ANS:D - always greater than

In hindered settling, the drag coefficient is generally greater than that in free settling.

Explanation:

1. Drag Coefficient in Settling:
   • The drag coefficient (CdC_dCd​) in the context of fluid mechanics and settling refers to the dimensionless coefficient that relates the drag force on a particle to its size, shape, and the fluid's properties.
   • In free settling, where particles settle through a quiescent fluid (such as water), the drag coefficient primarily depends on the Reynolds number (ReReRe) of the particle and is typically lower compared to hindered settling conditions.
2. Hindered Settling:
   • Hindered settling occurs when particles settle in a fluid that is in motion or when particles are settling in a concentrated suspension of particles. This situation leads to interactions between settling particles and other particles or the fluid, affecting the drag force experienced by each particle.
   • Due to the interactions and collisions between particles and the surrounding fluid or other particles, the effective drag coefficient in hindered settling is generally higher than in free settling.
3. Comparison of Drag Coefficients:
   • Less than: This option is incorrect because hindered settling typically involves more complex interactions and higher drag coefficients compared to free settling.
   • Equal to: While possible in specific conditions, hindered settling generally leads to higher drag coefficients compared to free settling.
   • Not necessarily greater than: This is incorrect because hindered settling conditions almost always result in higher drag coefficients due to increased interactions.
   • Always greater than: This correctly describes the general trend where the drag coefficient in hindered settling is higher than that in free settling due to increased particle-fluid and particle-particle interactions.

Conclusion: