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Let's imagine a theoretical car that uses 2.25" exhaust piping all of the way back from the motor to tailpipe. How much power loss would there be by installing a catalytic converter in there with a 2" exhaust diameter? How much loss from the actual catalyst, and the smaller pipe diameter?

As I understand it, flow restriction is linear to a point until it becomes critical and cannot flow any more. In other words, power loss from a small exhaust pipe would be a linear % of max output up until a certain point in which the engine is choking. Is this correct?

The actual vehicle I'm working on is a 92 Honda Prelude with a 2.3 liter 4-cylinder engine making between 160-170 horsepower.

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There's a huge amount of information you would need to know about your "theoretical car" before even a wild guess could be made.

As Rory mentioned, velocity is key. Sage old-school guys like Corky Bell chasing the best Volumetric Efficiency say this velocity needs to ideally about .7 mach on intake, and maybe a third of that on exhaust. But any "wive's tale" like that really is making a large number of assumptions.

Any expansion in exhaust diameter means a pressure drop, and by Boyle's Gas law we can expect a temperature drop as well. Which means slower, cooler exhaust gas, which is a restriction all by itself. You might even "wrap" the exhaust with high-temperature insulating material to maintain heat and velocity, but this tends to rot out everything in a hurry unless you fabricate in good austenitic stainless like 318 or 321.

On the other hand, exhaust will cool as it travels, so keeping the exhaust path as short as possible, with minimum bends, is also a design ideal.

Complicate all this with what you objectives are: Horsepower? Torque? Ultimate VE? A car that actually can be driven over the entire rev range?

All these things are in direct competition. There is no magic bullet. Does my juridiction require a muffler? A catalytic converter? Can I discharge exhaust safely under the doors?

A "No-rules" exhaust design would be a gradually tapering funnel, port-matched to manifold outlet size, and then the straightest shot possible, growing slightly over the length to allow for cooling without impeding velocity, but still long enough to provide a scavenging effect for better cylinder filling and torque.

Probably short of impossible on anything but a specialized race vehicle with a narrow powerband and no street "laws" to be concerned about.

However, there are several things that can be done to improve any exhaust system or modifications. Try to make the path as straight as possible. Avoid any change in diameter on any transistion; they should be as smooth as possible. When a diameter transition must be made, attempt to build adpaters with gradual tapers over a length. Even gasketed flanges (especially pre-cat) need to be smooth transistions.

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Exhaust diameters don't work exactly like that. You may actually get better exhaust flow with a 2" pipe than a 2.25" pipe with some engines and some rpm.

The important thing is to balance flow velocity - a fast exhaust pulse helps clear the cylinder of spent gases. So a smaller pipe diameter is best for that - and flow capacity, which at high rpm suffers in a small diameter pipe.

So at low rpm you want a small diameter exhaust, and as you increase diameter you actually lose power. But at high rpm you want a large diameter exhaust. Which is why various engines have multiple pathways - eg just having one pipe open at low rpm then opening another at higher rpm etc

And that doesn't take into account resonance - a tuned exhaust is set up such that an exhaust pulse exits the exhaust at exactly the right time to provide extra draw to the next exhaust pulse leaving the cylinder.

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