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For aerosol particles having sizes \(\gt\) 1 μm, the terminal settling velocity (\(V_{T}\)) of an aerosol particle varies with its diameter (D) as

  • A.\(V_{T} \propto D\)
  • B.\(V_{T} \propto D^{2}\)
  • C.\(V_{T} \propto D^{3}\)
  • D.\(V_{T} \propto D^{3/2}\)

Answer: B

For small particles in the laminar regime Stokes' law gives the terminal settling velocity\[ V_T = \frac{g\, D^{2}\,(\rho_p - \rho)}{18\,\mu} \]which means that V is proportional to the square of the diameter. For particles larger than about 1 micrometre gravitational settling dominates, and this relation applies until the particle becomes large enough for turbulent drag. A linear, cubic or three-halves power of D does not follow from the balance between gravity and viscous drag.

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