Shaft modelling

[Shisha Gamrah]

I am attempting to model an extract shaft, where there is an extraction fan at the head air extracting through the damper before it enters fan at head of duct and, I am interested in the pressure drop across duct. I would like to account for leakages due to dampers shaft lining etc. these affect the flow rate achieved at the bottom of shaft lets say where it connects to another corridor due to leakage.

So basically flow rate at head of shaft equates to flow rate required at low level damper + shaft leakage +dampers leakage across shaft.

And pressure drop is based on the darcy coefficient.

So what is the best way to model this