Question

The settling velocity of spherical particles falling through fluid governed by Stokes' law is proportional to

• A. 1/effective particle radius
• B. 1/viscosity of fluids
• C. Water
• D. 1/effective particle diameter

Hint:

Stokes' law: \(v_s = \frac{(\rho_p - \rho_f) g d^2}{18 \mu}\).
Applicable for: Small particles, laminar flow (Re < 1).
Settling velocity increases with particle size and density difference, decreases with fluid viscosity.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question tests knowledge of Stokes' law for settling of particles in fluids.

Step 2: Key Formula or Approach:
Stokes' law for settling velocity:
\[ v_s = \frac{(\rho_p - \rho_f) g d^2}{18 \mu} \] where:
\(v_s\) = settling velocity,
\(\rho_p\) = particle density,
\(\rho_f\) = fluid density,
\(d\) = particle diameter,
\(\mu\) = dynamic viscosity of fluid.

Step 3: Detailed Explanation:
From the formula:
- \(v_s \propto d^2\) (proportional to square of diameter).
- \(v_s \propto \frac{1}{\mu}\) (inversely proportional to viscosity).
Thus, settling velocity is inversely proportional to the viscosity of the fluid.
Other options:
- 1/effective particle radius (A): \(v_s \propto d^2\), not \(1/d\).
- Water (C): Not a proportionality.
- 1/effective particle diameter (D): \(v_s \propto d^2\), not \(1/d\).
Thus, the correct answer is \(1/\)viscosity of fluids.

Step 4: Final Answer:
Thus, the settling velocity is proportional to 1/viscosity of fluids.
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