SESA2022/SESS2022 Part C

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SESA2022/SESS2022

Part C

Q1.

Velocity measurements are taken through a boundary layer on a flat plate in a wind tunnel at a distance x = 1.5m from the leading edge. The flow speed is U = 10m/s, the fluid density and viscosity are measured to be ρ = 1.225kg/m3 , µ = 1.8 × 10−5k/(ms). The y posi-tion (in m) and measured average velocity u (in m/s) are given in the Jupyter notebook.

(i) Make a labeled plot of this velocity profile. How can you tell the boundary layer is turbulent? Estimate the boundary layer thickness δ and numerically calculate the displacement thickness δ* and momentum thickness θ to 3 significant digits. (6 marks)

(ii) Briefly explain the concept of the virtual origin x0 and transition point xt of the turbulent boundary layer. In-clude a sketch. Based on the value of θ you numerically calculated above, calculate x0 and xt to 3 significant dig-its. Provide a check confirming these values are reason-able based on your sketch (14 marks)