A laboratory wind tunnel has a test section that is square in cross section, with inlet width \(W_{1}\) and height \(H_{1}\), each equal to \(1 \mathrm{ft}\). At freestream speed \(U_{1}=80 \mathrm{ft} / \mathrm{s}\), measurements show the boundary-layer thickness is \(\delta_{1}=0.4\) in. with a \(\frac{1}{7}\)-power turbulent velocity profile. The pressure gradient in this region is given approximately by \(d p / d x=-0.035\) in. \(\mathrm{H}_{2} \mathrm{O} /\) in. Evaluate the reduction in effective flow area caused by the boundary layers on the tunnel bottom, top, and walls at section (1). Calculate the rate of change of boundary-layer momentum thickness, \(d \theta / d x\), at section (1). Estimate the momentum thickness at the end of the test section, located at \(L=10\) in downstream.