Chapter 9, Problem 52P

Air flows in a cylindrical duct of diameter D = 6 in. At section ①, the turbulent boundary layer is of thickness δ₁ = 0.4 in. and the velocity in the inviscid central core is U₁ = 80 ft/s. Further downstream, at section ②, the boundary layer is of thickness δ₂ = 1.2 in. The velocity profile in the boundary layer is approximated well by the $\frac{1}{7}$-power expression. Find the velocity, U₂, in the inviscid central core at the second section, and the pressure drop between the two sections. Does the magnitude of the pressure drop indicate that we are justified in approximating the flow between sections ① and ② as one with zero pressure gradient? Estimate the length of duct between sections ① and ②. Estimate the distance downstream from section ① at which the boundary layer thickness is δ = 0.6 in. Assume standard air.