Stoke's equation is valid in the Reynolds number range

ANS:A - 0.01 to 0.1

Stoke's equation is valid in the Reynolds number range 0.01 to 0.1. Here’s an explanation:

• Stoke's Law: Stoke's law describes the drag force experienced by spherical particles moving through a viscous fluid at low Reynolds numbers. It is given by: Fd=6πμRvF_d = 6 \pi \mu R vFd​=6πμRv where:
  • FdF_dFd​ is the drag force,
  • μ\muμ is the dynamic viscosity of the fluid,
  • RRR is the radius of the spherical particle,
  • vvv is the velocity of the particle relative to the fluid.
• Reynolds Number and Stoke's Law: The Reynolds number (ReReRe) is defined as Re=ρvRμRe = \frac{\rho v R}{\mu}Re=μρvR​, where ρ\rhoρ is the fluid density. For Stoke's law to be valid, the Reynolds number must be very low, typically in the range of 0.010.010.01 to 0.10.10.1.
• Explanation of Range: At very low Reynolds numbers (less than 1), viscous forces dominate over inertial forces, and the flow around the particle is laminar. Stoke's law assumes laminar flow conditions where the viscous drag force on the particle is directly proportional to its velocity and size.