I was wondering if there is any equation that helps to calculate flue gas velocity through a pipe? Can I use the Poiseuille Equation to solve this problem by assuming the flue gas is acting as a newtonian fluid?
The pipe diameter is 3.66m, change in pressure is 3atm, length of the pipe is 10m, density of the flue gas is 0.811kg/m$^3$ at 150 ˚C, and the viscosity (C$_p$) is 0.0232.
Are you sure your numbers are right? 3 atm of pressure drop is pretty large for 10 m length with that diameter.
Anyways what you need to do is
1) Guess a velocity, gas pipes are usually about 20 m/s but for flare headers it can go up about 90% of speed of sound. So the range is quite large.
2) Calculate Reynolds number and find friction factor from a Moody diagram.
3) Use the Darcy–Weisbach equation to calculate velocity. If this number is close enough to the guessed value in 1) then you're done. Otherwise use this new velocity in 1) and repeat until it converges.
ps. you can use Hagen-Poiseuille if it is laminar flow (low Reynolds, forgot the range) but I doubt it's the case with that pressure drop.
