I've seen airplanes (typically Cessna 172s) with a "Powerflow" exhaust system and then claim to get several more horsepower, resulting in faster cruise speeds. How does a Powerflow exhaust work, and why does it increase horsepower?
It has to do with resonance. Think of a pipe organ - each pipe resonates at a certain frequency, which we hear as a note or tone. The length of the pipe determines its note/tone/resonance frequency. Your plane's exhaust system has a certain resonance frequency.
Your plane's engine has a certain note or tone, too. That is largely determined by engine RPM. A powerflow exhaust matches the exhaust resonance frequency with the engine's rpm at a typical high cruise setting.
On a micro level, here is what happens. After a cylinder's power stroke, when the exhaust valve first opens, exhaust floods out into the exhaust system. Soon the exhaust valve shuts and the inertia of the gasses moving down the exhaust system cause the exhaust gas to continue towards the exit, creating a lower pressure behind it (near the exhaust valve). If the resonance frequency of the exhaust system matches the rpm, at that point the exhaust valve opens on the next cycle, and the lower pressure area in the exhaust assists in scavenging the exhaust out of the cylinder. On the subsequent intake stroke, there is less residual pressure in the cylinder and it can "suck in" more fuel/air mixture. More fuel/air, more power.
Another way to say this is that it takes power for the engine to force the exhaust out of the cylinder and through the exhaust system. The Powerflow system reduces the power required to do this.
Powerflow exhaust systems are based on the principle that an engine is, essentially, a large noisy air pump: air is drawn in through the intake, and pumped out the exhaust.
A limiting factor on how much horsepower an engine produces is how quickly you can move a given volume of air through the engine (because of restrictions in either the intake or exhaust system).
Some aircraft, like Cessna 172s or 140/150/160 horsepower Piper Cherokees, have an exhaust system that restricts how quickly exhaust gasses can be "pumped out", due to unfavorable geometry, narrow pipe sizes, or both.
Powerflow systems, like "tuned exhaust" systems you find on sports cars, provide a wide pipe and a geometry that encourages pulling as much of the exhaust gas out of the cylinder as possible, which means less energy is wasted pushing the piston up during the exhaust stroke, and more oxygen-rich air will be pulled into the cylinder during the subsequent intake stroke - both contributing to producing more usable horsepower.