A flow of \(68^{\circ} \mathrm{F}\) air develops in a flat horizontal duct following a well-rounded entrance section. The duct height is \(H=1 \mathrm{ft}\). Turbulent boundary layers grow on the duct walls, but the flow is not yet fully developed. Assume that the velocity profile in each boundary layer is \(u / U=(y / \delta)^{1 / 7}\). The inlet flow is uniform at \(V=40 \mathrm{ft} / \mathrm{s}\) at section (1). At section (2), the boundary-layer thickness on each wall of the channel is \(\delta_{2}=4\) in. Show that, for this flow, \(\delta^{*}=\delta / 8\). Evaluate the static gage pressure at section (1). Find the average wall shear stress between the entrance and section (2), located at \(L=20 \mathrm{ft}\).