Air flows in a horizontal cylindrical duct of diameter \(D=100 \mathrm{~mm}\). At a section a few meters from the entrance, the turbulent boundary layer is of thickness \(\delta_{1}=5.25 \mathrm{~mm}\), and the velocity in the inviscid central core is \(U_{1}=12.5 \mathrm{~m} / \mathrm{s}\). Farther downstream the boundary layer is of thickness \(\delta_{2}=24 \mathrm{~mm}\). The velocity profile in the boundary layer is approximated well by the \(\frac{1}{7}\)-power expression. Find the velocity, \(U_{2}\), in the inviscid central core at the second section, and the pressure drop between the two sections.