Question

Stoke's law is valid when \(N_{Re,p}\) is less than

• A. \(2\)
• B. \(100\)
• C. \(700\)
• D. \(2100\)

Hint:

Stoke's law applies to creeping flow around particles, where particle Reynolds number is very small.

Answer 1

The Correct Option is A

Stoke's law gives the drag force on a small spherical particle moving slowly through a viscous fluid. It is valid in the creeping flow region. Creeping flow means viscous forces dominate over inertial forces. The particle Reynolds number is: \[ N_{Re,p}=\frac{\rho v d_p}{\mu}. \] Here: \[ \rho=\text{fluid density}, \] \[ v=\text{particle velocity}, \] \[ d_p=\text{particle diameter}, \] and: \[ \mu=\text{fluid viscosity}. \] Stoke's law is valid for very small Reynolds number. According to the given options, the valid condition is: \[ N_{Re,p}<2. \] Therefore, Stoke's law is valid when: \[ N_{Re,p}<2. \]