A water tunnel has a test section cross-section of 0.8 m x 0.5 m and a test section length of 8 m. It operates at an inlet velocity of 2.5 m/s, which can be assumed to be uniform, and the water temperature is 20 degree C. The boundary layer thickness at the test section inlet (81) is negligible. In the test section, boundary layers grow on all four walls (top, bottom, and side walls). (a) Estimate the location of transition from laminar to turbulent boundary layer flow, assuming a transition Reynolds number, Rex, of 500,000.
(b) Calculate the thickness of the turbulent boundary layer at the end of the test section (hint: 0.k. to use correlation for turbulent flow, here you can assume that the entire boundary layer is turbulent).
(c) Now that you know the boundary layer thickness 02, assume that the boundary- layer velocity profiles are of power-law form, with u/U. (4/8)1/8. (Note: Y is the wall-normal direction.) Calculate the displacement thickness at the end of the test section, = 8 &* = S(1 – ým )dy. f 0
(d) The test section cross-section does not vary. How much does the flow velocity increase at the end of the test section, in the center of the tunnel, due to the growth of the boundary layers? (Hint: Use 1-D continuity with a reduced area at downstream end due to "displacement" of the flow by S*on each wall)