Originally Posted by inspectorD
Look at the plaster pressed through the wire mesh
I guess it's against Code to use a plumbing vent pipe as a range hood vent pipe.
Why not run a vertical 3-1/4" duct between the studs, up or down, until you can go horizontally, with maybe a 24vac booster fan at the distant end?
If Broan won't help with this, ask them for the Fan Curve http://www.greenheck.com/media/articles/Product_guide/perf_basics.pdf
for this hood blower and use the Engineering Toolbox to calc. the duct airflow resistance.