Contraction Diffuser Test section X2 Boundary layer (a) U(x) = V 8(x) BL FD (b)
A boundary layer develops along the walls of a rectangular wind tunnel. The air is at 20°C and atmospheric pressure. The boundary layer starts upstream of the contraction and grows into the test section. By the time it reaches the test section, the boundary layer is fully turbulent. The boundary layer profile and its thickness are measured at both the beginning (x = x1) and the end (x = x2) of the bottom wall of the wind tunnel test section. The test section is 1.8 m long and 0.50 m wide (into the page in Fig). The following measurements are made: ?1 = 4.2 cm ?2 = 7.7 cm V = 10.0 m/s At both locations the boundary layer profile fits better to a one-eighth-power law approximation than to the standard one-seventh-power law approximation, u/U ≅(y/?)1/8 for y ≤ ? u/U ≅ 1 for y > ? Estimate the total skin friction drag force FD acting on the bottom wall of the wind tunnel test section.
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