Need Exhaust Advice

Closet grower needs to exhaust through the room to the window. 4 x 2 x 6 tent in the closet with a fan and filter. The ducting needs to go through a 14 foot room to the window.

My question is will I have to add a little booster fan to ensure it pushed the air through the 14 foot room to the window? This is much more for temp control in the room over odor control. The room the closet is in gets way too hot in the winter. There is no separate heat control for that room.

Any ideas or formulas are greatly appreciated.

What size fan setup ? Maybe ridged ducting instead of the flex stuff for better air flow.

ChaosHunter said:

What size fan setup ? Maybe ridged ducting instead of the flex stuff for better air flow.

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its a 4inch fan. I forget the cfm but it is more than enough for the 4 x 2 tent. i would like to go smaller than 4 inch ducting if possible when it is run through the room to the window.