Ooooooooooooook. This is why you're both right and wrong, and both totally missing the point.
1. LHO is correct in saying that psi is psi no matter what turbo it comes from. Pressure is pressure. It is measured at the intake manifold, so if your boost gauge shows 4psi, you have 4psi. It's that simple. He is also correct in saying that the bigger turbo just applies that 4psi later in the rev range of the engine.
2. He is NOT correct in saying that the bigger turbo will make the same amount of power at the same pressure level as the smaller turbo- not unless both are pushing the same pressure at the same engine RPM, and at the same efficiency.
3. LHO's post about volume vs flow rate vs fixed volume of the intake manifold is correct. Pressure is pressure. 5psi on a manifold is going to flow the same amount at the same engine RPM no matter what turbo is pushing it.
4. T&A is correct in saying that 300cfm will make more power than 200cfm provided you have the fuel to use it- but only partially correct.
5. LHO's comeback saying that 10psi will make 250whp (arbitrary example) no matter which turbo its from is incorrect. He's leaving something out.
6. T&A's last comeback talking about different compressor maps is starting to show some understanding about the whole debate.... but doesn't lay it all out there.
Alrighty T&A (and LHO), let's all go to school.
----- I know a lot of you know a lot of this stuff already, but just sit tight. -----
Engines are big energy converters / reactors. They convert the latent energy contained in fuel to thermal energy that pushes pistons/rotors around, which act on lever arms (rods, crankshaft) to create torque. Power is a function of that torque applied over time. The faster you apply the torque (higher rpm), the more power you get- even if you have the same amount of torque.
Higher amounts of fuel and air mean more energy is released in the reaction (combustion), so you get more torque and therefore more power.
Now air on its own isn't the important part. Oxygen is- that's what reacts with the fuel to make a nice boom and push your pistons around.
Density is the key. With turbochargers, when you look at a compressor map, you see all those wonderful efficiency islands. Higher efficiency values mean higher air densities- and therefore higher oxygen densities.
Take an imaginary box. When it's full, this imaginary box holds one pound of air. Now let's squish that air to half its size- the equivalent of 14.7psi (1 atm) of boost. Squish more air the same amount and fill the box to the top. At 100% efficiency (not possible, but imagine), you'll have exactly two pounds of air in the box. Twice the air means twice the potential to burn more fuel, right? With 2 pounds of air in the box (or engine) that's designed to hold only 1 pound, you have the opportunity to burn twice as much fuel and make twice as much torque.
Let's say your turbo is only operating at 80% efficiency. At 1atm (14.7psi) of boost, you'll spend 20% of your turbo's work generating heat, and only 80% of the work will go to compressing air. The air heats up, and you have only 1.6 pounds that are usable to potentially burn fuel, not 2 pounds like you had before. The box is still full to the top. You have the same pressure, the same volume (so the same FLOW), but less oxygen available to burn fuel.
All of this assumes you have a box with no hole in it.
Your engine is this box with a hole in it. Well, I guess your intake manifold is, but you get the idea. The faster your engine is turning, the bigger the hole gets. This is where flow rate comes into play. The faster your engine runs, the more flow the turbo has to provide to establish the same pressure ratio. That's why small turbos run out up top- because they can't move enough air to maintain pressure against the engine once the engine is gobbling up more air.
Addressing points:
1. Yes, pressure is pressure- but assuming everything else is the same. LHO has to assume that both setups have engines of the exact same displacement running at the same speed. With a 2 liter engine running at a constant 4000rpm, a turbo pushing 4psi against it is always pushing the same volume of air, no matter what the turbo size. Pressure is pressure.
2. On the bigger turbo making the same amount of power but just at a different RPM, that makes no sense. LHO is already stating that the larger turbo will make boost at a higher engine speed than the smaller turbo, and that's correct. Everyone knows that. Assuming the same efficiency, a small turbo pushing 10psi at 5000rpm will make half as much power as a turbo pushing 10psi at 10000rpm. Both engine setups are making the same amount of torque- they're both burning the same amount of fuel per engine revolution- but since the 10000rpm engine is applying that force twice as fast as the 5000rpm engine, it makes twice as much power. Easy. So... if the larger turbo is making the same pressure as the smaller turbo but does it higher up in the rev range of the engine, then it will make more power at the same pressure level, not the same amount of power. That's just a function of engine speed.
I'm sure homie LHO would come back with something like "oh, the small turbo can make 10psi in the same place that the big turbo can," and he might be right- but then this is where all the efficiency fun comes into play. The small turbo might be able to push 10psi at 10k just like the bigger turbo, but it won't do it as efficiently as the larger turbo. Even at the same flow rate and the same pressure, the larger turbo will flow more MASS into the engine because it is operating more efficiently. The small turbo is just generating heat because it's out of range, while the larger turbo is working pushing more air. Same pressure, same CFMs, different mass flow rate, different power outputs.
3. See #1. 5psi is 5psi, assuming the engine is consuming air at the same speed in both cases (box with hole in it). You have a constant cross section for air to flow across, you have the same pressure differential, and you have the same amount of air going out. Everything is identical.
4. Yes, more flow = more power... generally. When you're reading the compressor maps for a turbocharger, they're mapped with pressure ratio vs flow rate. Just because a turbo can flow a certain amount of air volume doesn't mean that it can succesfully push that volume into an engine at a certain pressure. You could theoretically have a turbo that could push 500cfm, but only be capable of pushing it at 1psi. Any more resistance, and you don't get that flow rate. The turbo must have both the capability to flow the volume AND be able to maintain pressure to push it into an engine.
Also, talking about flow on its own without reference to the density of that flow is misleading. Flow on its own doesn't tell you anything. You can flow the same volume of light sugar water and thick molasses- and they will be the same flow rate- but you get totally different amounts of sweetness, right? I generally think that people who just talk "oh but this one FLOWS more CFMs" without mentioning efficiencies or air densities doesn't fully understand what they're talking about.
5. See efficiency.
6. Yay T&A! Talking about compressor maps... but it's not just the volume vs pressure that are important- the efficiency islands are the most important part of the compressor map.
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So basically- T&A is a lot more right than LHO, but LHO is technically right in most of his stuff. He just doesn't have the whole picture.
I hope that clears things for some people and doesn't muddy the waters for too many....