I want to know what is the correct size black pipe is used for the furnace and hot water tank 1/2" and 3/4"

Thank you

Depends upon the flow requirements

What is the boiler BTU/hr input rating?? Look at the ID plate... Your question needs more detail... I assume that you are questioning the water feed pipe size for your boiler (not a furnace)

If you mean black pipe size for gas fuel line for furnace and tank. We would need disatance from gas meter and btu's.