I don't believe the compressible gas formulas will apply to something you call an "exhaust stack." What process is the exhaust coming from - a boiler maybe?
I think the formula will apply, but you will be in the laminar area and you need to be carefull when calculating your friction factor. As noted rememebr the exit loss.
The chart you posted will give you the friction loss at Standard Conditions, typically at 70 degrees F and sea level.
Click on the link I posted below.
Scroll all the way down to near the end of the linked article, to "Air Density Correction." There you will see how to CORRECT the friction you calculated at Standard Conditions, to the friction you will have at the higher temperature and altitude.