In an air heating system, heated air at 40°c and 105 kpa absolute is distributed through a 0.2 m × 0.3 m rectangular duct made of commercial steel at a rate of 0.5 m3/s. determine the pressure drop and head loss through a 30-m-long section of the duct. the roughness of commercial steel surfaces is ε = 0.45 m. the dynamic viscosity of air at 40°c is μ = 1.918 × 10–5 kg/m·s, and it is independent of pressure.