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Minor concern

While the Titanic was tilting, a thin, plane, smooth sheet of steel was detached from the ship and fell into the ocean. The sheet was square, with an edge length of 3 m and a mass of 10 kg. One side of the sheet (side A) was perfectly smooth, while the other side (side B) had some decorations near the leading edge, which would serve like boundary layer trips and would generate a turbulent boundary layer from the start, if the flow conditions were such that a boundary layer would develop. The specific gravity of (very cold) salt water in the North Atlantic Ocean may be taken as about 1.09 and its kinematic viscosity may be taken as about 1.50×10-6 m2/s. The specific gravity of steel is 7.83.

a) Compute the terminal velocity of the sheet, if it sank with its flat sides vertical and such that two of its edges (“leading edge” and “trailing edge”) were horizontal. Compute the disturbance, displacement and momentum thicknesses of the boundary layer near the trailing edge of side B; compare these values with the corresponding values near the trailing edge of side A. Compare qualitatively the values of the skin friction coefficients near the trailing edge on sides A and B. Explain your answer.
b) Compute the terminal velocity of the sheet, if it would sink with its flat sides horizontal.
c) Assume that another sheet, having the same dimensions and weight as the one above but without decorations, was sinking next to the sheet above. Which sheet would sink faster in the two cases for which both sheets would sink with their flat sides i) vertical and ii) horizontal? Justify your answer.
d) Sketch a likely trajectory of the sheet if its flat side formed an angle of 5º with the vertical direction. Explain the sequence of events that would lead to a complex motion.


Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from www.andrew.cmu.edu/ user/mpj/.

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