Physics · Viscosity, Stoke's law, terminal velocity, streamline and turbulent flow, critical velocity

Which one of the following will make its way most easily through the tiny space

Which one of the following will make its way most easily through the tiny space between the fiber of the clothing:

  • A. glycerene at \( 10^{\circ} \mathrm{C} \)
  • B. water at \( 20^{\circ} \mathrm{C} \)
  • C. soap water at \( 20^{\circ} \mathrm{C} \)
  • D. water at \( 100^{\circ} \mathrm{C} \)

Step-by-step solution

Penetration through tiny spaces is governed by the ratio γcosθ/μ (from the Lucas-Washburn equation). For water at 100°C, viscosity μ is much lower (0.282 mPa·s) than at 20°C (1.002 mPa·s), and surface tension γ is also lower (58.9 vs 72.8 mN/m) but the viscosity drop dominates, leading to a higher ratio. Soap water at 20°C reduces surface tension to ~30 mN/m but viscosity remains near 1 mPa·s, giving a lower ratio than hot water. Glycerene is highly viscous and ineffective. Therefore, water at 100°C penetrates most easily.
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