Can upnorthairgunner explain barrel length vs power to us

I think we all need to take a seat and start taking notes because 1shot is fixing to school everyone on some physics!
Go ahead and drop that wisdom 1shot. You gotta bring us all up to your level. 
Upnorth probably ain’t gonna respond to some nonsense but I’d say conventional wisdom says that a longer barrel gives more velocity as long as the volume and pressure inside a valve remains sufficient to overcome the weight of the projectile and the friction it has with the barrel.
Everyone here would agree that the valve dwell time, plenum area, PSI and transfer port dimensions as well as barrel length and projectile weight and size to bore ratio are what determines power level. 
Please tell me what revelation you’ve had to add to the base of knowledge here? I am ready to learn. 
 
I think this simplifies it:

main-qimg-6cdad48ebf289de7a50fa74f3a3780cf-lq.1637943593.jpg


Source:
https://www.quora.com/What-is-the-most-complex-math-physics-computer-science-topic-equation-you-know


 
Of couse a longer barrel will give you more speed and you need it in larger calibers,I am trying to get time to shoot my guns at 1oo yards with the chrony on them with 15 inch barrels.Smaller calibers of course . .177 with 21 grain nielson just over 1100fps and 22 also 1100 fps ,both with stock barrels with choke cut off.I promise you it will be very shocking.And it seems that know person shows the capability of artemis p 12 airguns and of course there custom.I promise when i video and you see the speed and accuracy you will be shocked. I just need one good day in the back field with low wind.
 
I got a question isn't 1100 fps above sound barrier so won't it be loud even with a moderator especially with short barrel would need a hell of a blast of air to accelerate it in 15 inches isn't the whole point to stay quiet and stealthy if wanted 1100 or above I could always grab a 22 lr wouldn't really be any more dangerous than what he's saying for range wise 
 
I got a question isn't 1100 fps above sound barrier so won't it be loud even with a moderator especially with short barrel would need a hell of a blast of air to accelerate it in 15 inches isn't the whole point to stay quiet and stealthy if wanted 1100 or above I could always grab a 22 lr wouldn't really be any more dangerous than what he's saying for range wise

It's all about the oneupmanship. If he lived in South Africa he'd be knocking gnats off a monkey's butt at 400 meters using 40 grain .177 slugs from the worlds most accurate Daisy Red Rider that he modified by cutting 12 inches off the barrel and adding a pistol grip. Ya can't let minor things like facts or physics get in the way of a good day dream.