The ratio of the wall drag to the form drag in the Stoke's law range (for motion of spherical particles in a stationary fluid) is

ANS:C - 2

In the Stokes' law range, which applies to the motion of spherical particles in a stationary fluid at low Reynolds numbers, the ratio of wall drag to form drag is approximately 1.

Explanation:

1. Stokes' Law Range:
   • Stokes' law applies when the Reynolds number (ReReRe) is very low (typically Re<1Re < 1Re<1). In this range, the drag force FDF_DFD​ experienced by the particle is primarily due to viscous forces and can be given by: FD=6πμRvF_D = 6 \pi \mu R vFD​=6πμRv where:
     • 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.
2. Components of Drag:
   • Wall Drag: This is the drag force due to the shear stress at the surface of the particle interacting with the fluid. For a spherical particle in Stokes' flow, the wall drag contributes significantly to the total drag force.
   • Form Drag: Form drag arises due to the pressure difference between the front and rear of the particle as it moves through the fluid. In the Stokes' regime, the form drag is much smaller compared to the wall drag because the flow around the particle is largely laminar and streamlined.
3. Ratio of Wall Drag to Form Drag:
   • The ratio of wall drag to form drag is approximately 1 in the Stokes' law range. This means that the wall drag dominates the total drag force experienced by the spherical particle moving through the fluid.

Conclusion: