Here is what the equation on the bottom means.
w = air flow, in pounds mass of air per minute. this is uncorrected for atmospheric pressure and temperature. Any change in the local temperature or pressure will change the actual performance of the compressor.
The quantity under the radical are temperature correction. 519 is a standard correction term, but we'll use 545 to be consistent with the map.
T1c = local temperature, expressed in degrees Rankine. To convert degrees Fahrenheit, deg R = deg F + 459
The quantity in the denominator is the local pressure correction.
P1c = local atmospheric pressure, expressed in psia. Like I said, I think the 28.4 is a typo, but i could be wrong. Normal pressure corrections have 14.7psia; i am not sure why 28.4 is there. We'll use the 28.4 to be consistent with the map.
edit: found out the 28.4 is actually the measurement for standard (or close to) pressure measured in inches of mercury. I should have known that. We'll use 14.7 instead of the 28.4.
Here is an example:
The local temperature is 65 degrees fahrenheit, and the local pressure is a little low, say 14.5 psia. We want to run at 8psi on the street, and want to see how much flow that will be pushing. We will be needing the pressure ratio to read the vertical axis, so adding 8 psig (boost) to 14.5 psia(atmospheric pressure), and divide by the 14.5 psia. (8+14.5)/14.5 = 1.55.
We'll be using a T3 super 60 turbo
According to the map, within the best efficiency island, at a pressure ratio of 1.55, corrected flow will be anywhere from about 12 to 17 lbm/min, eyeballing the map. To give to an idea of what the uncorrected flow will be, the temperature correction factor will be sqrt((65+459)/545) = .98
The pressure correction factor will be 14.5/14.7 = .986
12lbm/min corrected will be 12*.98/.986 = 11.99 lbm/min actual.
17lbm/min corrected will be 17*.98/.986 = 16.98 lbm/min actual.
You can see that at near standard conditions, the actual and corrected values will be similar. If you're are living in arizona however, and the local temperature is 110 degrees F, and 14.5psi, you'll be seeing actual flow numbers from 12.4 to 17.6 lbm, a 3.5% difference. Not a big difference, but a 3% difference can mean the difference between a safe engine and a broken engine if you are tuning aggressively. Again, this is just one application.