In Stokes flow, inertial forces are negligible compared to viscous forces. Which statement best describes this regime?

In Stokes flow, inertial forces are negligible compared to viscous forces. Which statement best describes this regime?

• A. Inertial forces dominate
• B. Inertial forces are negligible
• C. Viscous forces dominate negligibly
• D. Both are equally important

Answer: (B)

In creeping or Stokes flow, the Reynolds number is very small, so the inertia term in the Navier–Stokes equations is negligible compared to the viscous term. This means the flow is governed mainly by viscosity resisting motion, with pressure gradients balancing those viscous stresses, and any body forces. The result is a regime where inertial forces are essentially absent relative to viscous forces, which is why the correct description is that inertial forces are negligible. This contrasts with higher-Reynolds-number flows where inertia plays a significant role, and it also isn’t accurate to say viscous forces dominate only slightly or that both are equally important in this regime.

In creeping or Stokes flow, the Reynolds number is very small, so the inertia term in the Navier–Stokes equations is negligible compared to the viscous term. This means the flow is governed mainly by viscosity resisting motion, with pressure gradients balancing those viscous stresses, and any body forces. The result is a regime where inertial forces are essentially absent relative to viscous forces, which is why the correct description is that inertial forces are negligible.

This contrasts with higher-Reynolds-number flows where inertia plays a significant role, and it also isn’t accurate to say viscous forces dominate only slightly or that both are equally important in this regime.