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I'm wondering if a hot gas traveling down a pipe leave a vacuum "trail" after it self as it cools down? Think of a car engine, as the exhaust gas leaves the combustion chamber it travels down the exhaust pipe. As the exhaust gas travels down the exhaust pipe it cools down since it does not get heat from combustion (if the combustion is finished) and thus decreases its displacement in the exhaust pipe. Which should leave a vacuum trail behind the burst of hot gas. Is this analasys correct or am I completely off track?

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in general, this is true, but mostly for a different reason. the hot gas enters the exhaust pipe with a lot of velocity, and after the exhaust valve closes, the hot gas wants to continue going fast because of its inertia and a weak vacuum pocket develops behind the initial burst of hot gas. this means the positive pressure pulse is followed by a brief negative pressure pulse. this effect is usually only apparent on single-cylinder engines with straight-thru mufflers when starting cold and running slowly but can be strong enough nonetheless to cause the exhaust pipe to blow visible smoke rings into the air.

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