Air enters a 7-m-long section of a rectangular duct of cross section 15 cm × 20 cm made of commercial steel at 1 atm and 35°c at an average velocity of 5 m/s. disregarding the entrance effects, determine the fan power needed to overcome the pressure losses in this section of the duct. the properties of air at 1 atm and 35°c are ρ = 1.145 kg/m3, μ = 1.895 × 10–5 kg/m·s, and ν = 1.655 × 10–5 m2/s. the roughness of commercial steel surfaces is ε = 0.45 m.