Chapter 9, Problem 51P

A laboratory wind tunnel has a flexible upper wall that can be adjusted to compensate for boundary-layer growth, giving zero pressure gradient along the test section. The wall boundary layers are well represented by the $\frac{1}{7}$-power-velocity profile. At the inlet the tunnel cross section is square, with height H₁ and width W₁, each equal to 1 ft. With freestream speed U₁ = 90 ft/s, measurements show that δ₁ = 0.5 in. and downstream δ₆ = 0.65 in. Calculate the height of the tunnel walls at ⑥. Determine the equivalent length of a flat plate that would produce the inlet boundary layer thickness. Estimate the streamwise distance between sections ① and ⑥ in the tunnel. Assume standard air.