I need some more information about this installation or just pick one of the “if’s” below. You've picked water heater category so I'm assuming this is a water heater you’re talking about – what type is it?
If it is a natural draft type with a cone shaped draft hood on its top you can only vent it through the chimney and not through the side wall.
If it is a power vent type water heater that uses PVC vent pipe you can go through the side wall of the house or roof / this water heater type cannot be vented through the chimney. You can find all information about such installation here – water heater power vent.
Direct venting applies to appliances that use air from exterior for combustion process. If your water heater is a direct vent type you can use 2 vent pipes or special double wall pipe (not a B-vent) designed to discharge exhaust and supply combustion air at the same time.
If the 10” opening you’ve mentioned is for the chimney connection it should be sealed around the vent pipe / pipe should penetrate the opening and terminate flush with the interior wall of the chimney flue.
If your water heater uses basement interior air for combustion process you have to make sure that it has enough of it. Check this example for calculation purposes – water heater combustion air