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EML 5709 Homework 6 Spring 1997

1. One side of the measurement section of a wind tunnel is a glass window, 20 cm long and 10 cm high. Find the shear force on the window, assuming that Blasius' solution applies for the boundary layer flow, and that the effective starting point of the boundary layer is 20 cm upstream of the upstream edge of the window. The air in the tunnel is at 15 degrees Centigrade and the velocity is 5 m/sec. Is Blasius' solution valid? (The boundary layer turns turbulent at ) Solution.
2. Consider laminar flow through a circular pipe. Far into the pipe we have Poiseuille flow. However, very close to the entrance of the pipe, we have a constant axial velocity profile, except for a very thin Blasius type boundary layer right at the pipe surface. This boundary layer thickens until it eventually fills the pipe. Roughly estimate the length of pipe required for this boundary layer to grow to fill the entire pipe and thus approach Poiseuille flow. Solution.
3. For the flow of the previous question, the increasing boundary layer displacement thickness produces an increasing potential flow velocity in the center of the pipe. Derive the variation of this velocity with the distance along the pipe. Solution.