Question

The terminal velocity of the solid particle in a fluid medium is proportional to -

• A. Square root of the diameter of the particle
• B. Square of the diameter of the particle
• C. Cube of the diameter of the particle
• D. Cube root of the diameter of the particle

Hint:

Stokes' Law is the physical basis behind the separation of starch, sedimentation of yeast cells, and centrifugal separation of cream in milk processing.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When a solid particle falls through a fluid medium under the influence of gravity, it experiences opposing drag and buoyant forces.
Eventually, these forces balance, and the particle falls at a constant maximum velocity called the terminal settling velocity (\(v_t\)).

Step 2: Key Formula or Approach:
For spherical particles in laminar flow (low Reynolds numbers, \(\text{Re} < 2\)), Stokes' Law describes the terminal velocity:
\[ v_t = \frac{g \cdot D_p^2 (\rho_p - \rho_f)}{18 \mu} \]
where:
- \(v_t\) is the terminal velocity.
- \(D_p\) is the particle diameter.
- \(\rho_p\) and \(\rho_f\) are the densities of the particle and fluid, respectively.
- \(\mu\) is the fluid viscosity.

Step 3: Detailed Explanation:
From Stokes' Law, we can see that:
\[ v_t \propto D_p^2 \]
Thus, the terminal velocity is directly proportional to the square of the diameter of the particle.

Step 4: Final Answer:
The terminal velocity is proportional to the square of the diameter of the particle, which corresponds to option (B).