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For a fully-developed turbulent hydrodynamic boundary layer for flow past a flat plate, the thickness of the boundary layer increases with distance $x$ from the leading edge of the plate, along the free-stream flow direction, as

  1. $x^{0.5}$
  2. $x^{1.5}$
  3. $x^{0.4}$
  4. $x^{0.8}$
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