Question

Which among the following is NOT a dimensionless number in food processing operations?

• A. Reynold's number
• B. Prandtl number
• C. Consistency Index
• D. Nusselt number

Hint:

$\text{Re}, \text{Pr}, \text{Nu}, \text{Bi}, \text{Fo}$ are all dimensionless groups; Consistency index ($K$) has units of $\text{Pa}\cdot\text{s}^n$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Dimensionless numbers are dimensionless groups used in transport phenomena to characterize fluid mechanics, heat transfer, and mass transfer.

Step 2: Key Formula or Approach:
Evaluating the dimensional status of each term:
1. Reynolds number ($\text{Re} = \frac{\rho v D}{\mu}$): Dimensionless (ratio of inertial to viscous forces).
2. Prandtl number ($\text{Pr} = \frac{c_p \mu}{k}$): Dimensionless (ratio of momentum diffusivity to thermal diffusivity).
3. Nusselt number ($\text{Nu} = \frac{h D}{k}$): Dimensionless (ratio of convective to conductive heat transfer).
4. Consistency Index ($K$ in Power Law model $\tau = K \dot{\gamma}^n$): Has physical dimensions of $\text{Pa}\cdot\text{s}^n$ ($\text{kg}\cdot\text{m}^{-1}\cdot\text{s}^{n-2}$), which varies with flow behavior index $n$.

Step 3: Detailed Explanation:
Thus, Consistency Index is NOT a dimensionless number.

Step 4: Final Answer:
Hence, the correct option is (C) Consistency Index.