and then flip the PRV handle up and down a few times, and leave it down/closed.
You may have grit in the PRV, which is common in areas with hard water, or well water which has not been carefully filtered. Do you use an inline hose filter like this one for both city water and filling your tank?
https://www.amazon.com/Camco-40645-T.../dp/B000BUU5V8
Photos will help.
Peter