2001 Chevy Silverado 1500 V8 4.8L Vortec. Repairs for this problem: New Radiator, hoses, and coolant overflow bucket. Question = About every month or 2 I have to top off the coolant level (1/4 - 1/2 a gallon)so there is a slow leak or burning of the coolant somewhere. As stated above, In Aug I replaced the radiator, The hoses, and the coolant overflow bucket. I hear it may be one of the gaskets somewhere, but I have no idea just looking for a better answer.
Answer: Unless you can actually see a leak, such as the water pump, on the ground or running down the engine, then you are losing the coolant internally. Adding that much, that often means there is definitely a problem somewhere. You could have a cylinder head gasket that is split and letting coolant get into the cylinders, which would be burned off during combustion.
If you can see white smoke coming out the exhaust while the engine is running at operating temperature, you are for sure burning it in the cylinders. The coolant could also be getting into the oil, so you would want to check the oil level on the dipstick to see if it is high or discolored or smells like coolant.
Most likely, you've got a small leak internally on one or both of the cylinder heads. If the truck has a lot of miles, it would benefit to do both heads at the same time and not just one.
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