Solve Problem 9.18 again with the velocity profile at
section bc given by the parabolic expression from Problem
9.10.
The test section of a low-speed wind tunnel is 5 ft long,
preceded by a nozzle with a diffuser at the outlet. The tunnel
cross section is 1 ft 3 1 ft. The wind tunnel is to operate with
100F air and have a design velocity of 160 ft/s in the test
section. A potential problem with such a wind tunnel is
boundary-layer blockage. The boundary-layer displacement
thickness reduces the effective cross-sectional area (the test
area, in which we have uniform flow); in addition, the uniform flow will be accelerated. If these effects are pronounced, we end up with a smaller useful test cross section
with a velocity somewhat higher than anticipated. If the
boundary layer thickness is 0.4 in. at the entrance and 1 in. at
the exit, and the boundary layer velocity profile is given by
u=U 5 ðy=δÞ
1=7
, estimate the displacement thickness at the
end of the test section and the percentage change in
the uniform velocity between the inlet and outlet.