A cylindrical air duct in an air conditioning system has a length of 3.5 m and a radius of 5.00 m. A fan forces air (ç = 1.8 Pa·s) through the duct, such that the air in a room (volume = 242 m3) is replenished every 12 minutes. Determine the difference in pressure between the ends of the air duct.

Answer 1

This kind of pipe flow problem needs to be solved with a friction factors based upon the Reynolds number. You do not explain the meaning of the term ç = 1.8 Pa·s. I don't know any relevant gas property with dimensions of Pascal-seconds.

Your duct length is less than the radius, which I consider highly unlikely.

You are wasting your time posting poorly proofread problems here.