A hot water vent pipe not properly sized won’t move acidic moisture out of the house before it condenses. Your chimney was not designed for today’s efficient appliances. Acidic moisture from the combustion of your hot water tank condenses on the inside of the chimney. Get a metal flue liner.
You may see water stains coming from the hot water vent pipe where it goes into the chimney because a new closed combustion furnace may vent out the sidewall of the house so the hot water tank is all that is using the chimney. There won’t be chimney cracks and the chimney cap is fine.
The vapor condenses because there is not enough heat to keep it in a gaseous state all the way to the roof. Besides staining your chimney in the basement, the acid-rich moisture is eating away at the flue walls, ruining the chimney. As mortar joints dissolve, carbon monoxide gas can leak into the living area of your home.
What needs to be done is reduce the size of the chimney flue so the exhaust gases from the hot water tank stay hot all the way to the top of the chimney.
This will keep the acidic moisture in a gaseous state and no deposits will be left behind.
This is accomplished with a metal flue liner sized to the fuel burning appliances attached to it.
Because of the sizing and difficulty of installation, I recommend using a licensed mechanical contractor for this job.
If you are happy with your furnace man, give them a call and start your estimates there.
Properly vent your furnace and hot water tank to operate more efficiently.