Question

Lewis number of air water mixture is defined as:

• A. Pr.Sc
• B. Pr/Sc
• C. Sc/Pr
• D. Re.Sc

Hint:

A simple way to remember: $Le = Sc/Pr$.
Think of alphabetical order: $S$ comes before $P$ in "Schmidt/Prandtl".
For air-water mixtures, $Le \approx 1$, meaning thermal and mass boundary layers have nearly equal thickness.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the definition of the Lewis number ($Le$) in terms of other dimensionless numbers (Prandtl number $Pr$ and Schmidt number $Sc$) for an air-water mixture.
The Lewis number is an important dimensionless parameter used in simultaneous heat and mass transfer operations, such as humidification and drying.

Step 2: Key Formula or Approach:
Let us write down the fundamental definitions of the dimensionless numbers involved:
1. Lewis number ($Le$): Ratio of thermal diffusivity ($\alpha$) to mass diffusivity ($D_{AB}$):
\[ Le = \frac{\alpha}{D_{AB}} \] 2. Prandtl number ($Pr$): Ratio of momentum diffusivity ($\nu$) to thermal diffusivity ($\alpha$):
\[ Pr = \frac{\nu}{\alpha} \] 3. Schmidt number ($Sc$): Ratio of momentum diffusivity ($\nu$) to mass diffusivity ($D_{AB}$):
\[ Sc = \frac{\nu}{D_{AB}} \]

Step 3: Detailed Explanation:
Let us express the Lewis number as a combination of $Pr$ and $Sc$:
From the definition of Prandtl number, we have: \[ \alpha = \frac{\nu}{Pr} \] From the definition of Schmidt number, we have: \[ D_{AB} = \frac{\nu}{Sc} \] Now, substitute these expressions into the definition of the Lewis number: \[ Le = \frac{\alpha}{D_{AB}} = \frac{\nu / Pr}{\nu / Sc} \] Simplifying the fraction by canceling the kinematic viscosity ($\nu$): \[ Le = \frac{Sc}{Pr} \] Thus, the Lewis number is mathematically equivalent to the ratio of the Schmidt number to the Prandtl number.
For air-water systems, the Lewis number is approximately equal to 1, which simplifies psychrometric calculations (the Lewis relation).

Step 4: Final Answer
The Lewis number is defined as $Sc/Pr$, which corresponds to option (C).