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I have a 71 convertible with stock 350 4spd. I find that after running the car my passenger and I smell like exhaust. I have had the engine tunned and the carb rebuilt.
My father in law thinks the mufflers are rotted inside from age. I know it doesn't have cats, but I have had alot of other muscle cars without cats and I don't smell like an exhaust pipe after driving it.
Sounds like it's running very rich and/or check for an exhaust leaks at the manifold to pipe connection on back until you are sure it's not leaking. Best method is to put it on a lift and have someone rev it up and down to listen for the noise that a leak will indicate (kind of a popping sound on de-celleration). Worked for me.
Had a similar problem. Car was too lean. Upped the jet size, smell went away. Had the car too rich at one opoint and the car smelled more like raw fuel when I shut her off.
If the mix is too lean, you tend to get more hydrocarbons released. That is the heavy exhaust smell that hangs in the air and on your clothes. If you smell like 'gas vapors', the mix is too rich.
The exhaust is welded all the way back, and both shift boots have been replaced with new ones. Carb has been rebuilt and adjust by a carb shop.
Also, the car never came with emissions devices.
Since you have (should if stock) a Rochester carb, I will be of no help. Since a shop recently tuned it, see if they can run the car to test for emissions (assuming that have a machine to do so). That should verify the problem. Then adjustment of the carb would be next.
Do you get headaches??
Be VERY wary of carbon monoxide--the silent killer.
I had an '81 camaro in high school, and once had a bent tailpipe route exhaust into the trunk through a hole in the plastic bumper. Myself and three friends almost went to the emergency room after a 5 hour road trip!!!!
Man WHAT A HEADACHE I HAD from the CO poisoning!!!!
Get it taken care of!