Question

The dimensionless number that represents the ratio of the momentum diffusivity to mass diffusivity in a fluid is termed as

• A. Schmidt number
• B. Biot number
• C. Reynolds number
• D. Nusselt number

Hint:

Keep these transport analogies in mind:
- Prandtl Number (\( Pr \)) \(\rightarrow\) Ratio of Momentum to Thermal diffusivity (\( \nu / \alpha \)).
- Schmidt Number (\( Sc \)) \(\rightarrow\) Ratio of Momentum to Mass diffusivity (\( \nu / D \)).
- Lewis Number (\( Le \)) \(\rightarrow\) Ratio of Thermal to Mass diffusivity (\( \alpha / D \)).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question asks for the name of the dimensionless parameter that expresses the relative magnitude of momentum transport to mass transport within a fluid medium.

Step 2: Key Formula or Approach:
Let:
- Momentum diffusivity be kinematic viscosity: \( \nu = \frac{\mu}{\rho} \)
- Mass diffusivity be diffusion coefficient: \( D \)
The ratio of these two diffusivities is defined as the Schmidt Number (\( Sc \)):
\[ Sc = \frac{\text{Momentum Diffusivity}}{\text{Mass Diffusivity}} = \frac{\nu}{D} = \frac{\mu}{\rho D} \]
where:
\( \mu \) is dynamic viscosity.
\( \rho \) is fluid density.

Step 3: Detailed Explanation:

• Physical Meaning of Schmidt Number: The Schmidt number physically describes the relative thickness of the hydrodynamic (velocity) boundary layer compared to the concentration (mass transfer) boundary layer in fluid mechanics.

• Defining Other Options:
-

Biot Number (\( Bi \)): Measures the ratio of conduction resistance inside a solid to convection resistance at its surface (\( Bi = \frac{h L_c}{k_s} \)).
-

Reynolds Number (\( Re \clean \)): Measures the ratio of inertial forces to viscous forces in a fluid flow (\( Re = \frac{\rho v L}{\mu} \)).
-

Nusselt Number (\( Nu \)): Measures the ratio of convective heat transfer to conductive heat transfer across a fluid boundary layer (\( Nu = \frac{h L}{k_f} \)).


Step 4: Final Answer:
The dimensionless ratio of momentum diffusivity to mass diffusivity is defined as the Schmidt number.
Therefore, option (A) is the correct choice.