how do you find the diameter of an industrial chimney having only discharge flowrate and discharge velocity
Divide the discharge flow rate (in cubic meters per second) by the discharge velocity im m/s. This wil give you the chimney inside cross section pi D^2/4, in square meters.
Multiply that area by (4/pi) and take the square root of the result, for the diameter, D.
In other words,
D = sqrt[(4/pi)*flow rate/velocity]
This problem requires a bit of physics as well as math.